BPH-22-005

BPH-22-005

# Test of lepton flavor universality in $\PBpm\\!\to\\!\PKpm\MM$ and
$\PBpm\\!\to\\!\PKpm\EE$ decays in proton-proton collisions at
$\sqrt{s}=13\TeV$

###### Abstract

A test of lepton flavor universality in $\PBpm\\!\to\\!\PKpm\MM$ and
$\PBpm\\!\to\\!\PKpm\EE$ decays, as well as a measurement of differential and
integrated branching fractions of a nonresonant $\PBpm\\!\to\\!\PKpm\MM$ decay
are presented. The analysis is made possible by a dedicated data set of
proton-proton collisions at $\sqrt{s}=13$recorded in 2018, by the CMS
experiment at the LHC, using a special high-rate data stream designed for
collecting about 10 billion unbiased hadron decays. The ratio of the branching
fractions $\mathcal{B}(\PBpm\\!\to\\!\PKpm\MM)$ to
$\mathcal{B}(\PBpm\\!\to\\!\PKpm\EE)$ is determined from the measured double
ratio $R(\PK)$ of these decays to the respective branching fractions of the
$\PBpm\\!\to\\!\JPsi\PKpm$ with $\JPsi\\!\to\\!\MM$ and $\EE$ decays, which
allow for significant cancellation of systematic uncertainties. The ratio
$R(\PK)$ is measured in the range $1.1<q^{2}<6.0\GeV^{2}$, where $q$ is the
invariant mass of the lepton pair, and is found to be
$R(\PK)=0.78^{+0.47}_{-0.23}$, in agreement with the standard model
expectation $R(\PK)\approx 1$. This measurement is limited by the statistical
precision of the electron channel. The integrated branching fraction in the
same $q^{2}$ range, $\mathcal{B}(\PBpm\\!\to\\!\PKpm\MM)=(12.42\pm 0.68)\times
10^{-8}$, is consistent with the present world-average value and has a
comparable precision.

##  0.1 Introduction

In the standard model (SM) of particle physics [1, 2, 3], the charged leptons
(electrons , muons , and leptons) have identical couplings to the gauge bosons
and thus exhibit a similar behavior, up to the kinematic differences related
to their different masses. This is commonly known as lepton flavor
universality (LFU). Several tests of LFU have been performed in and boson
decays, which are generally found to be in excellent agreement with the SM
predictions [4]. The only hint of possible LFU violation (LFUV), at 2.7
standard deviations $(\sigma)$ in the decay of bosons to vs. light leptons
from the CERN LEP era [5], was ruled out by the ATLAS [6] and CMS [7]
experiments at the CERN LHC.

Rare hadron decays provide an excellent and complementary environment to test
LFU. In particular, the $\PBp\\!\to\\!\PKp\ell^{+}\ell^{-}$ process where a
bottom antiquark () decays into a strange antiquark () and a lepton
($\ell=\PGm$ or $\Pe$) pair is forbidden at tree level and only proceeds via
loop diagrams, , the one shown in Fig. 1 (left). Therefore, the SM branching
fractions ($\mathcal{B}$) for these decays are very small ($\sim$10-7) [4].
This process is referred to as a $\PAQb\\!\to\\!\PAQs\ell^{+}\ell^{-}$
transition (in what follows, the charge-conjugated states are implied unless
explicitly stated otherwise).

Since both the electron and muon masses are negligible with respect to the
meson mass, the available phase space for the two decays
($\PBp\\!\to\\!\PKp\MM$ and $\PBp\\!\to\\!\PKp\EE$) is the same to an
excellent approximation, which makes the ratio of these branching fractions
very close to unity in the SM. On the other hand, beyond-the-SM (BSM) physics
processes could modify the corresponding branching fractions differently for
different lepton species, as illustrated in Fig. 1 (right) for the case of a
leptoquark with flavor-dependent couplings, thus resulting in LFUV in
$\PAQb\\!\to\\!\PAQs\ell^{+}\ell^{-}$ transitions. A recent review of various
BSM models describing LFUV in meson decays can be found in Ref. [8] and
references therein, as well as in an extensive list of references in Ref. [9].

Figure 1: Representative Feynman diagrams for the decay of a meson into a
meson and a lepton pair in the SM (left) and in a BSM scenario that introduces
a leptoquark (LQ) with flavor-dependent couplings (right).

Over the past decade, the LHCb experiment has reported mounting evidence for
LFUV in $\PBp\\!\to\\!\PKp\ell^{+}\ell^{-}$ [10, 11, 9],
$\PBz\\!\to\\!\PK^{\ast}(892)^{0}\ell^{+}\ell^{-}$ [12],
$\PBz\\!\to\\!\PKzS\ell^{+}\ell^{-}$, and
$\PBp\\!\to\\!\PK^{\ast}(892)^{+}\ell^{+}\ell^{-}$ [13] decays with the
significance reaching 3.1$\sigma$ in the first channel [9]. In these analyses
the muon decays are measured to be suppressed compared to the electron ones.
In addition, multiple measurements of branching fractions of several
$\PAQb\\!\to\\!\PAQs\MM$ decays by LHCb indicate their suppression with
respect to the available SM predictions [14, 15, 16, 17]. These predictions,
however, are subject to potentially large and poorly understood uncertainties
from long-range charm loop contributions [18]. While the claim of possible
LFUV in meson decays has largely disappeared in the latest LHCb publications
[19, 20], the interest in $\PAQb\\!\to\\!\PAQs\ell^{+}\ell^{-}$ decays in
general and in potential LFUV in these processes remains strong [21].

In this paper we describe a search for LFUV in
$\PBp\\!\to\\!\PKp\ell^{+}\ell^{-}$ decays using data collected by the CMS
experiment at the LHC in 2018. A special trigger and storage strategy was used
to collect a large unbiased sample of $\sim$10 billion hadron decays. We also
report a measurement of the branching fraction of the $\PBp\\!\to\\!\PKp\MM$
decay, both differentially over the dimuon mass squared $q^{2}$ and integrated
over two different $q^{2}$ ranges. The numeric values corresponding to figures
and tables in this paper can be found in the HEPdata database [22].

This paper is organized as follows. After discussing the measurement strategy
in Section 0.2, followed by the detector description in Section 0.3, we
introduce the data and simulated samples in Section 0.4, and event
reconstruction in Section 0.5. We discuss the maximum likelihood fit to the
$\PKp\ell^{+}\ell^{-}$ invariant mass distributions in Section 0.6, followed
by the description of the systematic uncertainties in Section 0.7. The results
are presented in Section 0.8, followed by the summary of the paper in Section
0.9. Additional plots and details of the $R(\PK)$ measurement formalism can be
found in Appendix .10.

##  0.2 Measurement strategy

To maximize the sensitivity to LFUV in $\PAQb\\!\to\\!\PAQs\ell^{+}\ell^{-}$
decays, it is advantageous to use an observable that minimizes the theoretical
uncertainty in its prediction. Given that the absolute
$\PAQb\\!\to\\!\PAQs\ell^{+}\ell^{-}$ rates are poorly understood because of
the potentially large long-range corrections [18], a more robust variable is
the ratio of muon to electron decays within a certain range of the dilepton
mass squared, $q^{2}_{\text{min}}<q^{2}<q^{2}_{\text{max}}$:

$R(\PK)_{\text{theory}}[q^{2}_{\text{min}},q^{2}_{\text{max}}]=\frac{\mathcal{B}(\PBp\\!\to\\!\PKp\MM)[q^{2}_{\text{min}},q^{2}_{\text{max}}]}{\mathcal{B}(\PBp\\!\to\\!\PKp\EE)[q^{2}_{\text{min}},q^{2}_{\text{max}}]}.$
(1)

This ratio is very close to unity in the SM [23, 24, 25, 26] and known to a
precision of about 1%. Furthermore, the experimental systematic uncertainties
related to signal reconstruction and selection can be reduced by measuring
$R(\PK)$ as a double ratio normalized to the corresponding
$\PBp\\!\to\\!\JPsi\PKp$ decay channels:

$R(\PK)(q^{2})[q^{2}_{\text{min}},q^{2}_{\text{max}}]=\left.\frac{\mathcal{B}(\PBp\\!\to\\!\PKp\MM)[q^{2}_{\text{min}},q^{2}_{\text{max}}]}{\mathcal{B}(\PBp\\!\to\\!\JPsi(\MM)\PKp)}\middle/\frac{\mathcal{B}(\PBp\\!\to\\!\PKp\EE)[q^{2}_{\text{min}},q^{2}_{\text{max}}]}{\mathcal{B}(\PBp\\!\to\\!\JPsi(\EE)\PKp)}\right..$
(2)

This definition of $R(\PK)$ benefits from the fact that the branching
fractions $\mathcal{B}(\JPsi\\!\to\\!\MM)$ and
$\mathcal{B}(\JPsi\\!\to\\!\EE)$ are measured to be the same within a
precision of about 0.7% [4], which ensures that this extra normalization does
not change the value of $R(\PK)$ with respect to the definition in Eq. (1).
Additionally, since the leptons from the nonresonant
$\PBp\\!\to\\!\PKp\ell^{+}\ell^{-}$ and the resonant
$\PBp\\!\to\\!\JPsi(\ell^{+}\ell^{-})\PKp$ decays occupy a similar phase
space, with a similar acceptance and efficiency after the final selection,
most of the systematic uncertainties related to the lepton momentum scale and
identification cancel in Eq. (2), making it an excellent experimental
observable directly related to $R(\PK)_{\text{theory}}$.

The $R(\PK)$ ratio in Eq. (2) is measured in the $q^{2}$ region from 1.1 to
6.0$\GeV^{2}$, referred to as the “low-$q^{2}$” region, which is free of
dilepton resonances. This choice is optimized to exclude the contributions of
the $\PGfP{1020}$ and lighter resonances at the lower end of the $q^{2}$
spectrum, and the tail of the resonance at the higher end. In addition, the
chosen lower boundary reduces the kinematic difference between the muon and
electron decay channels due to the differences in their masses.

For the differential branching fraction measurement in the
$\PBp\\!\to\\!\PKp\MM$ channel, the $q^{2}$ range is extended downward by
adding a $q^{2}<0.98\GeV^{2}$ bin, below the $\PGfP{1020}$ resonance, and
upward by introducing nine bins up to the kinematic limit of
$q^{2}=22.9\GeV^{2}$, excluding the $\JPsi$ and $\PGyP{2S}$ resonance $q^{2}$
ranges. Furthermore, the low-$q^{2}$ region is split into five finer bins. The
definition of the 15 $q^{2}$ bins used for the differential measurement is
given in Section 0.8 (Table 0.8.1). The chosen binning ensures a sufficient
number of events per bin to reliably extract the branching fraction of the
$\PBp\\!\to\\!\PKp\MM$ decay and is similar to that used in the LHCb analysis
[15], which presently dominates the precision of these differential branching
fraction measurements [4].

In addition to the low-$q^{2}$ region, part of which is defined as the signal
region (SR) as described in Section 0.5, two control regions (CRs) are defined
based on the dilepton $q^{2}$, as follows.

  * •

CR: the $8.41<q^{2}<10.24\GeV^{2}$ range is used for the
$\PBp\\!\to\\!\JPsi(\ell^{+}\ell^{-})\PKp$ decay, which is the main
normalization channel used in the $R(\PK)$ measurement.

  * •

$\PGyP{2S}$ CR: the $12.6<q^{2}<14.44\GeV^{2}$ range is used for the
$\PBp\\!\to\\!\PGyP{2S}(\ell^{+}\ell^{-})\PKp$ decay, which is the secondary
normalization channel, used as an additional cross-check, with the
$R_{\PGyP{2S}}$ ratio defined as:

$R_{\PGyP{2S}}=\left.\frac{\mathcal{B}(\PBp\\!\to\\!\PGyP{2S}(\MM)\PKp)}{\mathcal{B}(\PBp\\!\to\\!\JPsi(\MM)\PKp)}\middle/\frac{\mathcal{B}(\PBp\\!\to\\!\PGyP{2S}(\EE)\PKp)}{\mathcal{B}(\PBp\\!\to\\!\JPsi(\EE)\PKp)}\right..$
(3)

This ratio is very close to unity in the SM and has been measured to a
precision of about 8%, with the uncertainty dominated by the current precision
of the measurement of the $\PGyP{2S}\\!\to\\!\MM$ branching fraction [4].

The analysis is conducted using the “data blinding” concept [27]. In the muon
channel, a random scale factor is initially applied to the nonresonant signal
yields in each $q^{2}$ bin. In the electron channel, the $\PKp\EE$ invariant
mass spectrum in the vicinity of the peak in the low-$q^{2}$ region is
initially kept blind. The entire analysis is optimized using simulated samples
and resonant CRs, and the unblinding of the data in both channels is done only
as the final step.

##  0.3 The CMS detector

The central feature of the CMS apparatus is a superconducting solenoid of 6m
internal diameter, providing a magnetic field of 3.8T. Within the solenoid
volume are a silicon pixel and strip tracker, a lead tungstate crystal
electromagnetic calorimeter (ECAL), and a brass and scintillator hadron
calorimeter, each composed of a barrel and two endcap sections. Forward
calorimeters extend the pseudorapidity ($\eta$) coverage provided by the
barrel and endcap detectors. The ECAL consists of 75 848 lead tungstate
crystals, which provide coverage in a barrel region, $\abs{\eta}<1.48$, and
two endcap regions, $1.48<\abs{\eta}<3.0$. Muons are measured in gas-
ionization detectors embedded in the steel flux-return yoke outside the
solenoid. The procedure followed for aligning the detector is described in
Ref. [28].

The silicon tracker measures charged particles within the range
$\abs{\eta}<3.0$. During the 2018 LHC running period, when the data used in
this paper were recorded, the silicon tracker consisted of 1856 silicon pixel
[29] and 15 148 silicon strip detector modules. For nonisolated particles with
transverse momentum in the $1<\pt<10\GeV$ range, the track resolutions are
typically 1.5% in and 20–75in the transverse impact parameter [30]. Muons are
measured in the $\abs{\eta}<2.4$ range, with detection planes made using three
technologies: drift tubes, cathode strip chambers, and resistive-plate
chambers. Matching muons to tracks measured in the silicon tracker results in
a relative transverse momentum resolution, for muons with up to 100, of 1% in
the barrel and 3% in the endcaps [31]. The efficiency to reconstruct and
identify muons is greater than 96%. The electron momentum is estimated by
combining the energy measurement in the ECAL with the momentum measurement in
the tracker. The momentum resolution is typically better than 5% for electrons
in the range $1<\pt<10\GeV$. It is generally better in the barrel region than
in the endcaps, and also depends on the bremsstrahlung energy emitted by the
electron as it traverses the material in front of the ECAL [32, 33, 34].

Events of interest are selected using a two-tiered trigger system. The first
level (L1), composed of custom hardware processors, uses information from the
calorimeters and muon detectors to select events at a rate of around 100kHz
within a fixed latency of 4 [35]. The second level, known as the high-level
trigger (HLT), consists of a farm of processors running a version of the full
event reconstruction software optimized for fast processing, and further
reduces the event rate before data storage [36].

A more detailed description of the CMS detector, together with a definition of
the coordinate system used and the relevant kinematic variables, can be found
in Ref. [37].

##  0.4 Data and simulated samples

###  0.4.1  parking data sample

For the purpose of this analysis, we deployed a novel trigger and data
processing strategy in CMS during the 2018 data-taking period at the proton-
proton $(\Pp\Pp)$ center-of-mass energy of 13, referred to as “parking”. This
strategy enabled the collection of order $10^{10}$ unbiased hadron decays [33]
by exploiting the fact that hadrons are predominately produced in pairs, and
therefore one can trigger on one hadron of the pair using a specific decay
mode (“tag-side” hadron), while the other hadron (“probe-side” hadron) decay
is unbiased by the trigger.

The trigger strategy relies on tag-side final states that include a muon with
a relatively high and a significant displacement from the $\Pp\Pp$ collision
point. This strategy is motivated by the significant fraction (nearly 40%) of
events that include at least one muon from a hadron (or subsequent charm
hadron) decay, combined with the relatively low rate of L1 single-muon
triggers. In addition, the parking strategy takes advantage of the gradual
decrease of the L1 trigger rate and online computing resources use by the
nominal CMS physics program as the instantaneous luminosity decreases during
each LHC fill. To exploit the available L1 (HLT) bandwidth of up to 30 (5.4)
kHz, the parking trigger requirements were gradually relaxed during each LHC
fill. This strategy does not affect the main, high-physics program of CMS,
while offering a significant increase in the CMS potential in flavor physics,
including the present $R(\PK)$ measurement.

Summary of the loosest muon trigger requirements imposed by the L1 and HLT
algorithms for each instantaneous luminosity scenario: the L1 and HLT muon
transverse momentum thresholds $p^{\PGm}_{\mathrm{T}}$, and the HLT muon
impact parameter significance $\text{IP}_{\text{sig}}$. Also shown are the
trigger purity, peak HLT rate, and
$\int\\!\\!\\!\;{\mathcal{L}}{\mathrm{d}}t$. The second trigger was the
highest threshold one during early data taking, corresponding to
$\int\\!\\!\\!\;{\mathcal{L}}{\mathrm{d}}t=6.9\fbinv$, and then the second-
highest for the rest of the data taking, accumulating
$\int\\!\\!\\!\;{\mathcal{L}}{\mathrm{d}}t=26.7\fbinv$ out of $34.7\fbinv$
collected by the highest threshold trigger.  L1 $p^{\PGm}_{\mathrm{T}}$ HLT
$p^{\PGm}_{\mathrm{T}}$ HLT $\text{IP}_{\text{sig}}$ Purity Peak HLT
$\int\\!\\!\\!\;{\mathcal{L}}{\mathrm{d}}t$
$[10^{34}\unit{cm}^{-2}\unit{s}^{-1}]$ thr. [$\GeVns$] thr. [$\GeVns$] thr.
[%] rate [kHz] [$\\!\fbinv$] 1.7 12 12 6 92 1.5 34.7 1.5 10 9 6 87 2.8
$6.9+26.7$ 1.3 9 9 5 86 3.0 20.9 1.1 8 8 5 83 3.7 8.3 0.9 7 7 4 59 5.4 6.9

Table 0.4.1 summarizes the parking muon trigger requirements imposed by the L1
and HLT algorithms. The L1 trigger logic requires the presence of a muon with
$\abs{\eta}<1.5$ and with a variable minimum threshold. These requirements
help to control the L1 rate by removing events with muons at low and large η,
which are dominated by those produced in pileup interactions (additional
minimum bias interactions within the same or adjacent bunch crossings). In
addition, a single-muon L1 trigger with $\pt>22\GeV$ in the full
pseudorapidity range $\abs{\eta}<2.4$ is used. Since the muon displacement
information is not available at L1, only and $\abs{\eta}$ thresholds are used
to control the rate. At the HLT, the threshold is sharpened, given the more
precise momentum reconstruction compared to that at L1, and a minimum
requirement is imposed on the two-dimensional (2D) muon track impact parameter
significance $\text{IP}_{\text{sig}}$, defined as the distance of closest
approach of the track to the beam line (the measured line of the proton beams
inside the CMS detector [38]), divided by its uncertainty. These triggers are
“nested”, , the most restrictive trigger is exposed to the largest integrated
luminosity ($\int\\!\\!\\!\;{\mathcal{L}}{\mathrm{d}}t$), while the looser
ones have progressively higher efficiency but lower
$\int\\!\\!\\!\;{\mathcal{L}}{\mathrm{d}}t$.

The purity of the parking sample is defined as the fraction of triggered
events containing a hadron decay and is evaluated by counting the number of
$\PBz\\!\to\\!\PDstp\PGmm\PAGnGm\\!\to\\!\PDz\PGp^{+}_{\text{soft}}\PGmm\PAGnGm\\!\to\\!\PKm\PGpp\PGp^{+}_{\text{soft}}\PGmm\PAGnGm$
events, using the known meson production fraction $f_{\PQd}$ and the relevant
branching fractions [4]. For the $\PGp^{+}_{\text{soft}}$, the threshold is
set at 0.5. The purity is measured both in data and in simulation (described
in Section 0.4.2), with good agreement between the two estimates. The purity
ranges between 59 and 92%, depending on the trigger thresholds, with an
average of $\approx$80% in the collected data set.

The parking data set corresponds to
$\int\\!\\!\\!\;{\mathcal{L}}{\mathrm{d}}t=41.6\pm 1.0$ [39], about 30% less
than the $\int\\!\\!\\!\;{\mathcal{L}}{\mathrm{d}}t$ of 59.8collected with the
main physics triggers operating during the entire 2018 data taking. It took
about a year to fully reconstruct these data during the LHC Long Shutdown 2;
hence the name: parking.

###  0.4.2 Event simulation

Monte Carlo (MC) simulated samples are used to optimize the analysis and model
various background sources. Signal and background processes are generated with
8.230 [40], including parton showering, fragmentation, and hadronization. The
output is interfaced with 1.3.0 [41], which simulates various hadron decays.
The underlying event is also modeled with , using the CP5 tune [42]. The
parton distribution functions (PDFs) are taken from the NNPDF3.1 set [43].
Final-state photon radiation is modeled with 3.61 [44]. The generated samples
include $\PBp\\!\to\\!\PKp\ell^{+}\ell^{-}$ signal (generated with the
BTOSLLBALL, setting 6, model of the decay library, based on form-factors from
Ref. [45]), complemented with the $\PBp\\!\to\\!\JPsi\PKp$ and
$\PBp\\!\to\\!\PGyP{2S}\PKp$ resonant decays, and
$\PBz\\!\to\\!\JPsi\PK^{\ast}(892)^{0}$,
$\PBz\\!\to\\!\PGyP{2S}\PK^{\ast}(892)^{0}$,
$\PBz\\!\to\\!\PK^{\ast}(892)^{0}\ell^{+}\ell^{-}$,
$\PBp\\!\to\\!\JPsi\PK^{\ast}(892)^{+}$,
$\PBp\\!\to\\!\PGyP{2S}\PK^{\ast}(892)^{+}$, and
$\PBp\\!\to\\!\PK^{\ast}(892)^{+}\ell^{+}\ell^{-}$ backgrounds, as well as
inclusive hadron samples, and Cabibbo-suppressed $\PBp\\!\to\\!\JPsi\PGpp$,
$\PBp\\!\to\\!\PGyP{2S}\PGpp$, and $\PBp\\!\to\\!\PGpp\ell^{+}\ell^{-}$
decays, with and without emulation of the trigger requirements. The CMS
detector response is simulated using [46]. All MC samples are reconstructed
with the same software packages as used for collision data and include effects
of pileup by overlaying simulated minimum bias events on the hard-scattering
event, with the multiplicity distribution matching that in data.

##  0.5 Event reconstruction and selection

The particle-flow (PF) algorithm [47] aims to reconstruct and identify each
individual particle (muon, electron, photon, and charged and neutral hadrons)
in an event, with an optimized combination of information from the various
elements of the CMS detector.

Muons are identified as tracks in the silicon tracker consistent with either a
track or several hits in the muon system, and associated with calorimeter
deposits compatible with the muon hypothesis [31]. A muon that triggered the
event readout is required to pass the “medium” muon identification criteria of
Ref. [31]. As multiple $\Pp\Pp$ collision vertices are reconstructed from each
beam crossing, we select a single primary vertex (PV) as the one whose $z$
position is closest to that of the point of closest approach of this muon to
the beam line. In addition, for the electron channel, only electron candidates
consistent with originating from this PV are considered. This procedure
significantly reduces the contamination from pileup interactions. To simplify
the trigger efficiency calculations, the muon channel analysis uses only one
HLT path, which requires a muon with $\pt>9\GeV$ and
$\text{IP}_{\text{sig}}>6$. This trigger was the highest threshold one during
early parking data taking, corresponding to
$\int\\!\\!\\!\;{\mathcal{L}}{\mathrm{d}}t=6.9\fbinv$, and then the second-
highest for the rest of the data taking, accumulating an additional
$\int\\!\\!\\!\;{\mathcal{L}}{\mathrm{d}}t=26.7\fbinv$. Therefore, the
$\int\\!\\!\\!\;{\mathcal{L}}{\mathrm{d}}t$ used for the muon channel is
$33.6\fbinv$, as shown in the second row of Table 0.4.1.

The PF algorithm used for electron reconstruction imposes an implicit minimum
electron $\pt$ requirement of $2\GeV$. To recover the efficiency loss for
low-(LP) electrons, an additional algorithm (“LP electron reconstruction”) was
specifically developed. As is the case for the PF algorithm, in the LP
algorithm, the determination of the charged-particle track parameters for
electron candidates, in the presence of bremsstrahlung energy loss, relies on
the use of a Gaussian sum filter [32]. The LP electron candidate
reconstruction is started with a combination of two boosted decision trees
(BDTs), which are trained on samples of low-$\pt$ electrons and result in
looser reconstruction requirements than for the PF electrons. The LP electrons
in this analysis are reconstructed down to 1, which ensures that they reach
the ECAL. In case of duplicates, we preferentially select PF electrons over LP
ones. To optimize the performance of the electron identification, several
electron candidate characteristics are combined using a BDT into a single
discriminating variable, referred to as ID, analogously to what was done in
Ref. [32]. The ID BDTs are trained separately for PF and LP electrons. The PF
electron ID BDTs were retrained specifically for this analysis to improve the
performance at low . The training was done separately for two ranges,
$2<\pt<5\GeV$ and $\pt>5\GeV$, while a single training is used for the LP
electron ID in the entire range. The input variables for the ID BDTs include
both track-related quantities and calorimetric shower shapes, as well as
variables related to the matching of the extrapolated track to the calorimeter
cluster and the difference between the track momentum at the innermost and
outermost tracker layers. The electron ID BDTs were trained with the XGBoost
algorithm [48] on a simulated sample of $\PBp\\!\to\\!\JPsi(\EE)\PKp$ events.
The electron and $\eta$ distributions of the training sample have been
reweighted to reproduce those for the background, to avoid biases. The “tag-
and-probe” method [49] using $\JPsi\\!\to\\!\EE$ decays in data is used to
check the accuracy of the simulation for the ID BDT input variables, as well
as for the output distribution. We find these variables for both the PF and LP
electrons in data to be consistent with those in simulation, within
statistical uncertainties.

To measure $R(\PK)$, we select events for which either a
$\PBp\\!\to\\!\PKp\MM$ candidate (used in the numerator of the $R(\PK)$ ratio)
is found on the tag side, , a muon from the $\PBp\\!\to\\!\PKp\MM$ candidate
must satisfy the trigger conditions, or a $\PBp\\!\to\\!\PKp\EE$ candidate
(used in the denominator of the $R(\PK)$ ratio) is found on the probe side.
While using the tag side for the muon channel and probe side for the electron
channel complicates the analysis, as the trigger efficiency does not cancel in
the $R(\PK)$ ratio, this choice ensures a large number of events collected in
the $\PBp\\!\to\\!\PKp\MM$ channel and not only maximizes the sensitivity of
the $R(\PK)$ measurement, but also enables high-precision measurements of the
$\PBp\\!\to\\!\PKp\MM$ branching fraction.

The candidates are formed using a pair of opposite-sign (OS) same-flavor
leptons with an invariant mass below $5\GeV$ and a positively charged track,
to which the kaon mass is assigned. Several quality criteria are applied to
each muon, electron, and track candidates to reduce the number of
misreconstructed objects. Specifically, tracks are required to pass the “high-
purity” track quality criteria [50, 47] with $\pt>1\GeV$ and $\abs{\eta}<2.4$.
Since the triggering object is a muon, to reconstruct the
$\PBp\\!\to\\!\PKp\MM$ decay only one additional muon is needed. This muon is
required to have OS with respect to the triggering muon, pass the “medium”
muon identification criteria, have $\pt>2\GeV$, and satisfy $\abs{\eta}<2.4$.
In the electron channel, in order to increase the purity of the sample, we
require at least one of the electrons to be reconstructed with the PF
algorithm. Both electrons are required to have $\abs{\eta}<2.4$. The two
electrons must have points of origin separated, along the beam line direction,
by $\abs{\Delta z}<1\unit{cm}$ and with $\abs{\Delta z}<1\unit{cm}$ of the
point of origin of the muon that triggered the event. At this stage, we apply
only very loose requirements on the ID BDT output for the electrons, as it is
used as an input to the multivariate analysis described below. The transverse
momentum of the candidate is required to exceed 3 and 1.75in the muon and
electron channels, respectively.

The tracks of the three particles forming the candidate are fitted to a common
vertex, using their measured momentum vectors with the corresponding
uncertainties, to improve the mass measurement accuracy for both the candidate
and the lepton pair. The kinematic fit algorithm [51] constrains the tracks
belonging to the candidates to originate from a single vertex, and provides
the vertex position, covariance matrix, and $\chi^{2}$ of the fit. After the
vertexing is performed, the particle trajectories are refitted using this
secondary vertex (SV) as an additional constraint, and their momenta are
recomputed. The masses of the particles (leptons and kaon) are fixed to their
nominal values [4]. A loose set of criteria is imposed on the SV fit
probability, as well as the $L_{xy}/\sigma_{xy}$ and
$\cos\alpha_{\text{2D}}(\PBp)$ variables described in Table 0.5. The invariant
mass of the candidate is required to be in the range 5.0–5.6 (4.7–5.7)for the
muon (electron) channel. In addition, in the electron channel, the two
electron candidates are fitted to a common vertex (“dielectron vertex”), which
is used later in the analysis to define one of the discriminating variables,
$\abs{d_{\text{3D}}(\PKp,\,\EE)}$, described in Table 0.5.

A significant fraction of semileptonic decays of heavy-flavor hadrons,
containing a semileptonic charm meson decay or a hadronic
$\PDz\\!\to\\!\PKm\PGpp$ decay, remains in the preselected sample. The
hadronic decays enter the sample because of misidentification of the or meson
as a lepton. Therefore, a charm veto is applied by requiring that, for a
candidate, the invariant mass of the track, using the pion mass assignment,
and the OS lepton, using the kaon mass assignment, is larger than 2. In the
electron channel, we additionally require the invariant mass of the track,
using the kaon mass assignment, and the OS electron, using the pion mass
assignment, to also be larger than 2. This additional selection is not applied
in the muon channel, as the probability to reconstruct charged pions as muons
is significantly smaller than that for kaons. Finally, to suppress events
where a muon is misreconstructed as a kaon candidate, the track under the muon
mass hypothesis and the OS muon belonging to a candidate are required to have
an invariant mass away from known dimuon resonances.

The selected candidates are binned in $q^{2}$, as described in Section 0.2.
Events in each $q^{2}$ bin can be further divided in regions based on the
invariant mass of the candidate. The region where genuine candidates are
expected, $5.07<m_{\PKp\ell\ell}<5.49\GeV$, is denoted as the SR. The adjacent
mass regions $4.90<m_{\PKp\MM}<5.07$ ($4.91<m_{\PKp\EE}<5.07$)and
$5.49<m_{\PKp\ell\ell}<5.65\GeV$ are designated as sidebands (SBs). The low-
mass SB has a significant contamination from partially reconstructed meson
decays, while the high-mass SB is dominated by combinatorial background.

The final selection in each channel is based on a BDT, which combines several
variables into a classifier built using the XGBoost package. The input
variables used in the BDT are selected based on the forward elimination method
(, by adding one variable at a time and either keeping or dropping it based on
the observed improvement in the performance) and are summarized in Table 0.5.
In the electron channel, two independent BDTs are trained for the PF-PF and
PF-LP categories using the same input variables. Given the significantly
higher background in the electron channel, the corresponding BDTs have more
input variables and have all the momenta variables normalized to the candidate
mass $m_{\PKp\EE}$ to ensure that a BDT score selection does not introduce
peaks in the invariant mass distributions (“mass sculpting”). Both muon and
electron BDTs are tested thoroughly using data and simulated events to ensure
that they do not introduce any mass sculpting. The BDTs are trained in a
supervised manner with simulated $\PBp\\!\to\\!\PKp\ell^{+}\ell^{-}$ decays in
the low-$q^{2}$ bin as signal and data events from the low-$q^{2}$ bin SBs as
background.

Input variables used in the muon and electron channel BDTs.  Variable
Description Common variables $\cos\alpha_{\text{2D}}(\PBp)$ Cosine of the
angle in the plane transverse to the beams between the momentum vector of the
candidate and the line connecting the beam line and the SV.
$p(\text{\PBp~{}vtx})$ Probability of the SV kinematic fit.
$L_{xy}/\sigma_{xy}$ Significance of the SV displacement in the transverse
plane with respect to the beam line. $\pt(\PBp)$ Transverse momentum of the
candidate; in the electron channel it is divided by $m_{\PKp\EE}$. $\pt(\PKp)$
Transverse momentum of the candidate; in the electron channel it is divided by
$m_{\PKp\EE}$. Muon channel variables $\min\Delta R(\PGm,\PKp)$ $\Delta
R=\sqrt{\smash[b]{(\Delta\eta)^{2}+(\Delta\phi)^{2}}}$ distance between the
candidate and the closest muon candidate. $\min\Delta z(\PGm,\PKp)$ $\Delta z$
distance between the points of origin of the candidate and the closest muon
candidate along the beam line direction. Iso$(\mu_{\text{lead}})$ PF isolation
for the -leading muon candidate, defined as a scalar sum all PF candidates,
excluding the muon candidate itself, within $\Delta R<0.4$ of the muon
candidate and corrected for pileup. Electron channel variables
$\pt(\Pe_{i})/m_{\PKp\EE},\newline i=1,2$ Transverse momenta of the two
electron candidates, divided by $m_{\PKp\EE}$. $\Delta
z(\Pe_{i},\PKp),\;i=1,2$ Longitudinal distance between the points of origin of
each electron candidate and the kaon candidate.
$\smash[b]{\frac{\abs{d_{\text{3D}}(\PKp,\,\EE)}}{\sigma_{\abs{d_{\text{3D}}(\PKp,\,\EE)}}}}$
Kaon candidate 3D impact parameter significance with respect to the dielectron
vertex. $\Delta R(\Pep,\Pem)$ $\Delta R$ between the two electron candidates.
$\Delta R(\Pe_{i},\PKp),\;i=1,2$ $\Delta R$ between each electron candidate
and the kaon candidate.
$\frac{|\mathbf{p(\EE)}\times\mathbf{r}|-|\mathbf{p(\PKp)}\times\mathbf{r}|}{|\mathbf{p(\EE)}\times\mathbf{r}|+|\mathbf{p(\PKp)}\times\mathbf{r}|}$
Asymmetry of the momentum of the dielectron system and that of the $\PKp$
momentum with respect to the candidate trajectory, where $\mathbf{r}$ is a
unit vector connecting the PV and SV. ID($\Pe_{i},\;i=1,2$) Electron ID BDT
score for two electron candidates. $I_{\Delta
R=0.4}^{\text{rel}}(\Pe_{i}),\;i=1,2$
and $I_{\Delta R=0.4}^{\text{rel}}(\PKp)$ Relative track-based isolation of
the two electron candidates and the $\PKp$ candidate, respectively, defined as
a scalar sum of all additional tracks in a $\Delta R<0.4$ cone around the
candidate, divided by the candidate’s $\pt$.

It is checked that the simulation describes the data well. The comparisons are
performed for all BDT input variables, as well as the BDT output, using the
${}_{s}\mathcal{P}\text{lot}$ technique [52], where the reconstructed
candidate invariant mass is used as the discriminating variable. The test is
performed on the $\PBp\\!\to\\!\JPsi(\ell^{+}\ell^{-})\PKp$ CRs, and good
agreement between data and simulation is found for all three channels (muon,
PF-PF, and PF-LP). After training, the BDT output is a continuous function, as
shown in Fig. 2, where high (low) values correspond to signal-like
(background-like) events. In this figure, the background sample is obtained by
using the SR selection, with the inversion of the OS requirement for the two
leptons (the same-sign CR). The optimal BDT working point (WP) is chosen to
maximize the expected significance of the $\PBp\\!\to\\!\PKp\ell^{+}\ell^{-}$
signal in the low-$q^{2}$ region. In the muon channel, the same BDT selection
is applied to the $\JPsi$ and $\PGyP{2S}$ CRs to allow for maximum
cancellation of the systematic uncertainties, while in the electron channel,
where the dominant uncertainty is statistical, a looser BDT WP is used for the
resonance CRs to maximize the number of events in the normalization channel.
The muon, PF-PF, and PF-LP channels are then combined statistically for the
$R(\PK)$ extraction.

Figure 2: Analysis BDT output for signal (MC simulation, in black) and
background (same-sign dilepton data, in red) for the muon channel (left) and
for the PF-PF (center) and PF-LP (right) electron channels. The histograms are
normalized to unit area.

The product of the detector acceptance $\mathcal{A}$ and efficiency $\epsilon$
is evaluated using simulated samples without the trigger requirements. For the
muon channel, the trigger efficiency $\epsilon_{\text{trig}}$, determined from
simulated samples with and without the trigger requirement and no
reconstruction requirements, is found to be approximately 0.4%. The low value
of the trigger efficiency is mainly due to the muon and displacement
requirements. In the electron channel, since the $\PBp\\!\to\\!\PKp\EE$
candidates are found on the probe side, the $\epsilon_{\text{trig}}$ component
does not enter in the $R(\PK)$ extraction, as it is measured to be the same
for the low-$q^{2}$ and the regions and hence cancels completely in the
$R(\PK)$ ratio.

Slight differences between data and simulation in the muon channel are
mitigated with scale factors (SFs) applied to simulated events, and the
correction for the following effects are applied.

  * •

Trigger efficiency: The difference in the trigger response is corrected for by
an SF, as a function of muon $\eta$, , and the SV displacement significance
$L_{xy}/\sigma_{xy}$. The SF is measured with a tag-and-probe method [49],
exploiting the $\JPsi\\!\to\\!\MM$ decays.

  * •

Muon identification efficiency: The quality criteria imposed on the muons may
have different performance in data and simulation. This SF is measured with
the tag-and-probe method.

  * •

BDT efficiency: The BDT is using input variables that have small differences
between data and simulation. The corresponding SF is measured by comparing the
BDT output for the $\PBp\\!\to\\!\JPsi(\MM)\PKp$ events in data and
simulation.

  * •

Pileup: Simulated events are reweighted to match the evolving pileup
conditions of the analyzed data.

  * •

Higher-order corrections: Leading-order simulation is reweighted at the
generator-level so that the meson and rapidity spectra match those from fixed-
order perturbative quantum chromodynamics calculations with resummation of
large logarithms that arise from soft and collinear emissions [53, 54]. The
reweighting is done using the fixed-order plus next-to-leading logarithmic
(FONLL) calculations [55, 56], which are known to reproduce these spectra in
data with high accuracy.

It was found that applying the analogous SFs to the electron channel changes
the measured value of $R(\PK)$ by less than 1.2%, which has a negligible
effect on the final result given the large statistical uncertainty in the
electron channel. Therefore, the SFs are not applied in the electron channel.
The measured $\mathcal{A}\epsilon\epsilon_{\text{trig}}$ in the muon channel
for all $q^{2}$ bins, after applying these corrections, is shown in Fig.
.10.1. The $\mathcal{A}\epsilon\epsilon_{\text{trig}}$ or
$\mathcal{A}\epsilon$ values in the low-$q^{2}$ regions and two resonant CRs
for the muon or electron channel are listed in Table 0.5 .

The product of acceptance, and offline and trigger efficiency
($\mathcal{A}\epsilon\epsilon_{\text{trig}}$) for the signal in the
low-$q^{2}$ region and for the two resonance CRs. In the case of electrons,
the trigger efficiency is not included in the quoted $\mathcal{A}\epsilon$
numbers, as it cancels out in the $R(\PK)$ double ratio. Uncertainties are
statistical only.  $q^{2}$ range Muon
$\mathcal{A}\epsilon\epsilon_{\text{trig}}$ [%] PF-PF $\mathcal{A}\epsilon$
[%] PF-LP $\mathcal{A}\epsilon$ [%] Low $q^{2}$ $0.0825\pm 0.0013$ $2.95\pm
0.07$ $1.50\pm 0.05$ $0.0969\pm 0.0006$ $2.48\pm 0.03$ $1.08\pm 0.01$
$\PGyP{2S}$ $0.1112\pm 0.0004$ $1.82\pm 0.02$ $0.68\pm 0.01$

##  0.6 Mass fit

In each channel, the $\PBp\\!\to\\!\PKp\ell^{+}\ell^{-}$ signal yield is
extracted from an unbinned maximum likelihood fit to the invariant mass
spectrum of all candidates that pass the selection criteria. Signal and
background shapes are described by analytical functions or templates based on
studies of simulated events, with their normalization factors free to vary in
the fit to data. To allow a better description of the data, some parameters of
the analytical functions are constrained within the uncertainties obtained
from a fit to simulated samples, rather than being fixed. The same functional
forms describing the various contributions are shown to work well in all
$q^{2}$ bins in simulation; hence they are kept the same in the fit to data as
well.

###  0.6.1 Background composition

While the background composition differs from one $q^{2}$ bin to another and
from channel to channel, the background originates from the following common
sources:

  * •

Combinatorial background: This background stems from the combination of
objects from different hadron decays, or two muons from the same hadron decay
chain, with a random track. The shape is extracted by exploiting the fact that
this background dominates the upper mass SB, as well as the same-sign CR.

  * •

Partially reconstructed background: This background is dominated by the
$\PB^{\ast 0/+}\\!\to\\!\PK^{\ast}(892)^{0/+}\PX$ decays, where is ,
$\PGyP{2S}$, or a nonresonant $\ell^{+}\ell^{-}$ pair. This background arises
from $\PK^{\ast}(892)^{0}\\!\to\\!\PKp\PGpm$,
$\PK^{\ast}(892)^{+}\\!\to\\!\PKp\PGpz$, and
$\PK^{\ast}(892)^{+}\\!\to\\!\PKz\PGpp$ decays, where either the or track is
used together with the dilepton system to build a candidate, with the other
decay particle being either lost or ignored. In the latter case, potentially
two candidates are reconstructed by combining the dilepton system with either
of the two tracks; both have significantly lower mass than the nominal meson
mass due to the missing other particle, but still potentially contaminate the
signal window in the $\PK\ell^{+}\ell^{-}$ mass. Simulated $\PB^{\ast
0/+}\\!\to\\!\PK^{\ast}(892)^{0/+}\PX$ events are used to derive the invariant
mass distributions of the partially reconstructed backgrounds.

  * •

Cabibbo-suppressed background: This background is present in both the resonant
CRs and nonresonant SR, and it is very similar to the signal signature, just
with the kaon replaced by a pion. This background cannot be discriminated from
the signal decay and it is accounted for using simulated events.

  * •

Resonant background “leakage”: This background comes from the fact that
leptons produced in the $\PBp\\!\to\\!\JPsi(\ell^{+}\ell^{-})\PKp$ and
$\PBp\\!\to\\!\PGyP{2S}(\ell^{+}\ell^{-})\PKp$ decays can radiate final-state
photons. In the case of muons, no photon recovery algorithm is used, so these
photons are not accounted for in the muon momentum reconstruction; in the case
of electrons, while most of these photons are picked by the Gaussian sum
filter algorithm and added to the momentum of the reconstructed electrons,
large-angle radiation may still be missed. These effects reduce the $q^{2}$ to
lower values and generally result in migration of events across the $q^{2}$
bins. The finite detector resolution and a much larger branching fraction to
the resonant mode can also contribute tails on the high side. This background
source is significant only in the $q^{2}$ bins in the vicinity of the and
$\PGyP{2S}$ resonances, and is estimated using simulated samples.

  * •

Other hadron decays: This is the most general background that includes all
partially reconstructed hadron decays that do not fit in any of the previous
categories. Depending on the $q^{2}$ bin, different specific decays dominate
in this category.

A potential peaking background in the electron channel could arise from
hadrons misidentified as electrons in the all-hadronic decays of the type
$\PBp\\!\to\\!\PKp\mathrm{h_{1}h_{2}}$, where h1,2 are hadrons, dominated by
$\PBp\\!\to\\!\PKp\PGpp\PGpm$ decays (with the branching fraction of
${\sim}10^{-5}$, once the resonant charm $\PADz\PGpp$ contribution is
subtracted). The peaking structure is particularly pronounced in the
low-$q^{2}$ region where the dipion system generally has large momentum, and
replacing it with the dielectron hypothesis consequently does not shift
sizably the reconstructed invariant mass. This background, missed in early
$R(\PK)$ measurements [10, 11, 9], was largely responsible for the claimed
anomaly, and after accounting for it, the $R(\PK)$ value is found to be
compatible with the SM expectation [19, 20]. In the present analysis, we have
developed the identification of low-electrons and optimized the identification
of PF electrons specifically to reduce the probability of such
misidentification. A typical misidentification rate after the BDT selection is
$10^{-3}$–$10^{-4}$ per electron, making the misidentified-hadron background
very small. Nevertheless, given the importance of the peaking background in
the LHCb case, we have made an explicit estimate of potential contributions of
the misidentified-hadron background. We use a large simulated sample of
$\PBp\\!\to\\!\PADz(\\!\to\\!\PKp\PGpm)\PGpp$ decays without applying the
charm veto (described in Section 0.5) to estimate the misidentification
efficiency. In addition, we use a small simulated sample of charmless
$\PBp\\!\to\\!\PKp\PGpm\PGpp$ decays to evaluate the charm veto efficiency for
this mode. The study showed that the charm veto plus the identification
requirements on PF and LP electrons work very well to suppress the
misidentification background to a low level, as expected from squaring the
misidentification probability and applying the relative branching fractions
for the signal and background processes. The total estimated number of
misidentified-hadron background events in the low-$q^{2}$ region after the
full analysis selection is less than 0.3 events in each of the PF-PF and PF-LP
categories. Compared to the expected signal yield, this peaking background
corresponds to $<$2 and $<$6%, respectively, for the two categories, which is
much smaller than the corresponding statistical uncertainty. As this
background is also shown to be negligible in the muon channel, it is not
included in the final results.

###  0.6.2 Muon channel signal extraction

In the muon channel, two independent unbinned maximum likelihood fits are
performed to the candidate invariant mass distribution: a “single” fit in the
low-$q^{2}$ region and a “simultaneous” fit across the 15 $q^{2}$ bins. The
former is used to measure $R(\PK)$ and the integrated branching fraction of
the $\PBp\\!\to\\!\PKp\MM$ decay, while the latter is used for the extraction
of the differential branching fraction. While the two fits give consistent
results in the low-$q^{2}$ region, both in terms of the central value and the
uncertainty, the strategy of having two fits achieves greater similarity
between the $\PBp\\!\to\\!\PKp\MM$ and $\PBp\\!\to\\!\PKp\EE$ channels and
reduces the $R(\PK)$ measurement uncertainty.

In both the single fit of the low-$q^{2}$ region and the simultaneous fit, the
signal is described with the sum of a double-sided Crystal Ball (DCB) function
[57, 58] and a Gaussian function. All of the parameters of the DCB function
are fixed based on simulation. The mean and the width of the Gaussian function
in the single fit are free parameters. In the simultaneous fit, while the
width is allowed to float, the mean of the Gaussian function is parameterized
as a linear function of $q^{2}$ with a slope of $0.0014\pm 0.0012\GeV^{-1}$ to
describe the observed dependence in simulation. The rest of the parameters in
the simultaneous fit are treated the same way as in the single fit.

  * •

The $\PBp\\!\to\\!\PK^{\ast}(892)^{0/+}\PX$ background is described by a DCB
function with the shape fixed from simulation. In the simultaneous fit, an
exponential function with parameters fixed from simulation is added to the DCB
function to account for the candidates built with the of the $\PKst(892)$
decay in the 11.0–19.24$\GeV^{2}$ $q^{2}$ range where the contribution of this
component is significant.

  * •

The sum of the combinatorial and other meson decays backgrounds is described
with a single exponential function, except for the last $q^{2}$ bin of the
simultaneous fit, where it is multiplied by $m_{\PKp\MM}-m_{\MM}-m_{\PKp}$ to
account for the phase space suppression.

  * •

The $\PBp\\!\to\\!\PGpp\PX$ background is described by a DCB function with the
shape and relative yield with respect to the $\PBp\\!\to\\!\PKp\PX$ signal
fixed from simulation.

  * •

The ($\PGyP{2S}$) resonant background leakage to nearby $q^{2}$ bins is
described with a DCB function with the normalization as a free parameter of
the fit and the shape parameters fixed by fitting simulated
$\PBp\\!\to\\!\JPsi(\MM)\PKp$ ($\PBp\\!\to\\!\PGyP{2S}(\MM)\PKp$) events in
the specific $q^{2}$ bin. This contribution is included only in the
simultaneous fit in the following $q^{2}$ bins: 6.0–7.0 and 7.0–8.0$\GeV^{2}$
for the $\PBp\\!\to\\!\JPsi(\MM)\PKp$ background, and 11.0–11.8, 11.8–12.5,
and 14.82–16.0$\GeV^{2}$ for the $\PBp\\!\to\\!\PGyP{2S}(\MM)\PKp$ background.

For the $\PBp\\!\to\\!\JPsi(\MM)\PKp$ CRs, the fit is kept as close as
possible to the single fit in the low-$q^{2}$ region in terms of template
functions and parameter treatment. Nevertheless, because of the much smaller
radiative tail due to the tight $2.9<m_{\MM}<3.2\GeV$ requirement in the CR
and the different background sources, some of the templates are different from
the ones used for nonresonant signal. The signal is described by a sum of
three Gaussian functions with all shape parameters constrained within the
uncertainties from a fit to simulated data. The
$\PBp\\!\to\\!\JPsi(\MM)\PK^{\ast}(892)^{+}$ background is described with the
sum of a DCB function and an exponential function, with all the shape
parameters fixed from simulation, as in the 11.0–19.24$\GeV^{2}$ $q^{2}$ range
of the simultaneous fit.

The $\PBp\\!\to\\!\PGyP{2S}(\MM)\PKp$ CR is not used directly in the analysis,
but is utilized for several cross checks (such as the $R_{\PGyP{2S}}$
measurement). For validation purposes, the functions used for the fit in the
$\PBp\\!\to\\!\PGyP{2S}(\MM)\PKp$ CR are exactly the same as in the
low-$q^{2}$ region, except for the
$\PBp\\!\to\\!\JPsi(\MM)\PK^{\ast}(892)^{+}$ background, which is described
with the sum of a DCB function and an exponential function with all the shape
parameters fixed from simulation, as in the 11–19.24$\GeV^{2}$ $q^{2}$ range
of the simultaneous fit.

The functions used in the fit are summarized in Table
LABEL:tab:fit_function_muons. The results of the unbinned maximum likelihood
fit, with the systematic uncertainties represented by the nuisance parameters
in the likelihood with Gaussian priors, are shown in Table 0.6.2 and Fig. 3
for the low-$q^{2}$ bin and resonant CRs and in Table 0.8.1 and Figs.
.10.3–.10.4 for the simultaneous fit.

Fit functions used for signal and background sources in each $q^{2}$ bin in
the muon channel. The symbol indicates this background is not included in this
region.  Process $\PBp\\!\to\\!\PKp\MM$ $\PBp\\!\to\\!\JPsi(\MM)\PKp$
$\PBp\\!\to\\!\PGyP{2S}(\MM)\PKp$ Signal DCB $+$ Gaussian Sum of 3 Gaussians
DCB $+$ Gaussian Comb. & other bkg. Exponential† Exponential Exponential
$\PBp\\!\to\\!\PK^{\ast}(892)^{0/+}\PX$ DCB ($+$ expon.) DCB $+$ exponential
DCB $+$ exponential $\PBp\\!\to\\!\PGpp\PX$ DCB DCB DCB
$\PBp\\!\to\\!\JPsi(\MM)\PKp$ DCB (nearby $q^{2}$)
$\PBp\\!\to\\!\PGyP{2S}(\MM)\PKp$ DCB (nearby $q^{2}$)

† In the last $q^{2}$ bin the exponential function is multiplied by
$m_{\PKp\MM}-m_{\MM}-m_{\PKp}$ to account for the phase space suppression.

Signal yields in the muon channel in the low-$q^{2}$ bin and resonant CRs.
Channel $q^{2}$ range [$\GeVns^{2}$] Yield $\PBp\\!\to\\!\PKp\MM$ 1.1– 6.0
1267 $\pm$ 55 $\PBp\\!\to\\!\JPsi(\MM)\PKp$ 8.41– 10.24 728 000 $\pm$ 1000
$\PBp\\!\to\\!\PGyP{2S}(\MM)\PKp$ 12.60– 14.44 68 300 $\pm$ 500

Figure 3: Results of an unbinned likelihood fit to the $\PKp\MM$ invariant
mass distributions in the low-$q^{2}$ bin (upper), and in the
$\PBp\\!\to\\!\JPsi(\MM)\PKp$ (lower left) and
$\PBp\\!\to\\!\PGyP{2S}(\MM)\PKp$ (lower right) CRs. The error bars show the
statistical uncertainty in data. The lower panels show the distribution of the
pull, which is defined as the Poisson probability to observe the number of
event counts in data, given the fit function, expressed in terms of the
Gaussian significance.

###  0.6.3 Electron channel signal extraction

To extract the number of signal events, unbinned maximum likelihood fits to
the candidate invariant mass distribution are performed in three $q^{2}$
regions. The $q^{2}$ regions considered are: low-$q^{2}$ aiming at the signal
$\PBp\\!\to\\!\PKp\EE$ decay, and two CRs aiming at
$\PBp\\!\to\\!\JPsi(\EE)\PKp$ and $\PBp\\!\to\\!\PGyP{2S}(\EE)\PKp$ decays.
The high-$q^{2}$ bin, above the $\PGyP{2S}$ resonance, has been studied, but
the backgrounds in this bin are too large to extract the
$\PBp\\!\to\\!\PKp\EE$ signal reliably; consequently, it is not included in
the analysis. Fits are done independently in the PF-PF and PF-LP categories.
Signal shapes are described by either a DCB function or the sum of a one-sided
Crystal Ball (CB) function [57] and a Gaussian function. The same background
sources as in the muon channel also contribute here, albeit with different
relative importance. The partially reconstructed background is similar to that
in the muon channel. The combinatorial background is more prominent with
respect to the muon channel, because of the higher fraction of hadrons
misreconstructed as electrons. Finally, the other hadron decay background is
represented by a separate template. In the electron channel, we use simulated
distributions directly to construct various background templates. This is
achieved using the kernel density estimator (KDE) method [59] applied to
simulated events. The only exception is the combinatorial background, for
which a simple exponential with the slope and normalization floating in the
fit is used. The Cabibbo-suppressed decay background is negligible for the
low-$q^{2}$ and $\PGyP{2S}$ bins, and therefore is accounted for only in the
$\PBp\\!\to\\!\JPsi(\EE)\PKp$ CR. The relative normalization of this
background to the signal is fixed from simulation. The shapes of various
backgrounds are fixed from simulation and the normalizations are free
parameters of the fit, unless specified otherwise. The functions used in the
fit are presented in Table 0.6.3. Figure 4 shows the $\PKp\EE$ invariant mass
distribution for the electron channels in the three $q^{2}$ regions for the
PF-PF and PF-LP categories. The signal yields in these regions are listed in
Table 0.6.3.

Fit functions used to describe signal and various background components for
the electron channel. The symbol indicates this background is not included in
this region.  Process $\PBp\\!\to\\!\PKp\EE$ $\PBp\\!\to\\!\JPsi(\EE)\PKp$
$\PBp\\!\to\\!\PGyP{2S}(\EE)\PKp$ Signal DCB function CB $+$ Gaussian CB +
Gaussian Comb. background Exponential Exponential Exponential
$\PBp\\!\to\\!\PK^{\ast}(892)^{0/+}\PX$ KDE template KDE template
$\PBp\\!\to\\!\PGpp\PX$ CB function $\PBp\\!\to\\!\JPsi(\EE)\PKp$ KDE template
Other decays KDE template KDE template

Signal yields in the electron channel in the low-$q^{2}$ bin and resonant CRs.
Channel $q^{2}$ range [$\GeVns^{2}$] PF-PF yield PF-LP yield
$\PBp\\!\to\\!\PKp\EE$ 1.1– 6.0 17.9 $\pm$ 7.2 3.0 $\pm$ 5.9
$\PBp\\!\to\\!\JPsi(\EE)\PKp$ 8.41– 10.24 4857 $\pm$ 84 2098 $\pm$ 58
$\PBp\\!\to\\!\PGyP{2S}(\EE)\PKp$ 12.60– 14.44 320 $\pm$ 20 94 $\pm$ 11

Figure 4: The $\PKp\EE$ invariant mass spectrum with the results of the fit
shown with the red line in the low-$q^{2}$ region (upper row),
$\PBp\\!\to\\!\JPsi(\EE)\PKp$ CR (middle row), and
$\PBp\\!\to\\!\PGyP{2S}(\EE)\PKp$ CR (lower row) for the PF-PF (left column)
and PF-LP (right column) categories. The shoulder below the nominal meson mass
for the $\PGyP{2S}$ CR is due to the narrow $q^{2}$ range in this bin compared
to the size of the radiative tail. Notations are as in Fig. 3.

##  0.7 Systematic uncertainties

Statistical uncertainties in the signal yields are propagated into the
measurement of $R(\PK)$. The final statistical uncertainty in $R(\PK)$ is
dominated by the yield in the low-$q^{2}$ bin in the electron channel, which
is of order of 40% (as can be seen in Fig. 4).

Systematic uncertainties in this analysis fall into two categories: those due
to the finite size of the signal MC samples used for the $\mathcal{A}\epsilon$
estimates, which are statistical in nature, and those that reflect certain
assumptions made in the analysis. Systematic uncertainties are calculated
independently for the muon and electron channel parts of $R(\PK)$, because
they largely cancel in the single ratios,
$\PBp\\!\to\\!\PKp\ell^{+}\ell^{-}/\PBp\\!\to\\!\JPsi(\ell^{+}\ell^{-})\PKp$,
in each of the two channels. Consequently, only the uncertainties that do not
cancel or cancel partially are discussed in this section. The uncertainties in
the muon and electron channels are treated as uncorrelated, which is supported
by the fact that the two channels have different sources of systematic
uncertainties due to differences in the trigger, kinematics (because of the
tag-side vs. probe-side selection), and lepton reconstruction. To evaluate the
impact of a systematic source, the $R(\PK)$ ratio is remeasured after changing
the central value for the source under study by ${\pm}1\sigma$. The difference
between the modified and nominal values of the single ratio is used as the
systematic uncertainty.

###  0.7.1 Systematic uncertainties in the muon channel single ratio

The dominant systematic uncertainties in the single ratio
$\PBp\\!\to\\!\PKp\MM/\PBp\\!\to\\!\JPsi(\MM)\PKp$, in order of importance,
are as follows:

  * •

Parameterization of the background function of the $\PBp\\!\to\\!\PKp\MM$ fit:
This uncertainty is estimated by using a falling tail of a Gaussian function
instead of an exponential function to describe the dominant combinatorial plus
other meson decays background. The effect is 1.8%.

  * •

Operating below the trigger plateau: The uncertainty in the trigger turn-on
effects was estimated by repeating the measurement after tightening the
offline requirements. The corresponding uncertainty is 1.3%.

  * •

Uncertainty in the FONLL scale factors: Simulated events are reweighted in and
rapidity of the candidate according to the FONLL predictions. The
corresponding uncertainty is 0.9%.

  * •

Parameterization of the background function in the
$\PBp\\!\to\\!\JPsi(\MM)\PKp$ CR fit: The uncertainty is estimated the same
way as in the SR. The effect is 0.6%.

  * •

Description of the meson radiative tail: Events in the
$\PBp\\!\to\\!\JPsi(\MM)\PKp$ channel are selected using a fixed $q^{2}$
window. A mismodeling of the tail can lead to an incorrect calculation of
efficiency. This effect is estimated by repeating the measurement in a larger
$q^{2}$ window, by relaxing the lower boundary from 2.9 to 2.8. The effect is
0.5%.

  * •

Pileup: The pileup profile is reweighted using a ${\pm}4.6\%$ variation in the
total inelastic $\Pp\Pp$ cross section [60]. The corresponding uncertainty is
0.4%.

  * •

Parameterization of the signal shape in the low-$q^{2}$ $\PBp\\!\to\\!\PKp\MM$
fit: The uncertainty due to the signal description is estimated by adding an
extra Gaussian function to the signal template and repeating the fit. The
corresponding systematic uncertainty is 0.3%.

  * •

Uncertainty in the trigger scale factors: The combined statistical and
systematic uncertainty from the SF measurement is obtained using the tag-and-
probe method. The effect is 0.2%.

  * •

Parameterization of the signal shape in the $\PBp\\!\to\\!\JPsi(\MM)\PKp$ fit:
This uncertainty is evaluated in the same way as in the low-$q^{2}$ bin. The
corresponding uncertainty is 0.1%.

  * •

The nonresonant $\PBp\\!\to\\!\PKp\MM$ contribution in the
$\PBp\\!\to\\!\JPsi(\MM)\PKp$ CR: The predicted $\PBp\\!\to\\!\PKp\MM$
contribution in the $q^{2}$ range using is subtracted from the signal yield.
The effect is 0.1%.

Other uncertainty sources were also studied (e.g., several SFs related to the
BDT), but found to have a negligible effect ($<$0.01%) and are therefore
omitted. The systematic sources are treated as uncorrelated, and the overall
uncertainty in the low-$q^{2}$ bin is found to be 2.6%. The statistical
uncertainty in the same bin is 7.5% and the uncertainty from the limited size
of the simulation sample used for the $\mathcal{A}\epsilon$ calculations is
1.7%. The uncertainties in the
$\PBp\\!\to\\!\PKp\MM$/$\PBp\\!\to\\!\JPsi(\MM)\PKp$ ratio measurement are
summarized in Table 0.7.1. For the differential branching fraction measurement
the same systematic sources are evaluated in each $q^{2}$ bin and the
resulting uncertainties are shown in Fig. .10.2. In most $q^{2}$ bins, the
data statistical uncertainty is dominant.

Major sources of uncertainty in the
$\PBp\\!\to\\!\PKp\MM$/$\PBp\\!\to\\!\JPsi(\MM)\PKp$ ratio measurement.
Source Impact on the $R(\PK)$ ratio [%] Background description, low-$q^{2}$
bin 1.8 Trigger turn-on 1.3 Reweighting in and rapidity 0.9 Background
description, CR 0.6 meson radiative tail description 0.5 Pileup 0.4 Signal
shape description 0.3 Trigger efficiency 0.2 resonance shape description 0.1
Nonresonant contribution to the CR 0.1 Total systematic uncertainty 2.6
Statistical uncertainty in MC samples 1.7 Statistical uncertainty in data 7.5
Total uncertainty 8.1

###  0.7.2 Systematic uncertainties in the electron channel single ratio

Since the yield of $\PBp\\!\to\\!\PKp\EE$ events in the low-$q^{2}$ bin is
small, the overall uncertainty is dominated by the statistical uncertainty.
The sources of systematic uncertainties in the electron channel are generally
different from those in the muon channel, due to different kinematics and
reconstruction performance.

The dominant uncertainties in the single ratio
$\PBp\\!\to\\!\PKp\EE$/$\PBp\\!\to\\!\JPsi(\EE)\PKp$, in order of importance,
are as follows:

  * •

Parameterization of signal and background shapes: Both the signal and
background shapes in the fits of the low-$q^{2}$ SR and CR are modified and
the difference is taken as an uncertainty. The modification is done by
replacing the KDE-based templates with analytical functions similar to the
ones used in the muon channel. The signal description in the low-$q^{2}$ bin
was modified by adding an extra Gaussian function, and the exponential
describing the combinatorial background was replaced by a second-order
Chebyshev polynomial. The combined uncertainty in the fit parameterization
because of the signal and background variations is about 5% each in the PF-PF
and PF-LP categories.

  * •

Constraint on the $\PBp\\!\to\\!\JPsi(\EE)\PKp$ contribution: The
normalization of the meson leakage background in the $\PBp\\!\to\\!\PKp\EE$
channel in the low-$q^{2}$ region is constrained to the expected yield from
the fit in the $\PBp\\!\to\\!\JPsi(\EE)\PKp$ CR. The uncertainty is dominated
by the statistical uncertainty in the yield of this background and is
estimated using pseudo-experiments, while the contribution from the radiative
tail mismodeling is negligible. The uncertainty amounts to 4 (9)% in the PF-PF
(PF-LP) category.

  * •

The BDT efficiency stability: The BDT WP is chosen to maximize the expected
significance of the $\PBp\\!\to\\!\PKp\EE$ signal in the low-$q^{2}$ region. A
variation of the WP corresponding to a variation of $\pm 10\%$ in the expected
significance is chosen to evaluate the stability. The corresponding systematic
uncertainty is 2 (5)% for the PF-PF (PF-LP) category.

  * •

The BDT cross-validation: To allow for the entire data set to be used both in
the BDT training and testing, an eight-fold cross validation is used,
resulting in eight different BDTs. The spread in the efficiency of these BDTs
is used as the uncertainty, amounting to 2 (3)% in the PF-PF (PF-LP) category.

  * •

Triggers in the parking data set: In the electron channel all the parking
triggers are used for the measurement. The small kinematical correlation
between the tag and probe sides could have an impact on the $R(\PK)$ value.
Due to a complicated mixture of L1 and HLT triggers, some of which are
prescaled as a function of the instantaneous luminosity, the composition in
terms of trigger paths is different in simulated samples than in data. To
account for this, the trigger efficiency ratio between the low-$q^{2}$ SR and
CR is estimated for several individual trigger paths and the variation of this
ratio is taken as a systematic uncertainty amounting to 1 (4)% for the PF-PF
(PF-LP) category.

  * •

The BDT scale factor: This SF accounts for the differences in the BDT WP
efficiency between data and simulation. The efficiency of the nominal WP with
respect to a loose selection, which is nearly fully efficient for signal, is
computed in the CR, and transferred to the low-$q^{2}$ bin using simulation.
The uncertainty from this source is 1 (2)% in the PF-PF (PF-LP) category.

  * •

Description of the meson radiative tail: This uncertainty is estimated in the
same way as in the muon channel, except that the enlargement of the $q^{2}$
window is bigger in the case of electrons to account for the larger radiative
tail. The effect is 1% for both PF-PF and PF-LP categories.

Other sources of uncertainty have an impact of less than 1% on the
$\PBp\\!\to\\!\PKp\EE$/$\PBp\\!\to\\!\JPsi(\EE)\PKp$ ratio. The reason the
uncertainties in the BDT performance are much larger in the electron channel
than in the muon one is the much tighter WP used, which results in effectively
smaller training samples and higher sensitivity to data-to-simulation
differences in the tails of the distributions of the various input variables.
All sources of systematic uncertainties are treated as uncorrelated, which
results in an overall systematic uncertainty in the
$\PBp\\!\to\\!\PKp\EE$/$\PBp\\!\to\\!\JPsi(\EE)\PKp$ single ratio of 7 and 13%
for the PF-PF and PF-LP categories, respectively. The systematic uncertainties
are small compared to the statistical ones which are 40 (200)% for the PF-PF
(PF-LP) channel. Table 0.7.2 summarizes the uncertainties in the electron
channel.

Major sources of uncertainty in the
$\PBp\\!\to\\!\PKp\EE$/$\PBp\\!\to\\!\JPsi(\EE)\PKp$ ratio measurement in the
PF-PF and PF-LP categories. The last row shows the statistical uncertainty,
which is the same as the total uncertainty within the quoted precision.
Source Impact on the $R(\PK)$ ratio [%] PF-PF PF-LP Signal and background
description 5 5 event leakage to the low-$q^{2}$ bin 4 9 BDT efficiency
stability 2 5 BDT cross validation 2 3 Trigger efficiency 1 4 BDT
data/simulation difference 1 2 meson radiative tail description 1 1 Total
systematic uncertainty 7 13 Statistical and total uncertainty 40 200

##  0.8 Results

In this section, we report the following results:

  * •

measurement of the differential branching fraction of the
$\PBp\\!\to\\!\PKp\MM$ decay in the full $q^{2}$ range, excluding the and
$\PGyP{2S}$ resonances;

  * •

measurement of the integrated branching fractions of the
$\PBp\\!\to\\!\PKp\MM$ decay in the low-$q^{2}$ region and in the full $q^{2}$
range; and

  * •

measurement of $R(\PK)$ in the low-$q^{2}$ region.

To validate the analysis procedure we performed several cross-checks, the two
most important ones being the measurement of the $R_{\PGyP{2S}}$ and
$R_{\JPsi}$ ratios. The former is defined by Eq. (3), , exchanging the
$\PBp\\!\to\\!\PKp\ell^{+}\ell^{-}$ decay by the
$\PBp\\!\to\\!\PGyP{2S}(\ell^{+}\ell^{-})\PKp$ one. The latter is the ratio of
the $\PBp\\!\to\\!\JPsi(\MM)\PKp$ and $\PBp\\!\to\\!\JPsi(\EE)\PKp$ branching
fractions. Both these ratios are expected and measured [4] to be flavor-
universal (, equal to unity), with high precision. An important added value of
the $R_{\JPsi}$ cross-check is that various efficiencies and corrections that
cancel out in the $R(\PK)$ double ratio, only partially cancel or do not
cancel in the $R_{\JPsi}$ single ratio. Therefore, this cross check also
validates the systematic uncertainties that cancel in the $R(\PK)$ ratio.

The results of our measurement in the combination of the PF-PF and PF-LP
categories are: $R_{\PGyP{2S}}=0.966^{+0.071}_{-0.066}$ and
$R_{\JPsi}=1.006^{+0.020}_{-0.019}$, where the uncertainties shown are
statistical only. Both the $R_{\PGyP{2S}}$ and $R_{\JPsi}$ measurements are
consistent with unity within one standard deviation, with a precision of a few
percent. The systematic uncertainty due to the lack of cancellation of various
efficiencies and from sources discussed in Section 0.7 for both ratios is
estimated to be around 7%. Consistent results are obtained in the PF-PF and
PF-LP categories separately, albeit with larger statistical uncertainties.

###  0.8.1 Measurement of the differential $\mathcal{B}$ ($\to\PKp$
$\mu^{+}\mu^{-}$)

To reduce the systematic uncertainty, the differential branching fraction in
each $q^{2}$ bin is normalized to $\mathcal{B}(\PBp\\!\to\\!\JPsi(\MM)\PKp)$,

$\mathcal{B}(\PBp\\!\to\\!\PKp\MM)[q^{2}_{\text{min}},q^{2}_{\text{max}}]=\frac{N_{\PBp\\!\to\\!\PKp\MM}[q^{2}_{\text{min}},q^{2}_{\text{max}}]}{N_{\PBp\\!\to\\!\JPsi(\MM)\PKp}[8.41,10.24]\GeV^{2}}\\\
\times\frac{(\mathcal{A}\epsilon\epsilon_{\text{trig}})_{\PBp\\!\to\\!\JPsi(\MM)\PKp}[8.41,10.24]\GeV^{2}}{(\mathcal{A}\epsilon\epsilon_{\text{trig}})_{\PBp\\!\to\\!\PKp\MM}[q^{2}_{\text{min}},q^{2}_{\text{max}}]}\mathcal{B}(\PBp\\!\to\\!\JPsi\PKp)\mathcal{B}(\JPsi\\!\to\\!\MM),$
(4)

where $N_{\PBp\\!\to\\!\PKp\MM}$ and $N_{\PBp\\!\to\\!\JPsi(\MM)\PKp}$ are the
measured yields from the fit in the $q^{2}$ region indicated in the brackets
and $\mathcal{B}(\PBp\\!\to\\!\JPsi(\MM)\PKp)$ is the world-average value of
the $\PBp\\!\to\\!\JPsi(\MM)\PKp$ branching fraction [4]. The measured
differential branching fraction of the $\PBp\\!\to\\!\PKp\MM$ decay is
summarized in Table 0.8.1. The correlation matrix between the extracted values
of the differential branching fraction in different $q^{2}$ bins is shown in
Fig. .10.5.

Since there are various and somewhat different theoretical predictions for the
SM value of $\ddinline{\mathcal{B}(\PBp\\!\to\\!\PKp\MM)}{q^{2}}$, we compare
our measurement with the predictions from the hepfit [61, 62, 18, 63] v1.0,
superiso [64, 65] v4.1, flavio [66] v2.5.5, and eos [67, 68] v1.0.8 packages.
These models rely on different approaches in evaluating the effects of
nonlocal form-factor contributions (stemming from the charm quark loops) [69],
which is reflected in a sizable difference between the uncertainties in their
predictions. None of the calculations can reliably describe the regions
between the and $\PGyP{2S}$ resonances; hence the predictions are not shown in
this $q^{2}$ range. In addition, the hepfit package only gives predictions for
$q^{2}<8\GeV^{2}$. The comparison of our measurement with the prediction of
these models is shown in Fig. 5. The measured differential branching fraction
of the $\PBp\\!\to\\!\PKp\MM$ decay is generally lower than the theoretical
predictions for $q^{2}<17\GeV^{2}$, which is consistent with the results
reported by LHCb [14, 15].

The $\PBp\\!\to\\!\PKp\MM$ branching fraction,
$\ddinline{\mathcal{B}(\PBp\\!\to\\!\PKp\MM)}{q^{2}}$ integrated over the
specified $q^{2}$ range, for the individual $q^{2}$ bins.. The uncertainties
in the yields are statistical uncertainties from the fit, while the branching
fraction uncertainties include both the statistical and systematic components.
$q^{2}$ range Signal yield Branching fraction [$\GeVns^{2}$] [$10^{-8}$] 0.1–
0.98 $260\pm 20$ $2.91\pm 0.24$ 1.1– 2.0 $197\pm 19$ $1.93\pm 0.20$ 2.0– 3.0
$306\pm 23$ $3.06\pm 0.25$ 3.0– 4.0 $260\pm 21$ $2.54\pm 0.23$ 4.0– 5.0
$251\pm 23$ $2.47\pm 0.24$ 5.0– 6.0 $264\pm 27$ $2.53\pm 0.27$ 6.0– 7.0
$267\pm 21$ $2.50\pm 0.23$ 7.0– 8.0 $256\pm 23$ $2.34\pm 0.25$ 11.0– 11.8
$207\pm 19$ $1.62\pm 0.18$ 11.8– 12.5 $172\pm 16$ $1.26\pm 0.14$ 14.82– 16.0
$272\pm 20$ $1.83\pm 0.17$ 16.0– 17.0 $246\pm 17$ $1.57\pm 0.15$ 17.0– 18.0
$317\pm 19$ $2.11\pm 0.16$ 18.0– 19.24 $242\pm 19$ $1.74\pm 0.15$ 19.24– 22.9
$158\pm 19$ $2.02\pm 0.30$

Figure 5: Comparison of the measured differential $\PBp\\!\to\\!\PKp\MM$
branching fraction with the theoretical predictions obtained using hepfit,
superIso, flavio, and eos packages. The hepfit predictions are available only
for $q^{2}<8\GeV^{2}$.

###  0.8.2 Measurement of the integrated $\mathcal{B}$
($\to\PKp$$\mu^{+}\mu^{-}$)

The low-$q^{2}$ region is especially interesting because it is not affected by
higher-mass resonances and their interference effects. Consequently, the
branching fraction of the $\PBp\\!\to\\!\PKp\MM$ decay in this $q^{2}$ region
can be measured with relatively little theoretical dependence, using Eq. (4)
over the $[1.1,6.0]\GeV^{2}$ $q^{2}$ range. In this range, the acceptance
times efficiency is essentially independent of the $q^{2}$ value, as shown in
Fig. .10.1. Therefore, any dependence on theory can only arise from residual
differences in the kinematic distributions of the final-state particles
between theory and data. Since the acceptance times efficiency is evaluated
using events generated with the $\PBp\\!\to\\!\PKp\MM$ model (discussed in
Section 0.4.2), which has been tuned using $\Pep\Pem$ experimental data, as
well as lattice calculations, any such residual differences are expected to be
minimal. The resulting measurement is

$\mathcal{B}(\PBp\\!\to\\!\PKp\MM)[1.1,6.0]\GeV^{2}\\\ =(12.42\pm 0.54\stat\pm
0.11\,\text{(MC~{}stat)}\pm 0.40\syst)\times 10^{-8}=(12.42\pm 0.68)\times
10^{-8}.$ (5)

This result is consistent with the present world-average value of $(12.6\pm
1.2)\times 10^{-8}$ [4] in a very similar range, $1.0<q^{2}<6.0\GeV^{2}$, and
has a 40% smaller uncertainty. It is also consistent with and has a similar
uncertainty as the LHCb measurement [15] in the $1.1<q^{2}<6.0\GeV^{2}$ range,
$(11.86\pm 0.68)\times 10^{-8}$, which presently dominates the world-average
value. (The larger uncertainty in the world-average value is due to a scale
factor of 1.9 introduced to address the tension between the individual
results.) The comparison between our measurement and the theoretical
predictions described above is shown in Table 0.8.2. All of the theoretical
estimates are higher than our measurement in the low-$q^{2}$ region.

In order to determine the integrated $\mathcal{B}(\PBp\\!\to\\!\PKp\MM)$, the
result of Eq. (5) must be divided by the fraction of events in the low-$q^{2}$
bin. This fraction cannot be taken directly from data because of the
interference effects and resonant contributions. Two theoretical models are
used to obtain the differential branching fraction distribution in the full
$q^{2}$ range, based on the flavio and superiso packages. The resulting
$\mathcal{B}(\PBp\\!\to\\!\PKp\MM)$ integrated branching fractions are
$43.5\pm 1.9\stat\pm 0.4\,\text{(MC~{}stat)}\pm 1.4\syst=43.5\pm 2.4$ (flavio)
and $43.9\pm 1.9\stat\pm 0.4\,\text{(MC~{}stat)}\pm 1.4\syst=43.9\pm 2.4$
(superiso), where the theoretical model uncertainty is not included. Both
results are in good agreement with the world-average value of $(45.3\pm
3.5)\times 10^{-8}$ [4], as well as with the LHCb measurement of $(43.7\pm
2.7)\times 10^{-8}$ that explicitly subtracts various resonant contributions
[70]. For the calculation of the integrated branching fraction
$\mathcal{B}(\PBp\\!\to\\!\PKp\MM)$, only flavio and superiso are used because
eos and hepfit do not provide predictions for the entire $q^{2}$ range.

Comparison of the $\mathcal{B}(\PBp\\!\to\\!\PKp\MM)$ branching fraction
measurement in the low-$q^{2}$ range and the theoretical predictions based on
the eos, flavio, superiso, and hepfit packages.  Source
$\mathcal{B}(\PBp\\!\to\\!\PKp\MM)[1.1,6.0]\GeV^{2}$ [$10^{-8}$] Measurement
$12.42\pm 0.68$ eos $18.9\pm 1.3$ flavio $17.1\pm 2.7$ superiso $16.5\pm 3.4$
hepfit $19.8\pm 7.3$

###  0.8.3 Measurement of $R(\PK)$

For the $R(\PK)$ measurement, both the $\PBp\\!\to\\!\PKp\MM$ and
$\PBp\\!\to\\!\PKp\EE$ channels are used in the low-$q^{2}$ region, along with
the $\PBp\\!\to\\!\JPsi(\MM)\PKp$ and $\PBp\\!\to\\!\JPsi(\EE)\PKp$ CRs,
separately in the PF-PF and PF-LP electron channel categories and in their
combination,. The details are given in Appendix .10.2. The systematic
uncertainties are incorporated into the likelihood function assuming Gaussian
distributions. The correlation of a few minor uncertainties between the two
channels were found to have a negligible effect on the results. A profile
likelihood is used to obtain the confidence interval of the parameter of
interest, $R(\PK)^{-1}$.

The values of $R(\PK)^{-1}$ extracted in the PF-PF and PF-LP categories are
$1.40^{+0.63}_{-0.56}$ and $0.50^{+1.06}_{-0.88}$, respectively, where the
uncertainties are statistical only. These values are consistent with each
other and with unity. As expected from the corresponding signal yields, the
PF-PF result is much more precise. The maximum likelihood fit for the
combination of the PF-PF and PF-LP categories gives
$R(\PK)^{-1}=1.28^{+0.53}_{-0.47}$, where the uncertainties are statistical
only. The profile log likelihood of the combined fit, $\ln(L/L_{\text{min}})$,
as a function of $R(\PK)^{-1}$ is shown in Fig. 6. The measurement of $R(\PK)$
and its 68% confidence interval can be obtained from those for $R(\PK)^{-1}$,

$R(\PK)=0.78^{+0.46}_{-0.23}\stat^{+0.09}_{-0.05}\syst=0.78^{+0.47}_{-0.23},$
(6)

which is within one standard deviation from the SM prediction of approximately
unity.

Figure 6: Log likelihood function from the fit profiled as a function of
$R(\PK)^{-1}$. The dark and light grey area indicates the $\pm$ 1 and $\pm$ 2
$\sigma$ bands respectively.

##  0.9 Summary

We have reported the first test of lepton flavor universality with the CMS
experiment at the LHC in $\PBpm\\!\to\\!\PKpm\MM$ and $\PBpm\\!\to\\!\PKpm\EE$
decays, as well as a measurement of differential and integrated branching
fractions of the nonresonant $\PBpm\\!\to\\!\PKpm\MM$ decay. The analysis has
been made possible by a dedicated data set of proton-proton collisions at
$\sqrt{s}=13\TeV$ recorded in 2018, using a special high-rate data stream
designed for collecting about 10 billion unbiased hadron decays. The ratio of
the branching fractions $\mathcal{B}(\PBpm\\!\to\\!\PKpm\MM)$ to
$\mathcal{B}(\PBpm\\!\to\\!\PKpm\EE)$ has been is determined from the measured
double ratio $R(\PK)$ of these decays to the respective branching fractions of
the $\PBpm\\!\to\\!\JPsi\PKpm$ $(\JPsi\\!\to\\!\MM)$ and $(\JPsi\\!\to\\!\EE)$
decays, which allow for significant cancellation of systematic uncertainties.
The ratio $R(\PK)$ has been measured in the range $1.1<q^{2}<6.0\GeV^{2}$,
where $q$ is the invariant mass of the lepton pair, and was found to be
$R(\PK)=0.78^{+0.47}_{-0.23}$, in agreement with the standard model
expectation of $\approx$1\. This measurement is limited by the statistical
precision of the electron channel. The integrated branching fraction in the
same $q^{2}$ range, $\mathcal{B}(\PBpm\\!\to\\!\PKpm\MM)=(12.42\pm 0.68)\times
10^{-8}$, is consistent with and has a comparable precision to the present
world average. This work has demonstrated the flexibility of the CMS trigger
and data acquisition system and has paved the way to many other studies of a
large unbiased sample of hadron decays collected by CMS in 2018.

###### Acknowledgements.

We congratulate our colleagues in the CERN accelerator departments for the
excellent performance of the LHC and thank the technical and administrative
staffs at CERN and at other CMS institutes for their contributions to the
success of the CMS effort. In addition, we gratefully acknowledge the
computing centers and personnel of the Worldwide LHC Computing Grid and other
centers for delivering so effectively the computing infrastructure essential
to our analyses. Finally, we acknowledge the enduring support for the
construction and operation of the LHC, the CMS detector, and the supporting
computing infrastructure provided by the following funding agencies: SC
(Armenia), BMBWF and FWF (Austria); FNRS and FWO (Belgium); CNPq, CAPES,
FAPERJ, FAPERGS, and FAPESP (Brazil); MES and BNSF (Bulgaria); CERN; CAS,
MoST, and NSFC (China); MINCIENCIAS (Colombia); MSES and CSF (Croatia); RIF
(Cyprus); SENESCYT (Ecuador); MoER, ERC PUT and ERDF (Estonia); Academy of
Finland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); SRNSF (Georgia);
BMBF, DFG, and HGF (Germany); GSRI (Greece); NKFIH (Hungary); DAE and DST
(India); IPM (Iran); SFI (Ireland); INFN (Italy); MSIP and NRF (Republic of
Korea); MES (Latvia); LAS (Lithuania); MOE and UM (Malaysia); BUAP, CINVESTAV,
CONACYT, LNS, SEP, and UASLP-FAI (Mexico); MOS (Montenegro); MBIE (New
Zealand); PAEC (Pakistan); MES and NSC (Poland); FCT (Portugal); MESTD
(Serbia); MCIN/AEI and PCTI (Spain); MOSTR (Sri Lanka); Swiss Funding Agencies
(Switzerland); MST (Taipei); MHESI and NSTDA (Thailand); TUBITAK and TENMAK
(Turkey); NASU (Ukraine); STFC (United Kingdom); DOE and NSF (USA).
Individuals have received support from the Marie-Curie program and the
European Research Council and Horizon 2020 Grant, contract Nos. 675440,
724704, 752730, 758316, 765710, 824093, and COST Action CA16108 (European
Union); the Leventis Foundation; the Alfred P. Sloan Foundation; the Alexander
von Humboldt Foundation; the Science Committee, project no. 22rl-037
(Armenia); the Belgian Federal Science Policy Office; the Fonds pour la
Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA-
Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-
Belgium); the F.R.S.-FNRS and FWO (Belgium) under the “Excellence of Science –
EOS” – be.h project n. 30820817; the Beijing Municipal Science & Technology
Commission, No. Z191100007219010 and Fundamental Research Funds for the
Central Universities (China); the Ministry of Education, Youth and Sports
(MEYS) of the Czech Republic; the Shota Rustaveli National Science Foundation,
grant FR-22-985 (Georgia); the Deutsche Forschungsgemeinschaft (DFG), under
Germany’s Excellence Strategy – EXC 2121 “Quantum Universe” – 390833306, and
under project number 400140256 - GRK2497; the Hellenic Foundation for Research
and Innovation (HFRI), Project Number 2288 (Greece); the Hungarian Academy of
Sciences, the New National Excellence Program - ÚNKP, the NKFIH research
grants K 124845, K 124850, K 128713, K 128786, K 129058, K 131991, K 133046, K
138136, K 143460, K 143477, 2020-2.2.1-ED-2021-00181, and TKP2021-NKTA-64
(Hungary); the Council of Science and Industrial Research, India; ICSC –
National Research Center for High Performance Computing, Big Data and Quantum
Computing, funded by the EU NexGeneration program (Italy); the Latvian Council
of Science; the Ministry of Education and Science, project no. 2022/WK/14, and
the National Science Center, contracts Opus 2021/41/B/ST2/01369 and
2021/43/B/ST2/01552 (Poland); the Fundação para a Ciência e a Tecnologia,
grant CEECIND/01334/2018 (Portugal); the National Priorities Research Program
by Qatar National Research Fund; MCIN/AEI/10.13039/501100011033, ERDF “a way
of making Europe”, and the Programa Estatal de Fomento de la Investigación
Científica y Técnica de Excelencia María de Maeztu, grant MDM-2017-0765 and
Programa Severo Ochoa del Principado de Asturias (Spain); the Chulalongkorn
Academic into Its 2nd Century Project Advancement Project, and the National
Science, Research and Innovation Fund via the Program Management Unit for
Human Resources & Institutional Development, Research and Innovation, grant
B37G660013 (Thailand); the Kavli Foundation; the Nvidia Corporation; the
SuperMicro Corporation; the Welch Foundation, contract C-1845; and the Weston
Havens Foundation (USA)

## References

  * [1] S. L. Glashow, “Partial symmetries of weak interactions”,  Nucl. Phys. 22 (1961) 579, 10.1016/0029-5582(61)90469-2.
  * [2] S. Weinberg, “A model of leptons”,  Phys. Rev. Lett. 19 (1967) 1264, 10.1103/PhysRevLett.19.1264.
  * [3] A. Salam, “Weak and electromagnetic interactions”,  N. Svartholm (Ed.), Proc. 8-th Nobel Symp., Almquist and Wiksell, Stockholm (1968) 367.
  * [4] Particle Data Group, “Review of particle physics”,  PTEP 2022 (2022) 083C01, 10.1093/ptep/ptac097.
  * [5] ALEPH, DELPHI, L3, OPAL, LEP Electroweak Collaboration, “Electroweak measurements in electron-positron collisions at W-boson-pair energies at LEP”,  Phys. Rept. 532 (2013) 119, 10.1016/j.physrep.2013.07.004, arXiv:1302.3415.
  * [6] ATLAS Collaboration, “Test of the universality of $\tau$ and $\mu$ lepton couplings in $W$-boson decays with the ATLAS detector”,  Nature Phys. 17 (2021) 813, 10.1038/s41567-021-01236-w, arXiv:2007.14040.
  * [7] CMS Collaboration, “Precision measurement of the boson decay branching fractions in proton-proton collisions at $\sqrt{s}$ = 13 TeV”,  Phys. Rev. D 105 (2022) 072008, 10.1103/PhysRevD.105.072008, arXiv:2201.07861.
  * [8] D. London and J. Matias, “$B$ flavour anomalies: 2021 theoretical status report”,  Ann. Rev. Nucl. Part. Sci. 72 (2022) 37, 10.1146/annurev-nucl-102020-090209, arXiv:2110.13270.
  * [9] LHCb Collaboration, “Test of lepton universality in beauty-quark decays”,  Nature Phys. 18 (2022) 277, 10.1038/s41567-021-01478-8, arXiv:2103.11769.
  * [10] LHCb Collaboration, “Test of lepton universality using $B^{+}\to K^{+}\ell^{+}\ell^{-}$ decays”,  Phys. Rev. Lett. 113 (2014) 151601, 10.1103/PhysRevLett.113.151601, arXiv:1406.6482.
  * [11] LHCb Collaboration, “Search for lepton-universality violation in $B^{+}\to K^{+}\ell^{+}\ell^{-}$ decays”,  Phys. Rev. Lett. 122 (2019) 191801, 10.1103/PhysRevLett.122.191801, arXiv:1903.09252.
  * [12] LHCb Collaboration, “Test of lepton universality with $B^{0}\to K^{*0}\ell^{+}\ell^{-}$ decays”,  JHEP 08 (2017) 055, 10.1007/JHEP08(2017)055, arXiv:1705.05802.
  * [13] LHCb Collaboration, “Tests of lepton universality using $B^{0}\to K^{0}_{S}\ell^{+}\ell^{-}$ and $B^{+}\to K^{*+}\ell^{+}\ell^{-}$ decays”,  Phys. Rev. Lett. 128 (2022) 191802, 10.1103/PhysRevLett.128.191802, arXiv:2110.09501.
  * [14] LHCb Collaboration, “Measurement of the isospin asymmetry in $B\to K^{(*)}\mu^{+}\mu^{-}$ decays”,  JHEP 07 (2012) 133, 10.1007/JHEP07(2012)133, arXiv:1205.3422.
  * [15] LHCb Collaboration, “Differential branching fractions and isospin asymmetries of $B\to K^{(*)}\mu^{+}\mu^{-}$ decays”,  JHEP 06 (2014) 133, 10.1007/JHEP06(2014)133, arXiv:1403.8044.
  * [16] LHCb Collaboration, “Measurements of the S-wave fraction in $B^{0}\to K^{+}\pi^{-}\mu^{+}\mu^{-}$ decays and the $B^{0}\to K^{*}(892)^{0}\mu^{+}\mu^{-}$ differential branching fraction”,  JHEP 11 (2016) 047, 10.1007/JHEP11(2016)047, arXiv:1606.04731. [Erratum: 10.1007/JHEP04(2017)142].
  * [17] LHCb Collaboration, “Branching fraction measurements of the rare $B^{0}_{s}\to\phi\mu^{+}\mu^{-}$ and $B^{0}_{s}\to f_{2}^{\prime}(1525)\mu^{+}\mu^{-}$ decays”,  Phys. Rev. Lett. 127 (2021) 151801, 10.1103/PhysRevLett.127.151801, arXiv:2105.14007.
  * [18] M. Ciuchini et al., “Charming penguins and lepton universality violation in $b\to s\ell^{+}\ell^{-}$ decays”,  Eur. Phys. J. C 83 (2023) 64, 10.1140/epjc/s10052-023-11191-w, arXiv:2110.10126.
  * [19] LHCb Collaboration, “Test of lepton universality in $b\to s\ell^{+}\ell^{-}$ decays”,  Phys. Rev. Lett. 131 (2023) 051803, 10.1103/PhysRevLett.131.051803, arXiv:2212.09152.
  * [20] LHCb Collaboration, “Measurement of lepton universality parameters in $B^{+}\to K^{+}\ell^{+}\ell^{-}$ and $B^{0}\to K^{*0}\ell^{+}\ell^{-}$ decays”,  Phys. Rev. D 108 (2023) 032002, 10.1103/PhysRevD.108.032002, arXiv:2212.09153.
  * [21] S. Patnaik, L. Nayak, and R. Singh, “Assessing lepton flavor universality violations in semileptonic decays”, 2023. arXiv:2308.05677.
  * [22] HEPData record for this analysis, 2024.  10.17182/hepdata.146018.
  * [23] G. Hiller and F. Kruger, “More model-independent analysis of $b\to s$ processes”,  Phys. Rev. D 69 (2004) 074020, 10.1103/PhysRevD.69.074020, arXiv:hep-ph/0310219.
  * [24] M. Bordone, G. Isidori, and A. Pattori, “On the Standard Model predictions for $R_{K}$ and $R_{K^{*}}$”,  Eur. Phys. J. C 76 (2016) 440, 10.1140/epjc/s10052-016-4274-7, arXiv:1605.07633.
  * [25] G. Isidori, S. Nabeebaccus, and R. Zwicky, “QED corrections in $\overline{B}\to\overline{K}{\mathrm{\ell}}^{+}{\mathrm{\ell}}^{-}$ at the double-differential level”,  JHEP 12 (2020) 104, 10.1007/JHEP12(2020)104, arXiv:2009.00929.
  * [26] G. Isidori, D. Lancierini, S. Nabeebaccus, and R. Zwicky, “QED in $\overline{B}\to\overline{K}\ell^{+}\ell^{-}$ LFU ratios: theory versus experiment, a Monte Carlo study”,  JHEP 10 (2022) 146, 10.1007/JHEP10(2022)146, arXiv:2205.08635.
  * [27] A. Roodman, “Blind analysis in particle physics”, 2003. arXiv:physics/0312102.
  * [28] CMS Collaboration, “Strategies and performance of the CMS silicon tracker alignment during LHC Run 2”,  Nucl. Instrum. Meth. A 1037 (2022) 166795, 10.1016/j.nima.2022.166795, arXiv:2111.08757.
  * [29] CMS Tracker Group Collaboration, “The CMS Phase-1 pixel detector upgrade”,  JINST 16 (2021) P02027, 10.1088/1748-0221/16/02/P02027, arXiv:2012.14304.
  * [30] CMS Collaboration, “Track impact parameter resolution for the full pseudo rapidity coverage in the 2017 dataset with the CMS Phase-1 pixel detector”, CMS Detector Performance Summary CMS-DP-2020-049, 2020.
  * [31] CMS Collaboration, “Performance of the CMS muon detector and muon reconstruction with proton-proton collisions at $\sqrt{s}=13\TeV$”,  JINST 13 (2018) P06015, 10.1088/1748-0221/13/06/P06015, arXiv:1804.04528.
  * [32] CMS Collaboration, “Electron and photon reconstruction and identification with the CMS experiment at the CERN LHC”,  JINST 16 (2021) P05014, 10.1088/1748-0221/16/05/P05014, arXiv:2012.06888.
  * [33] CMS Collaboration, “Recording and reconstructing 10 billion unbiased hadron decays in CMS”, CMS Detector Performance Summary CMS-DP-2019-043, 2019.
  * [34] CMS Collaboration, “ECAL 2016 refined calibration and Run 2 summary plots”, CMS Detector Performance Summary CMS-DP-2020-021, 2020.
  * [35] CMS Collaboration, “Performance of the CMS Level-1 trigger in proton-proton collisions at $\sqrt{s}=13$ TeV”,  JINST 15 (2020) P10017, 10.1088/1748-0221/15/10/P10017, arXiv:2006.10165.
  * [36] CMS Collaboration, “The CMS trigger system”,  JINST 12 (2017) P01020, 10.1088/1748-0221/12/01/P01020, arXiv:1609.02366.
  * [37] CMS Collaboration, “The CMS experiment at the CERN LHC”,  JINST 3 (2008) S08004, 10.1088/1748-0221/3/08/S08004.
  * [38] CMS Collaboration, “Description and performance of track and primary-vertex reconstruction with the CMS tracker”,  JINST 9 (2014) P10009, 10.1088/1748-0221/9/10/P10009, arXiv:1405.6569.
  * [39] CMS Collaboration, “CMS luminosity measurements for the 2018 data-taking period at $\sqrt{s}=13\TeV$”, CMS Physics Analysis Summary CMS-PAS-LUM-18-001, 2018.
  * [40] T. Sjöstrand et al., “An introduction to PYTHIA 8.2”,  Comput. Phys. Commun. 191 (2015) 159, 10.1016/j.cpc.2015.01.024, arXiv:1410.3012.
  * [41] D. J. Lange, “The EvtGen particle decay simulation package”,  Nucl. Instrum. Meth. A 462 (2001) 152, 10.1016/S0168-9002(01)00089-4.
  * [42] CMS Collaboration, “Extraction and validation of a new set of CMS PYTHIA8 tunes from underlying-event measurements”,  Eur. Phys. J. C 80 (2020) 4, 10.1140/epjc/s10052-019-7499-4, arXiv:1903.12179.
  * [43] NNPDF Collaboration, “Parton distributions from high-precision collider data”,  Eur. Phys. J. C 77 (2017) 663, 10.1140/epjc/s10052-017-5199-5, arXiv:1706.00428.
  * [44] E. Barberio and Z. Wa̧s, “PHOTOS: a universal Monte Carlo for QED radiative corrections. Version 2.0”,  Comput. Phys. Commun. 79 (1994) 291, 10.1016/0010-4655(94)90074-4.
  * [45] P. Ball and R. Zwicky, “$B_{d,s}\to\rho,\omega,K^{*},\phi$ decay form-factors from light-cone sum rules revisited”,  Phys. Rev. D 71 (2005) 014029, 10.1103/PhysRevD.71.014029, arXiv:hep-ph/0412079.
  * [46] GEANT4 Collaboration, “—a simulation toolkit”,  Nucl. Instrum. Meth. A 506 (2003) 250, 10.1016/S0168-9002(03)01368-8.
  * [47] CMS Collaboration, “Particle-flow reconstruction and global event description with the CMS detector”,  JINST 12 (2017) P10003, 10.1088/1748-0221/12/10/P10003, arXiv:1706.04965.
  * [48] T. Chen and C. Guestrin, “XGBoost: a scalable tree boosting system”, 2016. arXiv:1603.02754.
  * [49] CMS Collaboration, “Measurements of inclusive and cross sections in $\Pp\Pp$ collisions at $\sqrt{s}=7$”,  JHEP 01 (2011) 080, 10.1007/JHEP01(2011)080, arXiv:1012.2466.
  * [50] CMS Collaboration, “CMS tracking performance results from early LHC operation”,  Eur. Phys. J. C 70 (2010) 1165, 10.1140/epjc/s10052-010-1491-3, arXiv:1007.1988.
  * [51] K. Prokofiev and T. Speer, “A kinematic fit and a decay chain reconstruction library”, in  Vol1 Proceedings of Computing in High Energy and Nuclear Physics 2004.  2005\.  CERN-2005-002. 10.5170/CERN-2005-002.411.
  * [52] M. Pivk and F. R. Le Diberder, “${}_{s}\mathcal{P}\text{lot}$: a statistical tool to unfold data distributions”,  Nucl. Instrum. Meth. A 555 (2005) 356, 10.1016/j.nima.2005.08.106, arXiv:physics/0402083.
  * [53] M. Cacciari, M. Greco, and P. Nason, “The $\pt$ spectrum in heavy-flavour hadroproduction”,  JHEP 05 (1998) 007, 10.1088/1126-6708/1998/05/007, arXiv:hep-ph/9803400.
  * [54] M. Cacciari, S. Frixione, and P. Nason, “The $\pt$ spectrum in heavy-flavour photoproduction”,  JHEP 03 (2001) 006, 10.1088/1126-6708/2001/03/006, arXiv:hep-ph/0102134.
  * [55] M. Cacciari et al., “Theoretical predictions for charm and bottom production at the LHC”,  JHEP 10 (2012) 137, 10.1007/JHEP10(2012)137, arXiv:1205.6344.
  * [56] M. Cacciari, M. L. Mangano, and P. Nason, “Gluon PDF constraints from the ratio of forward heavy-quark production at the LHC at $\sqrt{s}=7$ and 13”,  Eur. Phys. J. C 75 (2015) 610, 10.1140/epjc/s10052-015-3814-x, arXiv:1507.06197.
  * [57] M. J. Oreglia, “A study of the reactions $\psi^{\prime}\to\gamma\gamma\psi$”.  PhD thesis, Stanford University, 1980.  SLAC Report SLAC-R-236.
  * [58] J. E. Gaiser, “Charmonium spectroscopy from radiative decays of and $\psi^{\prime}$”.  PhD thesis, Stanford University, 1982.  SLAC Report SLAC-R-255.
  * [59] K. S. Cranmer, “Kernel estimation in high-energy physics”,  Comput. Phys. Commun. 136 (2001) 198, 10.1016/S0010-4655(00)00243-5, arXiv:hep-ex/0011057.
  * [60] CMS Collaboration, “Measurement of the inelastic proton-proton cross section at $\sqrt{s}=13$”,  JHEP 07 (2018) 161, 10.1007/JHEP07(2018)161, arXiv:1802.02613.
  * [61] J. de Blas et al., “HEPfit: a code for the combination of indirect and direct constraints on high energy physics models”,  Eur. Phys. J. C 80 (2020) 456, 10.1140/epjc/s10052-020-7904-z, arXiv:1910.14012.
  * [62] L. Alasfar et al., “$B$ anomalies under the lens of electroweak precision”,  JHEP 12 (2020) 016, 10.1007/JHEP12(2020)016, arXiv:2007.04400.
  * [63] M. Ciuchini et al., “Constraints on lepton universality violation from rare decays”,  Phys. Rev. D 107 (2023) 055036, 10.1103/PhysRevD.107.055036, arXiv:2212.10516.
  * [64] F. Mahmoudi, “SuperIso: a program for calculating the isospin asymmetry of $B\to K^{*}\gamma$ in the MSSM”,  Comput. Phys. Commun. 178 (2008) 745, 10.1016/j.cpc.2007.12.006, arXiv:0710.2067.
  * [65] F. Mahmoudi, “SuperIso v2.3: a program for calculating flavor physics observables in supersymmetry”,  Comput. Phys. Commun. 180 (2009) 1579, 10.1016/j.cpc.2009.02.017, arXiv:0808.3144.
  * [66] D. M. Straub, “flavio: a Python package for flavour and precision phenomenology in the Standard Model and beyond”, 2018. arXiv:1810.08132.
  * [67] EOS Collaboration, “EOS: a software for flavor physics phenomenology”,  Eur. Phys. J. C 82 (2022) 569, 10.1140/epjc/s10052-022-10177-4, arXiv:2111.15428.
  * [68] N. Gubernari, M. Reboud, D. van Dyk, and J. Virto, “Improved theory predictions and global analysis of exclusive $b\to s\mu^{+}\mu^{-}$ processes”,  JHEP 09 (2022) 133, 10.1007/JHEP09(2022)133, arXiv:2206.03797.
  * [69] N. Gubernari, M. Reboud, D. van Dyk, and J. Virto, “Dispersive analysis of $B\to K^{(*)}$ and $B_{s}\to\phi$ form factors”, 2023. arXiv:2305.06301.
  * [70] LHCb Collaboration, “Measurement of the phase difference between short- and long-distance amplitudes in the $B^{+}\to K^{+}\mu^{+}\mu^{-}$ decay”,  Eur. Phys. J. C 77 (2017) 161, 10.1140/epjc/s10052-017-4703-2, arXiv:1612.06764.
  * [71] BaBar Collaboration, “Measurement of branching fractions and rate asymmetries in the rare decays $B\to K^{(*)}\ell^{+}\ell^{-}$”,  Phys. Rev. D 86 (2012) 032012, 10.1103/PhysRevD.86.032012, arXiv:1204.3933.
  * [72] BELLE Collaboration, “Test of lepton flavor universality and search for lepton flavor violation in $B\to K\ell\ell$ decays”,  JHEP 03 (2021) 105, 10.1007/JHEP03(2021)105, arXiv:1908.01848.

##  .10 Appendix

###  .10.1 Additional figures

In this section, we include auxiliary figures that are omitted from the main
body of the paper.

10.1.Figure: The product of acceptance and efficiency ($\mathcal{A}\epsilon$)
of the $\PBp\\!\to\\!\PKp\MM$ channel, as a function of the muon pair $q^{2}$,
as measured in simulated signal events, after all the corrections applied.
Regions corresponding to resonances are displayed with red markers.
10.2.Figure: Relative uncertainties in the differential branching fraction
measurement of $\PBp\\!\to\\!\PKp\MM$ per $q^{2}$ bin. Different colors
correspond to data statistical, simulation statistical, and systematic
uncertainties.

10.3.Figure: The invariant mass distributions in various $q^{2}$ bins, with
the result of the simultaneous fit overlaid in blue and the individual fit
components as described in the legends for (from upper left to lower right):
$[0,0.98]$, $[1.1,2.0]$, $[2.0,3.0]$ $[3.0,4.0]$, $[4.0,5.0]$, $[5.0,6.0]$,
$[6.0,7.0]$, and $[7.0,8.0]$, $q^{2}$ bins. Notations are as in Fig. 3.

10.4.Figure: The invariant mass distributions in various $q^{2}$ bins, with
the result of the simultaneous fit overlaid in blue and the individual fit
components as described in the legends for (from upper left to lower right):
$[11.0,11.8]$, $[11.8,12.5]$, $[14.82,16.0]$, $[16.0,17.0]$, $[17.0,18.0]$,
$[18.0,19.24]$, and $[19.24,22.9]\GeV^{2}$ $q^{2}$ bins. Notations are as in
Fig. 3. 10.5.Figure: Correlation matrix for the differential branching
fraction extraction between different $q^{2}$ bins in the simultaneous fit.
10.6.Figure: Summary of $R(\PK)$ measurements from BaBar [71], Belle [72], and
LHCb [10, 11, 9] experiments, as well as the present CMS measurement. The pink
data points of the first three LHCb measurements were superseded by the latest
one, shown as the red point.

###  .10.2 ${\boldmath R(\PK)}$ measurement formalism

The experimentally accessible equivalent of Eq. (2) can be written as follows,
using the event yields $N$ from the fits to the candidate mass spectra and the
products of acceptances and efficiencies
$(\mathcal{A}\epsilon\epsilon_{\text{trig}}$ in the muon channel and
$\mathcal{A}\epsilon$ in the electron channel):

$R(\PK)=\left(\frac{N_{\PBp\\!\to\\!\PKp\MM}/N_{\PBp\\!\to\\!\JPsi(\MM)\PKp}}{N_{\PBp\\!\to\\!\PKp\EE}/N_{\PBp\\!\to\\!\JPsi(\EE)\PKp}}\right)\\\
\times\left(\frac{(\mathcal{A}\epsilon)_{\PBp\\!\to\\!\PKp\EE}/(\mathcal{A}\epsilon)_{\PBp\\!\to\\!\JPsi(\EE)\PKp}}{(\mathcal{A}\epsilon\epsilon_{\text{trig}})_{\PBp\\!\to\\!\PKp\MM}/(\mathcal{A}\epsilon\epsilon_{\text{trig}})_{\PBp\\!\to\\!\JPsi(\MM)\PKp}}\right).$
(7)

In order to obtain the best fit value of $R(\PK)$ and its confidence interval,
the measured quantities $N_{\PBp\\!\to\\!\PKp\MM}$ and
$N_{\PBp\\!\to\\!\PKp\EE}$ are expressed as

$N_{\PBp\\!\to\\!\PKp\MM}=R_{\mathcal{B}}\frac{N_{\PBp\\!\to\\!\JPsi(\MM)\PKp}}{\mathcal{B}(\JPsi\\!\to\\!\MM)}\frac{(\mathcal{A}\epsilon\epsilon_{\text{trig}})_{\PBp\\!\to\\!\PKp\MM}}{(\mathcal{A}\epsilon\epsilon_{\text{trig}})_{\PBp\\!\to\\!\JPsi(\MM)\PKp}}$
(8)

and

$N_{\PBp\\!\to\\!\PKp\EE}=R(\PK)^{-1}R_{\mathcal{B}}\frac{N_{\PBp\\!\to\\!\JPsi(\EE)\PKp}}{\mathcal{B}(\JPsi\\!\to\\!\EE)}\cdot\frac{(\mathcal{A}\epsilon)_{\PBp\\!\to\\!\PKp\EE}}{(\mathcal{A}\epsilon)_{\PBp\\!\to\\!\JPsi(\EE)\PKp}},$
(9)

where
$R_{\mathcal{B}}=\frac{\mathcal{B}\left(\PBp\\!\to\\!\PKp\MM\right)}{\mathcal{B}\left(\PBp\\!\to\\!\PKp\JPsi\right)}$.
We note that $R(\PK)^{-1}$ is used as the parameter of interest instead of
$R(\PK)$ because this choice makes the likelihood significantly more Gaussian.

A simultaneous fit is done using Eqs. (8, 9), with the likelihood function in
each lepton channel defined as

$\mathcal{L}^{\PGm}=\mathcal{L}_{\text{low-$q^{2}$}}^{\PGm}(N_{\PBp\\!\to\\!\PKp\MM})\mathcal{L}_{\JPsi}^{\PGm}(N_{\PBp\\!\to\\!\JPsi(\MM)\PKp})\\\
\times
G((\mathcal{A}\epsilon\epsilon_{\text{trig}})_{\PBp\\!\to\\!\PKp\MM})G((\mathcal{A}\epsilon\epsilon_{\text{trig}})_{\PBp\\!\to\\!\JPsi(\MM)\PKp})G(\mathcal{B}_{\JPsi}^{\PGm}),$
(10)
$\mathcal{L}^{\Pe}=\mathcal{L}_{\text{low-$q^{2}$}}^{\Pe}(N_{\PBp\\!\to\\!\PKp\EE})\mathcal{L}_{\JPsi}^{\Pe}(N_{\PBp\\!\to\\!\JPsi(\EE)\PKp})\\\
\times
G((\mathcal{A}\epsilon)_{\PBp\\!\to\\!\PKp\EE})G((\mathcal{A}\epsilon)_{\PBp\\!\to\\!\JPsi(\EE)\PKp})G(\mathcal{B}_{\JPsi}^{\Pe}),$
(11)

where $\mathcal{L}_{\text{low-$q^{2}$}}^{\ell}$ and
$\mathcal{L}_{\JPsi}^{\ell}$ ($\ell=\PGm$ or $\Pe$) are the mass fit
likelihood function used in the low-$q^{2}$ and regions, respectively, $G$ is
the Gaussian function with the mean at the nominal value of the argument and
the RMS given by the corresponding uncertainty, and
$\mathcal{B}_{\JPsi}^{\ell}$ is the branching fraction of the
$\JPsi\\!\to\\!\ell\ell$ decay. The value of $R(\PK)$ is measured by
maximizing the likelihood function
$\mathcal{L}=\mathcal{L}^{\PGm}\mathcal{L}^{\Pe}$, either for a single
dielectron category or for the two categories simultaneously, which is
achieved by taking $\mathcal{L}^{\Pe}=\mathcal{L}^{\text{PF-
PF}}\mathcal{L}^{\text{PF-LP}}$.

##  .11 The CMS Collaboration

Yerevan Physics Institute, Yerevan, Armenia A. Hayrapetyan, A.
Tumasyan10009-0000-0684-6742

Institut für Hochenergiephysik, Vienna, Austria W. Adam0000-0001-9099-4341,
J.W. Andrejkovic, T. Bergauer0000-0002-5786-0293, S.
Chatterjee0000-0003-2660-0349, K. Damanakis0000-0001-5389-2872, M.
Dragicevic0000-0003-1967-6783, P.S. Hussain0000-0002-4825-5278, M.
Jeitler20000-0002-5141-9560, N. Krammer0000-0002-0548-0985, A.
Li0000-0002-4547-116X, D. Liko0000-0002-3380-473X, I.
Mikulec0000-0003-0385-2746, J. Schieck20000-0002-1058-8093, R.
Schöfbeck0000-0002-2332-8784, D. Schwarz0000-0002-3821-7331, M.
Sonawane0000-0003-0510-7010, S. Templ0000-0003-3137-5692, W.
Waltenberger0000-0002-6215-7228, C.-E. Wulz20000-0001-9226-5812

Universiteit Antwerpen, Antwerpen, Belgium M.R. Darwish30000-0003-2894-2377,
T. Janssen0000-0002-3998-4081, P. Van Mechelen0000-0002-8731-9051

Vrije Universiteit Brussel, Brussel, Belgium E.S. Bols0000-0002-8564-8732, J.
D’Hondt0000-0002-9598-6241, S. Dansana0000-0002-7752-7471, A. De
Moor0000-0001-5964-1935, M. Delcourt0000-0001-8206-1787, H. El
Faham0000-0001-8894-2390, S. Lowette0000-0003-3984-9987, I.
Makarenko0000-0002-8553-4508, D. Müller0000-0002-1752-4527, A.R.
Sahasransu0000-0003-1505-1743, S. Tavernier0000-0002-6792-9522, M.
Tytgat40000-0002-3990-2074, G.P. Van Onsem0000-0002-1664-2337, S. Van
Putte0000-0003-1559-3606, D. Vannerom0000-0002-2747-5095

Université Libre de Bruxelles, Bruxelles, Belgium B.
Clerbaux0000-0001-8547-8211, A.K. Das, G. De Lentdecker0000-0001-5124-7693, L.
Favart0000-0003-1645-7454, P. Gianneios0009-0003-7233-0738, D.
Hohov0000-0002-4760-1597, J. Jaramillo0000-0003-3885-6608, A. Khalilzadeh, K.
Lee0000-0003-0808-4184, M. Mahdavikhorrami0000-0002-8265-3595, A.
Malara0000-0001-8645-9282, S. Paredes0000-0001-8487-9603, N. Postiau, L.
Thomas0000-0002-2756-3853, M. Vanden Bemden0009-0000-7725-7945, C. Vander
Velde0000-0003-3392-7294, P. Vanlaer0000-0002-7931-4496

Ghent University, Ghent, Belgium M. De Coen0000-0002-5854-7442, D.
Dobur0000-0003-0012-4866, Y. Hong0000-0003-4752-2458, J.
Knolle0000-0002-4781-5704, L. Lambrecht0000-0001-9108-1560, G. Mestdach, K.
Mota Amarilo0000-0003-1707-3348, C. Rendón, A. Samalan, K.
Skovpen0000-0002-1160-0621, N. Van Den Bossche0000-0003-2973-4991, J. van der
Linden0000-0002-7174-781X, L. Wezenbeek0000-0001-6952-891X

Université Catholique de Louvain, Louvain-la-Neuve, Belgium A.
Benecke0000-0003-0252-3609, A. Bethani0000-0002-8150-7043, G.
Bruno0000-0001-8857-8197, C. Caputo0000-0001-7522-4808, C.
Delaere0000-0001-8707-6021, I.S. Donertas0000-0001-7485-412X, A.
Giammanco0000-0001-9640-8294, K. Jaffel0000-0001-7419-4248, Sa.
Jain0000-0001-5078-3689, V. Lemaitre, J. Lidrych0000-0003-1439-0196, P.
Mastrapasqua0000-0002-2043-2367, K. Mondal0000-0001-5967-1245, T.T.
Tran0000-0003-3060-350X, S. Wertz0000-0002-8645-3670

Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil G.A.
Alves0000-0002-8369-1446, E. Coelho0000-0001-6114-9907, C.
Hensel0000-0001-8874-7624, T. Menezes De Oliveira, A.
Moraes0000-0002-5157-5686, P. Rebello Teles0000-0001-9029-8506, M. Soeiro

Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil W.L. Aldá
Júnior0000-0001-5855-9817, M. Alves Gallo Pereira0000-0003-4296-7028, M.
Barroso Ferreira Filho0000-0003-3904-0571, H. Brandao
Malbouisson0000-0002-1326-318X, W. Carvalho0000-0003-0738-6615, J.
Chinellato5, E.M. Da Costa0000-0002-5016-6434, G.G. Da
Silveira60000-0003-3514-7056, D. De Jesus Damiao0000-0002-3769-1680, S.
Fonseca De Souza0000-0001-7830-0837, R. Gomes De Souza, J.
Martins70000-0002-2120-2782, C. Mora Herrera0000-0003-3915-3170, L.
Mundim0000-0001-9964-7805, H. Nogima0000-0001-7705-1066, J.P.
Pinheiro0000-0002-3233-8247, A. Santoro0000-0002-0568-665X, A.
Sznajder0000-0001-6998-1108, M. Thiel0000-0001-7139-7963, A. Vilela
Pereira0000-0003-3177-4626

Universidade Estadual Paulista, Universidade Federal do ABC, São Paulo, Brazil
C.A. Bernardes60000-0001-5790-9563, L. Calligaris0000-0002-9951-9448, T.R.
Fernandez Perez Tomei0000-0002-1809-5226, E.M. Gregores0000-0003-0205-1672,
P.G. Mercadante0000-0001-8333-4302, S.F. Novaes0000-0003-0471-8549, B.
Orzari0000-0003-4232-4743, Sandra S. Padula0000-0003-3071-0559

Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of
Sciences, Sofia, Bulgaria A. Aleksandrov0000-0001-6934-2541, G.
Antchev0000-0003-3210-5037, R. Hadjiiska0000-0003-1824-1737, P.
Iaydjiev0000-0001-6330-0607, M. Misheva0000-0003-4854-5301, M.
Shopova0000-0001-6664-2493, G. Sultanov0000-0002-8030-3866

University of Sofia, Sofia, Bulgaria A. Dimitrov0000-0003-2899-701X, L.
Litov0000-0002-8511-6883, B. Pavlov0000-0003-3635-0646, P.
Petkov0000-0002-0420-9480, A. Petrov0009-0003-8899-1514, E.
Shumka0000-0002-0104-2574

Instituto De Alta Investigación, Universidad de Tarapacá, Casilla 7 D, Arica,
Chile S. Keshri0000-0003-3280-2350, S. Thakur0000-0002-1647-0360

Beihang University, Beijing, China T. Cheng0000-0003-2954-9315, T.
Javaid0009-0007-2757-4054, L. Yuan0000-0002-6719-5397

Department of Physics, Tsinghua University, Beijing, China Z.
Hu0000-0001-8209-4343, J. Liu, K. Yi8,90000-0002-2459-1824

Institute of High Energy Physics, Beijing, China G.M.
Chen100000-0002-2629-5420, H.S. Chen100000-0001-8672-8227, M.
Chen100000-0003-0489-9669, F. Iemmi0000-0001-5911-4051, C.H. Jiang, A.
Kapoor110000-0002-1844-1504, H. Liao0000-0002-0124-6999, Z.-A.
Liu120000-0002-2896-1386, R. Sharma130000-0003-1181-1426, J.N. Song12, J.
Tao0000-0003-2006-3490, C. Wang10, J. Wang0000-0002-3103-1083, Z. Wang10, H.
Zhang0000-0001-8843-5209

State Key Laboratory of Nuclear Physics and Technology, Peking University,
Beijing, China A. Agapitos0000-0002-8953-1232, Y. Ban0000-0002-1912-0374, A.
Levin0000-0001-9565-4186, C. Li0000-0002-6339-8154, Q. Li0000-0002-8290-0517,
Y. Mao, S.J. Qian0000-0002-0630-481X, X. Sun0000-0003-4409-4574, D.
Wang0000-0002-9013-1199, H. Yang, L. Zhang0000-0001-7947-9007, C.
Zhou0000-0001-5904-7258

Sun Yat-Sen University, Guangzhou, China Z. You0000-0001-8324-3291

University of Science and Technology of China, Hefei, China N.
Lu0000-0002-2631-6770

Nanjing Normal University, Nanjing, China G. Bauer14

Institute of Modern Physics and Key Laboratory of Nuclear Physics and Ion-beam
Application (MOE) - Fudan University, Shanghai, China X.
Gao150000-0001-7205-2318, D. Leggat, H. Okawa0000-0002-2548-6567

Zhejiang University, Hangzhou, Zhejiang, China Z. Lin0000-0003-1812-3474, C.
Lu0000-0002-7421-0313, M. Xiao0000-0001-9628-9336

Universidad de Los Andes, Bogota, Colombia C. Avila0000-0002-5610-2693, D.A.
Barbosa Trujillo, A. Cabrera0000-0002-0486-6296, C. Florez0000-0002-3222-0249,
J. Fraga0000-0002-5137-8543, J.A. Reyes Vega

Universidad de Antioquia, Medellin, Colombia J. Mejia
Guisao0000-0002-1153-816X, F. Ramirez0000-0002-7178-0484, M.
Rodriguez0000-0002-9480-213X, J.D. Ruiz Alvarez0000-0002-3306-0363

University of Split, Faculty of Electrical Engineering, Mechanical Engineering
and Naval Architecture, Split, Croatia D. Giljanovic0009-0005-6792-6881, N.
Godinovic0000-0002-4674-9450, D. Lelas0000-0002-8269-5760, A.
Sculac0000-0001-7938-7559

University of Split, Faculty of Science, Split, Croatia M.
Kovac0000-0002-2391-4599, T. Sculac0000-0002-9578-4105

Institute Rudjer Boskovic, Zagreb, Croatia P. Bargassa0000-0001-8612-3332, V.
Brigljevic0000-0001-5847-0062, B.K. Chitroda0000-0002-0220-8441, D.
Ferencek0000-0001-9116-1202, S. Mishra0000-0002-3510-4833, A.
Starodumov160000-0001-9570-9255, T. Susa0000-0001-7430-2552

University of Cyprus, Nicosia, Cyprus A. Attikis0000-0002-4443-3794, K.
Christoforou0000-0003-2205-1100, S. Konstantinou0000-0003-0408-7636, J.
Mousa0000-0002-2978-2718, C. Nicolaou, F. Ptochos0000-0002-3432-3452, P.A.
Razis0000-0002-4855-0162, H. Rykaczewski, H. Saka0000-0001-7616-2573, A.
Stepennov0000-0001-7747-6582

Charles University, Prague, Czech Republic M. Finger0000-0002-7828-9970, M.
Finger Jr.0000-0003-3155-2484, A. Kveton0000-0001-8197-1914

Escuela Politecnica Nacional, Quito, Ecuador E. Ayala0000-0002-0363-9198

Universidad San Francisco de Quito, Quito, Ecuador E. Carrera
Jarrin0000-0002-0857-8507

Academy of Scientific Research and Technology of the Arab Republic of Egypt,
Egyptian Network of High Energy Physics, Cairo, Egypt A.A.
Abdelalim17,180000-0002-2056-7894, E. Salama19,200000-0002-9282-9806

Center for High Energy Physics (CHEP-FU), Fayoum University, El-Fayoum, Egypt
A. Lotfy0000-0003-4681-0079, M.A. Mahmoud0000-0001-8692-5458

National Institute of Chemical Physics and Biophysics, Tallinn, Estonia K.
Ehataht0000-0002-2387-4777, M. Kadastik, T. Lange0000-0001-6242-7331, S.
Nandan0000-0002-9380-8919, C. Nielsen0000-0002-3532-8132, J.
Pata0000-0002-5191-5759, M. Raidal0000-0001-7040-9491, L.
Tani0000-0002-6552-7255, C. Veelken0000-0002-3364-916X

Department of Physics, University of Helsinki, Helsinki, Finland H.
Kirschenmann0000-0001-7369-2536, K. Osterberg0000-0003-4807-0414, M.
Voutilainen0000-0002-5200-6477

Helsinki Institute of Physics, Helsinki, Finland S.
Bharthuar0000-0001-5871-9622, E. Brücken0000-0001-6066-8756, F.
Garcia0000-0002-4023-7964, K.T.S. Kallonen0000-0001-9769-7163, R. Kinnunen, T.
Lampén0000-0002-8398-4249, K. Lassila-Perini0000-0002-5502-1795, S.
Lehti0000-0003-1370-5598, T. Lindén0009-0002-4847-8882, L.
Martikainen0000-0003-1609-3515, M. Myllymäki0000-0003-0510-3810, M.m.
Rantanen0000-0002-6764-0016, H. Siikonen0000-0003-2039-5874, E.
Tuominen0000-0002-7073-7767, J. Tuominiemi0000-0003-0386-8633

Lappeenranta-Lahti University of Technology, Lappeenranta, Finland P.
Luukka0000-0003-2340-4641, H. Petrow0000-0002-1133-5485

IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France M.
Besancon0000-0003-3278-3671, F. Couderc0000-0003-2040-4099, M.
Dejardin0009-0008-2784-615X, D. Denegri, J.L. Faure, F.
Ferri0000-0002-9860-101X, S. Ganjour0000-0003-3090-9744, P.
Gras0000-0002-3932-5967, G. Hamel de Monchenault0000-0002-3872-3592, V.
Lohezic0009-0008-7976-851X, J. Malcles0000-0002-5388-5565, J. Rander, A.
Rosowsky0000-0001-7803-6650, M.Ö. Sahin0000-0001-6402-4050, A. Savoy-
Navarro210000-0002-9481-5168, P. Simkina0000-0002-9813-372X, M.
Titov0000-0002-1119-6614, M. Tornago0000-0001-6768-1056

Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut
Polytechnique de Paris, Palaiseau, France C. Baldenegro
Barrera0000-0002-6033-8885, F. Beaudette0000-0002-1194-8556, A. Buchot
Perraguin0000-0002-8597-647X, P. Busson0000-0001-6027-4511, A.
Cappati0000-0003-4386-0564, C. Charlot0000-0002-4087-8155, M.
Chiusi0000-0002-1097-7304, F. Damas0000-0001-6793-4359, O.
Davignon0000-0001-8710-992X, A. De Wit0000-0002-5291-1661, B.A. Fontana Santos
Alves0000-0001-9752-0624, S. Ghosh0009-0006-5692-5688, A.
Gilbert0000-0001-7560-5790, R. Granier de Cassagnac0000-0002-1275-7292, A.
Hakimi0009-0008-2093-8131, B. Harikrishnan0000-0003-0174-4020, L.
Kalipoliti0000-0002-5705-5059, G. Liu0000-0001-7002-0937, J.
Motta0000-0003-0985-913X, M. Nguyen0000-0001-7305-7102, C.
Ochando0000-0002-3836-1173, L. Portales0000-0002-9860-9185, R.
Salerno0000-0003-3735-2707, J.B. Sauvan0000-0001-5187-3571, Y.
Sirois0000-0001-5381-4807, A. Tarabini0000-0001-7098-5317, E.
Vernazza0000-0003-4957-2782, A. Zabi0000-0002-7214-0673, A.
Zghiche0000-0002-1178-1450

Université de Strasbourg, CNRS, IPHC UMR 7178, Strasbourg, France J.-L.
Agram220000-0001-7476-0158, J. Andrea0000-0002-8298-7560, D.
Apparu0009-0004-1837-0496, D. Bloch0000-0002-4535-5273, J.-M.
Brom0000-0003-0249-3622, E.C. Chabert0000-0003-2797-7690, C.
Collard0000-0002-5230-8387, S. Falke0000-0002-0264-1632, U.
Goerlach0000-0001-8955-1666, C. Grimault, R. Haeberle0009-0007-5007-6723,
A.-C. Le Bihan0000-0002-8545-0187, M. Meena0000-0003-4536-3967, G.
Saha0000-0002-6125-1941, M.A. Sessini0000-0003-2097-7065, P. Van
Hove0000-0002-2431-3381

Institut de Physique des 2 Infinis de Lyon (IP2I ), Villeurbanne, France S.
Beauceron0000-0002-8036-9267, B. Blancon0000-0001-9022-1509, G.
Boudoul0009-0002-9897-8439, N. Chanon0000-0002-2939-5646, J.
Choi0000-0002-6024-0992, D. Contardo0000-0001-6768-7466, P.
Depasse0000-0001-7556-2743, C. Dozen230000-0002-4301-634X, H. El Mamouni, J.
Fay0000-0001-5790-1780, S. Gascon0000-0002-7204-1624, M.
Gouzevitch0000-0002-5524-880X, C. Greenberg, G. Grenier0000-0002-1976-5877, B.
Ille0000-0002-8679-3878, I.B. Laktineh, M. Lethuillier0000-0001-6185-2045, L.
Mirabito, S. Perries, A. Purohit0000-0003-0881-612X, M. Vander
Donckt0000-0002-9253-8611, P. Verdier0000-0003-3090-2948, J.
Xiao0000-0002-7860-3958

Georgian Technical University, Tbilisi, Georgia D.
Chokheli0000-0001-7535-4186, I. Lomidze0009-0002-3901-2765, Z.
Tsamalaidze160000-0001-5377-3558

RWTH Aachen University, I. Physikalisches Institut, Aachen, Germany V.
Botta0000-0003-1661-9513, L. Feld0000-0001-9813-8646, K.
Klein0000-0002-1546-7880, M. Lipinski0000-0002-6839-0063, D.
Meuser0000-0002-2722-7526, A. Pauls0000-0002-8117-5376, N.
Röwert0000-0002-4745-5470, M. Teroerde0000-0002-5892-1377

RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany S.
Diekmann0009-0004-8867-0881, A. Dodonova0000-0002-5115-8487, N.
Eich0000-0001-9494-4317, D. Eliseev0000-0001-5844-8156, F.
Engelke0000-0002-9288-8144, J. Erdmann, M. Erdmann0000-0002-1653-1303, P.
Fackeldey0000-0003-4932-7162, B. Fischer0000-0002-3900-3482, T.
Hebbeker0000-0002-9736-266X, K. Hoepfner0000-0002-2008-8148, F.
Ivone0000-0002-2388-5548, A. Jung0000-0002-2511-1490, M.y.
Lee0000-0002-4430-1695, L. Mastrolorenzo, F. Mausolf0000-0003-2479-8419, M.
Merschmeyer0000-0003-2081-7141, A. Meyer0000-0001-9598-6623, S.
Mukherjee0000-0001-6341-9982, D. Noll0000-0002-0176-2360, F. Nowotny, A.
Pozdnyakov0000-0003-3478-9081, Y. Rath, W. Redjeb0000-0001-9794-8292, F. Rehm,
H. Reithler0000-0003-4409-702X, U. Sarkar0000-0002-9892-4601, V.
Sarkisovi0000-0001-9430-5419, A. Schmidt0000-0003-2711-8984, A.
Sharma0000-0002-5295-1460, J.L. Spah0000-0002-5215-3258, A.
Stein0000-0003-0713-811X, F. Torres Da Silva De Araujo240000-0002-4785-3057,
L. Vigilante, S. Wiedenbeck0000-0002-4692-9304, S. Zaleski

RWTH Aachen University, III. Physikalisches Institut B, Aachen, Germany C.
Dziwok0000-0001-9806-0244, G. Flügge0000-0003-3681-9272, W. Haj
Ahmad250000-0003-1491-0446, T. Kress0000-0002-2702-8201, A.
Nowack0000-0002-3522-5926, O. Pooth0000-0001-6445-6160, A.
Stahl0000-0002-8369-7506, T. Ziemons0000-0003-1697-2130, A.
Zotz0000-0002-1320-1712

Deutsches Elektronen-Synchrotron, Hamburg, Germany H. Aarup
Petersen0009-0005-6482-7466, M. Aldaya Martin0000-0003-1533-0945, J.
Alimena0000-0001-6030-3191, S. Amoroso, Y. An0000-0003-1299-1879, S.
Baxter0009-0008-4191-6716, M. Bayatmakou0009-0002-9905-0667, H. Becerril
Gonzalez0000-0001-5387-712X, O. Behnke0000-0002-4238-0991, A.
Belvedere0000-0002-2802-8203, S. Bhattacharya0000-0002-3197-0048, F.
Blekman260000-0002-7366-7098, K. Borras270000-0003-1111-249X, A.
Campbell0000-0003-4439-5748, A. Cardini0000-0003-1803-0999, C. Cheng, F.
Colombina0009-0008-7130-100X, S. Consuegra Rodríguez0000-0002-1383-1837, G.
Correia Silva0000-0001-6232-3591, M. De Silva0000-0002-5804-6226, G. Eckerlin,
D. Eckstein0000-0002-7366-6562, L.I. Estevez Banos0000-0001-6195-3102, O.
Filatov0000-0001-9850-6170, E. Gallo260000-0001-7200-5175, A.
Geiser0000-0003-0355-102X, A. Giraldi0000-0003-4423-2631, G. Greau, V.
Guglielmi0000-0003-3240-7393, M. Guthoff0000-0002-3974-589X, A.
Hinzmann0000-0002-2633-4696, A. Jafari280000-0001-7327-1870, L.
Jeppe0000-0002-1029-0318, N.Z. Jomhari0000-0001-9127-7408, B.
Kaech0000-0002-1194-2306, M. Kasemann0000-0002-0429-2448, C.
Kleinwort0000-0002-9017-9504, R. Kogler0000-0002-5336-4399, M.
Komm0000-0002-7669-4294, D. Krücker0000-0003-1610-8844, W. Lange, D. Leyva
Pernia0009-0009-8755-3698, K. Lipka290000-0002-8427-3748, W.
Lohmann300000-0002-8705-0857, R. Mankel0000-0003-2375-1563, I.-A. Melzer-
Pellmann0000-0001-7707-919X, M. Mendizabal Morentin0000-0002-6506-5177, A.B.
Meyer0000-0001-8532-2356, G. Milella0000-0002-2047-951X, A.
Mussgiller0000-0002-8331-8166, L.P. Nair0000-0002-2351-9265, A.
Nürnberg0000-0002-7876-3134, Y. Otarid, J. Park0000-0002-4683-6669, D. Pérez
Adán0000-0003-3416-0726, E. Ranken0000-0001-7472-5029, A.
Raspereza0000-0003-2167-498X, B. Ribeiro Lopes0000-0003-0823-447X, J.
Rübenach, A. Saggio0000-0002-7385-3317, M. Scham31,270000-0001-9494-2151, S.
Schnake270000-0003-3409-6584, P. Schütze0000-0003-4802-6990, C.
Schwanenberger260000-0001-6699-6662, D. Selivanova0000-0002-7031-9434, K.
Sharko0000-0002-7614-5236, M. Shchedrolosiev0000-0003-3510-2093, R.E. Sosa
Ricardo0000-0002-2240-6699, D. Stafford, F. Vazzoler0000-0001-8111-9318, A.
Ventura Barroso0000-0003-3233-6636, R. Walsh0000-0002-3872-4114, Q.
Wang0000-0003-1014-8677, Y. Wen0000-0002-8724-9604, K. Wichmann, L.
Wiens270000-0002-4423-4461, C. Wissing0000-0002-5090-8004, Y.
Yang0009-0009-3430-0558, A. Zimermmane Castro Santos0000-0001-9302-3102

University of Hamburg, Hamburg, Germany A. Albrecht0000-0001-6004-6180, S.
Albrecht0000-0002-5960-6803, M. Antonello0000-0001-9094-482X, S.
Bein0000-0001-9387-7407, L. Benato0000-0001-5135-7489, S. Bollweg, M.
Bonanomi0000-0003-3629-6264, P. Connor0000-0003-2500-1061, M. Eich, K. El
Morabit0000-0001-5886-220X, Y. Fischer0000-0002-3184-1457, A. Fröhlich, C.
Garbers0000-0001-5094-2256, E. Garutti0000-0003-0634-5539, A.
Grohsjean0000-0003-0748-8494, M. Hajheidari, J. Haller0000-0001-9347-7657,
H.R. Jabusch0000-0003-2444-1014, G. Kasieczka0000-0003-3457-2755, P. Keicher,
R. Klanner0000-0002-7004-9227, W. Korcari0000-0001-8017-5502, T.
Kramer0000-0002-7004-0214, V. Kutzner0000-0003-1985-3807, F.
Labe0000-0002-1870-9443, J. Lange0000-0001-7513-6330, A.
Lobanov0000-0002-5376-0877, C. Matthies0000-0001-7379-4540, A.
Mehta0000-0002-0433-4484, L. Moureaux0000-0002-2310-9266, M. Mrowietz, A.
Nigamova0000-0002-8522-8500, Y. Nissan, A. Paasch0000-0002-2208-5178, K.J.
Pena Rodriguez0000-0002-2877-9744, T. Quadfasel0000-0003-2360-351X, B.
Raciti0009-0005-5995-6685, M. Rieger0000-0003-0797-2606, D.
Savoiu0000-0001-6794-7475, J. Schindler0009-0006-6551-0660, P.
Schleper0000-0001-5628-6827, M. Schröder0000-0001-8058-9828, J.
Schwandt0000-0002-0052-597X, M. Sommerhalder0000-0001-5746-7371, H.
Stadie0000-0002-0513-8119, G. Steinbrück0000-0002-8355-2761, A. Tews, M.
Wolf0000-0003-3002-2430

Karlsruher Institut fuer Technologie, Karlsruhe, Germany S.
Brommer0000-0001-8988-2035, M. Burkart, E. Butz0000-0002-2403-5801, T.
Chwalek0000-0002-8009-3723, A. Dierlamm0000-0001-7804-9902, A. Droll, N.
Faltermann0000-0001-6506-3107, M. Giffels0000-0003-0193-3032, A.
Gottmann0000-0001-6696-349X, F. Hartmann320000-0001-8989-8387, R.
Hofsaess0009-0008-4575-5729, M. Horzela0000-0002-3190-7962, U.
Husemann0000-0002-6198-8388, J. Kieseler0000-0003-1644-7678, M.
Klute0000-0002-0869-5631, R. Koppenhöfer0000-0002-6256-5715, J.M.
Lawhorn0000-0002-8597-9259, M. Link, A. Lintuluoto0000-0002-0726-1452, S.
Maier0000-0001-9828-9778, S. Mitra0000-0002-3060-2278, M.
Mormile0000-0003-0456-7250, Th. Müller0000-0003-4337-0098, M. Neukum, M.
Oh0000-0003-2618-9203, M. Presilla0000-0003-2808-7315, G.
Quast0000-0002-4021-4260, K. Rabbertz0000-0001-7040-9846, B.
Regnery0000-0003-1539-923X, N. Shadskiy0000-0001-9894-2095, I.
Shvetsov0000-0002-7069-9019, H.J. Simonis0000-0002-7467-2980, M.
Toms0000-0002-7703-3973, N. Trevisani0000-0002-5223-9342, R.
Ulrich0000-0002-2535-402X, R.F. Von Cube0000-0002-6237-5209, M.
Wassmer0000-0002-0408-2811, S. Wieland0000-0003-3887-5358, F. Wittig, R.
Wolf0000-0001-9456-383X, X. Zuo0000-0002-0029-493X

Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos, Aghia
Paraskevi, Greece G. Anagnostou, G. Daskalakis0000-0001-6070-7698, A.
Kyriakis, A. Papadopoulos32, A. Stakia0000-0001-6277-7171

National and Kapodistrian University of Athens, Athens, Greece P.
Kontaxakis0000-0002-4860-5979, G. Melachroinos, A. Panagiotou, I.
Papavergou0000-0002-7992-2686, I. Paraskevas0000-0002-2375-5401, N.
Saoulidou0000-0001-6958-4196, K. Theofilatos0000-0001-8448-883X, E.
Tziaferi0000-0003-4958-0408, K. Vellidis0000-0001-5680-8357, I.
Zisopoulos0000-0001-5212-4353

National Technical University of Athens, Athens, Greece G.
Bakas0000-0003-0287-1937, T. Chatzistavrou, G. Karapostoli0000-0002-4280-2541,
K. Kousouris0000-0002-6360-0869, I. Papakrivopoulos0000-0002-8440-0487, E.
Siamarkou, G. Tsipolitis, A. Zacharopoulou

University of Ioánnina, Ioánnina, Greece K. Adamidis, I. Bestintzanos, I.
Evangelou0000-0002-5903-5481, C. Foudas, C. Kamtsikis, P. Katsoulis, P.
Kokkas0009-0009-3752-6253, P.G. Kosmoglou Kioseoglou0000-0002-7440-4396, N.
Manthos0000-0003-3247-8909, I. Papadopoulos0000-0002-9937-3063, J.
Strologas0000-0002-2225-7160

HUN-REN Wigner Research Centre for Physics, Budapest, Hungary M.
Bartók330000-0002-4440-2701, C. Hajdu0000-0002-7193-800X, D.
Horvath34,350000-0003-0091-477X, K. Márton, F. Sikler0000-0001-9608-3901, V.
Veszpremi0000-0001-9783-0315

MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd
University, Budapest, Hungary M. Csanád0000-0002-3154-6925, K.
Farkas0000-0003-1740-6974, M.M.A. Gadallah360000-0002-8305-6661, Á.
Kadlecsik0000-0001-5559-0106, P. Major0000-0002-5476-0414, K.
Mandal0000-0002-3966-7182, G. Pásztor0000-0003-0707-9762, A.J.
Rádl370000-0001-8810-0388, G.I. Veres0000-0002-5440-4356

Faculty of Informatics, University of Debrecen, Debrecen, Hungary P. Raics, B.
Ujvari0000-0003-0498-4265, G. Zilizi0000-0002-0480-0000

Institute of Nuclear Research ATOMKI, Debrecen, Hungary G. Bencze, S. Czellar,
J. Molnar, Z. Szillasi

Karoly Robert Campus, MATE Institute of Technology, Gyongyos, Hungary T.
Csorgo370000-0002-9110-9663, F. Nemes370000-0002-1451-6484, T.
Novak0000-0001-6253-4356

Panjab University, Chandigarh, India J. Babbar0000-0002-4080-4156, S.
Bansal0000-0003-1992-0336, S.B. Beri, V. Bhatnagar0000-0002-8392-9610, G.
Chaudhary0000-0003-0168-3336, S. Chauhan0000-0001-6974-4129, N.
Dhingra380000-0002-7200-6204, A. Kaur0000-0002-1640-9180, A.
Kaur0000-0003-3609-4777, H. Kaur0000-0002-8659-7092, M.
Kaur0000-0002-3440-2767, S. Kumar0000-0001-9212-9108, K.
Sandeep0000-0002-3220-3668, T. Sheokand, J.B. Singh0000-0001-9029-2462, A.
Singla0000-0003-2550-139X

University of Delhi, Delhi, India A. Ahmed0000-0002-4500-8853, A.
Bhardwaj0000-0002-7544-3258, A. Chhetri0000-0001-7495-1923, B.C.
Choudhary0000-0001-5029-1887, A. Kumar0000-0003-3407-4094, A.
Kumar0000-0002-5180-6595, M. Naimuddin0000-0003-4542-386X, K.
Ranjan0000-0002-5540-3750, S. Saumya0000-0001-7842-9518

Saha Institute of Nuclear Physics, HBNI, Kolkata, India S.
Baradia0000-0001-9860-7262, S. Barman390000-0001-8891-1674, S.
Bhattacharya0000-0002-8110-4957, S. Dutta0000-0001-9650-8121, S. Dutta, S.
Sarkar

Indian Institute of Technology Madras, Madras, India M.M.
Ameen0000-0002-1909-9843, P.K. Behera0000-0002-1527-2266, S.C.
Behera0000-0002-0798-2727, S. Chatterjee0000-0003-0185-9872, P.
Jana0000-0001-5310-5170, P. Kalbhor0000-0002-5892-3743, J.R.
Komaragiri400000-0002-9344-6655, D. Kumar400000-0002-6636-5331, L.
Panwar400000-0003-2461-4907, P.R. Pujahari0000-0002-0994-7212, N.R.
Saha0000-0002-7954-7898, A. Sharma0000-0002-0688-923X, A.K.
Sikdar0000-0002-5437-5217, S. Verma0000-0003-1163-6955

Tata Institute of Fundamental Research-A, Mumbai, India S. Dugad, M.
Kumar0000-0003-0312-057X, G.B. Mohanty0000-0001-6850-7666, P. Suryadevara

Tata Institute of Fundamental Research-B, Mumbai, India A.
Bala0000-0003-2565-1718, S. Banerjee0000-0002-7953-4683, R.M. Chatterjee, R.K.
Dewanjee410000-0001-6645-6244, M. Guchait0009-0004-0928-7922, Sh.
Jain0000-0003-1770-5309, A. Jaiswal, S. Karmakar0000-0001-9715-5663, S.
Kumar0000-0002-2405-915X, G. Majumder0000-0002-3815-5222, K.
Mazumdar0000-0003-3136-1653, S. Parolia0000-0002-9566-2490, A.
Thachayath0000-0001-6545-0350

National Institute of Science Education and Research, An OCC of Homi Bhabha
National Institute, Bhubaneswar, Odisha, India S.
Bahinipati420000-0002-3744-5332, C. Kar0000-0002-6407-6974, D.
Maity430000-0002-1989-6703, P. Mal0000-0002-0870-8420, T.
Mishra0000-0002-2121-3932, V.K. Muraleedharan Nair
Bindhu430000-0003-4671-815X, K. Naskar430000-0003-0638-4378, A.
Nayak430000-0002-7716-4981, P. Sadangi, P. Saha0000-0002-7013-8094, S.K.
Swain0000-0001-6871-3937, S. Varghese430009-0000-1318-8266, D.
Vats430009-0007-8224-4664

Indian Institute of Science Education and Research (IISER), Pune, India S.
Acharya440009-0001-2997-7523, A. Alpana0000-0003-3294-2345, S.
Dube0000-0002-5145-3777, B. Gomber440000-0002-4446-0258, B.
Kansal0000-0002-6604-1011, A. Laha0000-0001-9440-7028, B.
Sahu440000-0002-8073-5140, S. Sharma0000-0001-6886-0726, K.Y. Vaish

Isfahan University of Technology, Isfahan, Iran H.
Bakhshiansohi450000-0001-5741-3357, E. Khazaie460000-0001-9810-7743, M.
Zeinali470000-0001-8367-6257

Institute for Research in Fundamental Sciences (IPM), Tehran, Iran S.
Chenarani480000-0002-1425-076X, S.M. Etesami0000-0001-6501-4137, M.
Khakzad0000-0002-2212-5715, M. Mohammadi Najafabadi0000-0001-6131-5987

University College Dublin, Dublin, Ireland M. Grunewald0000-0002-5754-0388

INFN Sezione di Baria, Università di Barib, Politecnico di Baric, Bari, Italy
M. Abbresciaa,b0000-0001-8727-7544, R. Alya,c,170000-0001-6808-1335, A.
Colaleoa,b0000-0002-0711-6319, D. Creanzaa,c0000-0001-6153-3044, B.
D’Anzia,b0000-0002-9361-3142, N. De Filippisa,c0000-0002-0625-6811, M. De
Palmaa,b0000-0001-8240-1913, A. Di Florioa,c0000-0003-3719-8041, W.
Elmetenaweea,b,170000-0001-7069-0252, L. Fiorea0000-0002-9470-1320, G.
Iasellia,c0000-0003-2546-5341, M. Loukaa,b, G. Maggia,c0000-0001-5391-7689, M.
Maggia0000-0002-8431-3922, I. Margjekaa,b0000-0002-3198-3025, V.
Mastrapasquaa,b0000-0002-9082-5924, S. Mya,b0000-0002-9938-2680, S.
Nuzzoa,b0000-0003-1089-6317, A. Pellecchiaa,b0000-0003-3279-6114, A.
Pompilia,b0000-0003-1291-4005, G. Pugliesea,c0000-0001-5460-2638, R.
Radognaa0000-0002-1094-5038, G. Ramirez-Sancheza,c0000-0001-7804-5514, D.
Ramosa0000-0002-7165-1017, A. Ranieria0000-0001-7912-4062, L.
Silvestrisa0000-0002-8985-4891, F.M. Simonea,b0000-0002-1924-983X, Ü.
Sözbilira0000-0001-6833-3758, A. Stamerraa0000-0003-1434-1968, R.
Vendittia0000-0001-6925-8649, P. Verwilligena0000-0002-9285-8631, A.
Zazaa,b0000-0002-0969-7284

INFN Sezione di Bolognaa, Università di Bolognab, Bologna, Italy G.
Abbiendia0000-0003-4499-7562, C. Battilanaa,b0000-0002-3753-3068, D.
Bonacorsia,b0000-0002-0835-9574, L. Borgonovia0000-0001-8679-4443, R.
Campaninia,b0000-0002-2744-0597, P. Capiluppia,b0000-0003-4485-1897, A.