EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2016-259 LHCb-PAPER-2016-035 October 29, 2016

Measurement of $C\\!P$ asymmetry in ${{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}}$
decays

The LHCb collaboration†††Authors are listed at the end of this paper.

A measurement of the time-integrated $C\\!P$ asymmetry in the Cabibbo-
suppressed decay ${{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}}$ is performed using
$pp$ collision data, corresponding to an integrated luminosity of
3$\mbox{\,fb}^{-1}$, collected with the LHCb detector at centre-of-mass
energies of 7 and 8$\mathrm{\,Te\kern-1.00006ptV}$. The flavour of the charm
meson at production is determined from the charge of the pion in
${{D}^{*+}}\rightarrow{{D}^{0}}{{\pi}^{+}}$ and ${{D}^{*-}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}{{\pi}^{-}}$ decays. The time-
integrated $C\\!P$ asymmetry $A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$ is obtained
assuming negligible $C\\!P$ violation in charm mixing and in Cabibbo-favoured
${{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}$,
${{D}^{+}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$ and
${{D}^{+}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}{{\pi}^{+}}$ decays used as
calibration channels. It is found to be

$\displaystyle A_{{C\\!P}}({{K}^{-}}{{K}^{+}})=(0.14\pm
0.15\mathrm{\,(stat)}\pm 0.10\mathrm{\,(syst)})\%.$

A combination of this result with previous LHCb measurements yields

$\displaystyle A_{{C\\!P}}({{K}^{-}}{{K}^{+}})=(0.04\pm
0.12\mathrm{\,(stat)}\pm 0.10\mathrm{\,(syst)})\%,$ $\displaystyle
A_{{C\\!P}}({{\pi}^{-}}{{\pi}^{+}})=(0.07\pm 0.14\mathrm{\,(stat)}\pm
0.11\mathrm{\,(syst)})\%.$

These are the most precise measurements from a single experiment. The result
for $A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$ is the most precise determination of a
time-integrated $C\\!P$ asymmetry in the charm sector to date, and neither
measurement shows evidence of $C\\!P$ asymmetry.

Published in Phys. Lett. B

© CERN on behalf of the LHCb collaboration, licence CC-BY-4.0.

##  1 Introduction

In the Standard Model (SM), the violation of the charge-parity ($C\\!P$)
symmetry is governed by an irreducible complex phase in the Cabibbo-Kobayashi-
Maskawa (CKM) matrix. Charmed hadrons provide the only way to probe $C\\!P$
violation with up-type quarks. Recent studies of $C\\!P$ violation in weak
decays of $D$ mesons have not shown evidence of $C\\!P$ symmetry breaking [1],
while its violation is well established in decays of mesons with down-type
quarks (strange and beauty) [2, 3, 4, 5, 6].

The $C\\!P$-even decays111Throughout this Letter, charge conjugation is
implicit unless otherwise stated. ${{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}}$ and
${{D}^{0}}\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ are singly Cabibbo-suppressed,
and for these decays ${D}^{0}$ and ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ mesons share the same final
state. The amount of $C\\!P$ violation in these decays is expected to be below
the percent level [7, 8, 9, 10, 11, 12, 13, 14], but large theoretical
uncertainties due to long-distance interactions prevent precise SM
predictions. In the presence of physics beyond the SM, the expected $C\\!P$
asymmetries could be enhanced [15], although an observation near the current
experimental limits would be consistent with the SM expectation. The $C\\!P$
asymmetries in these decays are sensitive to both direct and indirect $C\\!P$
violation [1, 16]. The direct $C\\!P$ violation is associated with the
breaking of $C\\!P$ symmetry in the decay amplitude. Under $SU(3)$ flavour
symmetry, the direct $C\\!P$ asymmetries in the decays
${{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}}$ and
${{D}^{0}}\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ are expected to have the same
magnitudes and opposite sign [17]. Indirect $C\\!P$ violation, occurring
through ${D}^{0}$–${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$
mixing and interference processes in the mixing and the decay, is expected to
be small and is measured to be below $10^{-3}$ [1].

The most recent measurements of the time-integrated individual $C\\!P$
asymmetries in ${{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}}$ and
${{D}^{0}}\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ decays have been performed by the
LHCb [18], CDF [19], BaBar [20] and Belle [21, *Ko:2012jh] collaborations.

The measurement in Ref. [18] uses ${D}^{0}$ mesons produced in semileptonic
$b$-hadron decays (${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}}\rightarrow{{D}^{0}}{\mu^{-}}{{\overline{\nu}}_{\mu}}X$),
where the charge of the muon is used to identify (tag) the flavour of the
${D}^{0}$ meson at production, while the other measurements use ${D}^{0}$
mesons produced in the decay of the ${{D}^{*}}(2010)^{+}$ meson, hereafter
referred to as ${D}^{*+}$. Charmed hadrons may be produced at the $pp$
collision point either directly, or in the instantaneous decays of excited
charm states. These two sources are referred to as prompt. Charmed hadrons
produced in the decays of $b$-hadrons are called secondary charmed hadrons.

This Letter presents a measurement of the time-integrated $C\\!P$ asymmetry in
the ${{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}}$ decay rates

$\displaystyle
A_{{C\\!P}}({{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}})\equiv\frac{\Gamma(D^{0}\rightarrow
K^{-}K^{+})-\Gamma({{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\rightarrow
K^{-}K^{+})}{\Gamma(D^{0}\rightarrow K^{-}K^{+})+\Gamma({{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\rightarrow K^{-}K^{+})},$ (1)

using a data sample of proton-proton ($pp$) collisions at centre-of-mass
energies of 7 and 8$\mathrm{\,Te\kern-1.00006ptV}$, collected by the LHCb
detector in 2011 and 2012, corresponding to approximately 3$\mbox{\,fb}^{-1}$
of integrated luminosity. To distinguish the two $C\\!P$-conjugate decays, the
flavour of the ${D}^{0}$ at production must be known. In this analysis, the
flavour of the ${D}^{0}$ is tagged by the charge of the soft pion,
$\pi^{+}_{s}$, in the strong decay
${{D}^{*}}^{+}\rightarrow{{D}^{0}}\pi^{+}_{s}$. A combination with the recent
measurement of the difference between the time-integrated $C\\!P$ asymmetries
of $D^{0}\rightarrow K^{-}K^{+}$ and $D^{0}\rightarrow\pi^{-}\pi^{+}$ decays,
$\Delta A_{{C\\!P}}\equiv
A_{{C\\!P}}({{K}^{-}}{{K}^{+}})-A_{{C\\!P}}({{\pi}^{-}}{{\pi}^{+}})$, in
prompt charm decays [16] allows the determination of
$A_{{C\\!P}}({{\pi}^{-}}{{\pi}^{+}})$ taking into account the correlation
between $\Delta A_{{C\\!P}}$ and $A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$. In
addition, a combination of the measurements using prompt charm decays and the
measurements using secondary charm decays from semileptonic $b$-hadron decays
[18] at LHCb yields the most precise measurement of these quantities by a
single experiment.

The method to determine $A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$ follows the strategy
described in Ref. [18]. In the analysis of $D^{*+}\rightarrow
D^{0}(\rightarrow K^{-}K^{+})\pi_{s}^{+}$ decays, two nuisance asymmetries
must be considered, the production asymmetry of the ${D}^{*+}$ meson
$A_{P}(D^{*+})$, and the detection asymmetry $A_{D}(\pi^{+}_{s})$ of the soft
pion caused by non charge-symmetric interaction probabilities with the
detector material and instrumental asymmetry. The measured raw asymmetry in
the number of observed signal decays, defined as

$\displaystyle A_{\rm
raw}\equiv\frac{N({{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}})-N({{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\rightarrow{{K}^{-}}{{K}^{+}})}{N({{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}})+N({{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\rightarrow{{K}^{-}}{{K}^{+}})},$
(2)

is related to the $C\\!P$ asymmetry via

$\displaystyle A_{{C\\!P}}(D^{0}\rightarrow K^{-}K^{+})=A_{\rm
raw}(D^{0}\rightarrow K^{-}K^{+})-A_{P}(D^{*+})-A_{D}(\pi^{+}_{s}),$ (3)

assuming that the asymmetries are small and that the reconstruction
efficiencies can be factorised. The decay $D^{*+}\rightarrow D^{0}(\rightarrow
K^{-}\pi^{+})\pi_{s}^{+}$ is used as a calibration channel to determine the
production and detection asymmetries. Since this decay is Cabibbo-favoured, a
negligible $C\\!P$ asymmetry is assumed. In contrast to the decay into two
kaons, the final state $K^{-}\pi^{+}$ is not $C\\!P$ symmetric. Therefore,
additional detection asymmetries arising from the final state particles are
present, giving

$\displaystyle A_{\rm raw}(D^{0}\rightarrow K^{-}\pi^{+})$
$\displaystyle=A_{P}(D^{*+})+A_{D}(\pi^{+}_{s})+A_{D}(K^{-}\pi^{+}).$ (4)

In order to evaluate the detection asymmetry of the final state
$K^{-}\pi^{+}$, enhanced by the different interaction cross-sections of
positively and negatively charged kaons in the detector material, the Cabibbo-
favoured decay $D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$ is employed. In analogy
to the ${{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}$ decay, the raw asymmetry in
this channel is given by

$\displaystyle A_{\rm raw}(D^{+}\rightarrow K^{-}\pi^{+}\pi^{+})$
$\displaystyle=A_{P}(D^{+})+A_{D}(K^{-}\pi^{+}_{l})+A_{D}(\pi^{+}_{h}).$ (5)

The pion with the lower transverse momentum, $\pi^{+}_{l}$, is chosen to
cancel the effect of the detection asymmetry of the pion of the decay
$D^{0}\rightarrow K^{-}\pi^{+}$. The remaining production asymmetry of the
$D^{+}$ meson $A_{P}(D^{+})$, and the detection asymmetry of the other pion
$\pi^{+}_{h}$ are eliminated by incorporating the Cabibbo-favoured decay
$D^{+}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}\pi^{+}$ in the measurement.
There, the measured raw asymmetry consists of the production asymmetry
$A_{P}(D^{+})$, the detection asymmetry of the neutral kaon $A_{D}({{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}})$, and the detection asymmetry
of the pion $A_{D}(\pi^{+})$

$\displaystyle A_{\rm raw}(D^{+}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}\pi^{+})$
$\displaystyle=A_{P}(D^{+})+A_{D}({{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}})+A_{D}(\pi^{+}).$ (6)

The specific choice that the pion with the higher (lower) transverse momentum
in the decay $D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$ is used to cancel the
effect of the detection asymmetry of the pion in $D^{+}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}\pi^{+}$ ($D^{0}\rightarrow
K^{-}\pi^{+}$) is based on the comparison of the kinematic spectra of the
respective pions. The detection asymmetry $A_{D}({{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}})$ includes $C\\!P$ violation,
mixing and different cross-sections for the interaction of neutral kaons with
the detector material. However, all of these effects are known, and
$A_{D}({{\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}})$ is calculated
to be small since only neutral kaons that decay within the first part of the
detector are selected [18]. The combination of Eqs. 3–6 yields an expression
for $A_{{C\\!P}}(D^{0}\rightarrow K^{-}K^{+})$ that only depends on measurable
raw asymmetries and the calculable ${{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}$ detection asymmetry,

$\displaystyle A_{{C\\!P}}(D^{0}\rightarrow K^{-}K^{+})$ $\displaystyle=$
$\displaystyle A_{\rm raw}(D^{0}\rightarrow K^{-}K^{+})-A_{\rm
raw}(D^{0}\rightarrow K^{-}\pi^{+})$ $\displaystyle+$ $\displaystyle A_{\rm
raw}(D^{+}\rightarrow K^{-}\pi^{+}\pi^{+})-A_{\rm raw}(D^{+}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}\pi^{+})$ $\displaystyle+$
$\displaystyle A_{D}({{\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}).$

##  2 Detector and event selection

The LHCb detector [23, 24] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region, a large-area silicon-strip detector located upstream of a
dipole magnet with a bending power of about $4{\mathrm{\,Tm}}$, and three
stations of silicon-strip detectors and straw drift tubes placed downstream of
the magnet. The tracking system provides a measurement of the momentum of
charged particles with a relative uncertainty that varies from 0.5% at low
momentum to 1.0% at 200${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The minimum
distance of a track to a primary vertex (PV), the impact parameter (IP), is
measured with a resolution of
$(15+29/\mbox{$p_{\mathrm{T}}$}){\,\upmu\mathrm{m}}$, where $p_{\mathrm{T}}$
is the component of the momentum transverse to the beam, in
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$.

Different types of charged hadrons are distinguished using information from
two ring-imaging Cherenkov detectors. Photons, electrons and hadrons are
identified by a calorimeter system consisting of scintillating-pad and
preshower detectors, an electromagnetic calorimeter and a hadronic
calorimeter. Muons are identified by a system composed of alternating layers
of iron and multiwire proportional chambers. The magnetic field inside the
detector breaks the symmetry between trajectories of positively and negatively
charged particles as the positive particles are deflected in one direction,
and the negative particles in the opposite direction. Due to the imperfect
symmetry of the detector, this can lead to detection asymmetries. Periodically
reversing the magnetic field polarity throughout data-taking almost cancels
the effect. The configuration with the magnetic field pointing upwards, MagUp
(downwards, MagDown), bends positively (negatively) charged particles in the
horizontal plane towards the centre of the LHC ring.

The singly Cabibbo-suppressed decay mode
${{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}}$ and the Cabibbo-favoured modes
${{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}$,
${{D}^{+}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$ and
${{D}^{+}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}{{\pi}^{+}}$ are selected, where
the ${D}^{0}$ candidates come from the
${{D}^{*+}}\rightarrow{{D}^{0}}{{\pi}^{+}}$ decay. The ${D}^{*+}$ and
${D}^{+}$ candidates must satisfy an online event selection performed by a
trigger, which consists of a hardware and software stage, and a subsequent
offline selection. The hardware stage of the trigger is based on information
from the calorimeter and muon systems, followed by a software stage, which
applies a full event reconstruction. In order to avoid asymmetries arising
from the hardware trigger, each of the four decay channels is required to
satisfy a trigger that is independent of the decay considered. Both the
software trigger and offline event selection use kinematic variables and decay
time to isolate the signal decays from the background. To ensure a
cancellation of possible trigger asymmetries in the software stage, for each
of the calibration channels a specification about which particle triggers the
event is made.

All secondary particles from ${D}^{0}$ and ${D}^{+}$ decays are required to be
significantly displaced from any primary $pp$ interaction vertex, and have
momentum and transverse momentum $p_{\mathrm{T}}$ larger than a minimum value.
The final state hadrons are combined into a ${D}^{0}$ (${D}^{+}$) candidate.
The ${D}^{*+}$ vertex is formed by ${{D}^{0}}$ and $\pi_{s}^{+}$ candidates,
and is constrained to coincide with the associated PV [25]. Similarly, a
vertex fit of the ${D}^{+}$ decay products is made, where the ${D}^{+}$
candidate is constrained to originate from the corresponding PV. In
${{D}^{+}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}{{\pi}^{+}}$ decays, the neutral
kaon is reconstructed via decays into two charged pions, which are dominated
by decays of the short-lived neutral kaon,
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$. The mass of the ${\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}$ meson is constrained to the
nominal mass of the ${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ state [26].
Decays of ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{-}}$ are reconstructed using only
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ mesons that decay early enough for
the secondary pions to be reconstructed in the vertex detector.

Further requirements are placed on: the track fit quality; the ${{D}^{*+}}$
and ${D}^{0}$ (${D}^{+}$) vertex fit quality; the ${D}^{0}$ (${D}^{+}$) meson
transverse momentum and its decay distance; the smallest value of
$\chi^{2}_{\text{IP}}$, of both the ${D}^{0}$ (${D}^{+}$) candidate and its
decay products with respect to all PVs in the event. The
$\chi^{2}_{\text{IP}}$ is defined as the difference between the vertex-fit
$\chi^{2}$ of the PV reconstructed with and without the considered particle.
For ${D}^{0}$ candidates, a selection criterion is placed on the angle between
the ${D}^{0}$ momentum in the laboratory frame and the momentum of the kaon or
the pion in the ${D}^{0}$ rest frame. For ${D}^{+}$ candidates, additional
requirements on the pseudorapidities, momenta and transverse momenta of the
particles are applied in order to match the kinematic distributions of the two
${D}^{+}$ decay modes.

Cross-feed backgrounds from $D$ meson decays with a kaon misidentified as a
pion, and vice versa, are reduced using particle identification requirements.
After these selection criteria, the dominant background in
${{D}^{*+}}\rightarrow{{D}^{0}}\pi_{s}^{+}$ decays consists of genuine
${D}^{0}$ candidates paired with unrelated pions originating from the primary
interaction vertex. The main background in the distributions of
${{D}^{+}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$ and
${{D}^{+}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}{{\pi}^{+}}$ decays is
combinatorial. For the ${D}^{0}$ channels, fiducial requirements are imposed
to exclude kinematic regions having a large asymmetry in the soft pion
reconstruction efficiency [16]. These regions occur because low momentum
particles of one charge at large or small angles in the horizontal plane may
be deflected either out of the detector acceptance or into the non-
instrumented beam pipe region, whereas particles with the other charge are
more likely to remain within the acceptance. About 70% of the selected
candidates are retained after these fiducial requirements.

The ${D}^{0}$ candidates satisfying the selection criteria are accepted for
further analysis if the mass difference $\delta m\equiv
m(h^{+}h^{-}\pi^{+}_{s})-m(h^{+}h^{-})$ for $h=K,\pi$ is in the range
139.77–151.57${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. To reduce the
combinatorial background, the mass of the reconstructed ${D}^{0}$ candidate is
required to lie in the range
1850–1884${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and
1847–1887${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ for
${{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}}$ and
${{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}$ decays, respectively. This window
corresponds to about two standard deviations of the mass resolution, as
estimated from a fit to the mass distribution of the charm meson candidates.
The ${D}^{+}$ candidates are selected by requiring the reconstructed mass to
lie in a 1820–1920${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ mass window.

The data sample includes events with multiple ${D}^{*+}$ candidates. The
majority of these events contains the same reconstructed ${D}^{0}$ meson
combined with different soft pion candidates. The fraction of events with
multiple candidates in the considered range of $\delta m$ is about 6.5% for
${{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}}$ events and about 4.9% for
${{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}$ events. These fractions are
approximately the same for each magnet polarity. One of the multiple
candidates is randomly selected and retained, the others are discarded.

The full data sets recorded in 2011 and 2012 at 7 and
8$\mathrm{\,Te\kern-1.00006ptV}$, respectively, are used for this analysis.
They correspond to an integrated luminosity of about 1$\mbox{\,fb}^{-1}$ and
2$\mbox{\,fb}^{-1}$, respectively. In 2011, approximately 60% of the data was
recorded with magnet polarity MagDown, whereas in 2012 approximately the same
amount of data was taken with each magnet polarity. The data are split into
four subsamples according to the magnet polarity and the data-taking year.

##  3 Measurement of the asymmetries

The raw asymmetries and the signal yields are determined from binned
likelihood fits to the $\delta m$ distributions in the ${D}^{0}$ decay modes,
and to the invariant mass distributions $m({{D}^{+}})$ in the ${D}^{+}$
channels. The fits are simultaneous for both flavours and the background
yields are allowed to differ between them. The fits to the four decay channels
are made independently in the four subsamples.

The signal shape of the $\delta m$ distribution is described by the sum of
three Gaussian functions, two of which have a common mean. The means and
widths of the Gaussian distributions are allowed to differ between ${D}^{0}$
and ${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ because of a
possible charge-dependent bias in the measurement of the momentum, while all
the other parameters are shared. The background is described by an empirical
function consisting of the product of an exponential function and a power-law
function modelling the phase-space threshold [27]

$\mathcal{P}_{\rm bkg}(\delta m|A,B,\delta m_{0})\propto\left(\delta m-\delta
m_{0}\right)^{A}e^{-B(\delta m-\delta m_{0})},$ (8)

where the threshold $\delta m_{0}$ is fixed to the known ${\pi}^{+}$ mass
[26]. The parameters $A$ and $B$ describe the shape and are common to
${D}^{0}$ and ${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ decays.

The signal shape of the ${D}^{+}$ decays is described by the sum of two
Gaussian distributions and a bifurcated Gaussian distribution. The bifurcated
Gaussian distribution describes the asymmetric tails of the invariant mass
distribution arising from radiative processes in the decay. The background is
modelled by a single exponential function, with the same slope for the
${D}^{+}$ and ${D}^{-}$ states.

The production and detection asymmetries depend on the kinematics of the
particles involved. If the kinematic distributions are very different, this
may lead to an imperfect cancellation of the nuisance asymmetries in
$A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$. To remove any residual effect, the
kinematic distributions of the four decay channels are equalised by means of a
weighting procedure [19]. Fiducial regions where this weighting procedure is
not possible due to a lack of events in one of the channels are already
excluded by the requirements on kinematic variables of the D+ decays. Fits to
the ${\delta m}$ and $m({{D}^{+}})$ distributions of the unweighted data
samples are used to obtain the kinematic distribution of the signal component
by disentangling the signal and background components with the sPlot technique
[28]. Then, the normalised signal distributions of the four channels are
compared. To obtain the greatest possible statistical sensitivity, especially
for the channel with the lowest yield $D^{+}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}\pi^{+}$, the following order of
the weighting steps is chosen: first, the
${{D}^{+}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$ kinematic distributions
are weighted to reproduce the ${{D}^{+}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}{{\pi}^{+}}$ kinematics; second,
${{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}$ distributions are weighted to
reproduce the ${{D}^{+}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$
kinematics, and, last, the ${{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}}$
distributions are weighted to reproduce the
${{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}$ kinematics. At each step, the
weights already calculated in the previous steps are applied. Some of the
steps are repeated until a satisfactory agreement of the distributions is
achieved. The underlying ${D}^{*+}$ kinematic distributions are independent of
the ${D}^{0}$ decay mode, but the selection requirements can introduce
differences for the $K^{-}K^{+}$ and $K^{-}\pi^{+}$ final states, which are
observed in the kinematical distributions of the ${D}^{*+}$ candidates. The
variables used for the weighting procedure are: $p_{\mathrm{T}}$, $\eta$ and
azimuthal angle $\varphi$ of the ${D}^{*+}$ candidates; $p_{\mathrm{T}}$ and
$\eta$ of the ${D}^{+}$ mesons; $p_{\mathrm{T}}$, $\eta$ and $\varphi$ of the
pion in the ${{D}^{+}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}{{\pi}^{+}}$ channel and of the
higher-transverse-momentum pion in
${{D}^{+}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$ decays;
$\mbox{$p_{\mathrm{T}}$},\eta$ and $\varphi$ of the kaon and the pion in the
${{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}$ and
${{D}^{+}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$ modes. For the weighting
of the ${{D}^{+}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$ decay to agree
with the ${{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}$ decay, the pion with the
lower transverse momentum in the
${{D}^{+}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$ channel is used. For all
weighting steps, by default, each variable is divided in $20$ uniform bins. If
necessary, the transverse momenta are transformed to the interval [$0$,$1$] to
account for long tails in the distributions. The procedure leads to a few
events in scarcely populated bins having very large weights. In order to
mitigate such an effect, an upper bound to the weights is applied.

After applying the weights, the effective sample size is given by $N_{\rm
eff}=(\sum_{i=1}^{N}w_{i})^{2}/(\sum_{i=1}^{N}w_{i}^{2})$, where $w_{i}$ is
the weight of candidate $i$ and $N$ is the total number of candidates. The
numbers of signal decays determined from fits to the samples before and after
weighting are given in Table 1.

Table 1: Signal yields of the four channels before and after the kinematic weighting. In the case of the weighted samples, effective yields are given. Channel | Before weighting | After weighting
---|---|---
${{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}}$ | $5.56\,\text{M}$ | $~{}~{}1.63\,\text{M}$
${{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}$ | $32.4\,\text{M}$ | $~{}~{}2.61\,\text{M}$
${{D}^{+}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$ | $37.5\,\text{M}$ | $13.67\,\text{M}$
${{D}^{+}}\rightarrow{{\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}{{\pi}^{+}}$ | $1.06\,\text{M}$ | $~{}~{}1.06\,\text{M}$

The detection asymmetry $A_{D}({{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}})$ of the neutral kaon is
identified as one of the sources of the residual asymmetry. The method of
calculation is described in full detail in Ref. [18] and is applied here in
the same way. Based on the reconstructed trajectories and a model of the
detector material, the expected asymmetries are determined for all neutral
kaon candidates individually and then averaged. The calculated values are
$(-0.052\pm 0.013)\%$ for 2011, and $(-0.054\pm 0.014)\%$ for 2012 data. The
individual values for the different categories do not differ between samples
taken with different magnet polarities.

Figure 1: Fits to the ${\delta m}$ and to the $m({{D}^{+}})$ distributions
corresponding to the whole data sample and both flavours. Data samples after
the kinematic weighting described in the text are used.

The raw asymmetries of the weighted samples, determined by the fits to the
${\delta m}$ and $m({{D}^{+}})$ distributions shown in Fig. 1, are presented
in Table 2. The raw asymmetries are combined with the calculated detection
asymmetry of the neutral kaon. Testing the four independent measurements of
$A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$ for mutual consistency gives
$\chi^{2}/\rm{ndf}=0.80$, corresponding to a $p$-value of 0.50. The
asymmetries obtained with the two magnet polarities within each year are
arithmetically averaged in order to ensure the cancellation of detection
asymmetries which reverse sign with magnet polarity. The final result is then
calculated as the weighted mean of the two data-taking periods. The weighted
average of the values corresponding to all subsamples is calculated as
$A_{{C\\!P}}({{K}^{-}}{{K}^{+}})=(0.14\pm 0.15)\%$, where the uncertainty is
statistical. The weighting procedure shifts the observed value of
$A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$ by $0.04\%$.

Table 2: Measured asymmetries in $\%$ with their statistical uncertainties.

$2011$ |  MagUp |  MagDown |  Mean
---|---|---|---
$A_{\rm raw}(D^{0}\rightarrow K^{+}K^{-})$ |  $-1.85\pm 0.24$ |  $\hphantom{-}0.05\pm 0.20$ |  $-0.90\pm 0.16$
$A_{\rm raw}(D^{0}\rightarrow K^{-}\pi^{+})$ |  $-2.87\pm 0.18$ |  $-1.43\pm 0.15$ |  $-2.15\pm 0.12$
$A_{\rm raw}(D^{+}\rightarrow K^{-}\pi^{+}\pi^{+})$ |  $-1.946\pm 0.095$ |  $-2.044\pm 0.079$ |  $-1.995\pm 0.062$
$A_{\rm raw}({{D}^{+}}\rightarrow{{\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}{{\pi}^{+}})$ |  $-0.95\pm 0.30$ |  $-0.93\pm 0.25$ |  $-0.94\pm 0.20$
$A_{D}({{\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}})$ |  $-0.052$ |  $-0.052$ |  $-0.052$
$A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$ |  $-0.03\pm 0.43$ |  $\hphantom{-}0.32\pm 0.37$ |  $\hphantom{-}0.14\pm 0.28$

$2012\hphantom{+2012}$ |  MagUp |  MagDown |  Mean
---|---|---|---
$A_{\rm raw}({{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}})$ |  $-1.92\pm 0.15$ |  $-0.03\pm 0.15$ |  $-0.98\pm 0.10$
$A_{\rm raw}({{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}})$ |  $-2.23\pm 0.11$ |  $-1.65\pm 0.11$ |  $-1.939\pm 0.079$
$A_{\rm raw}({{D}^{+}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}})$ |  $-1.291\pm 0.045$ |  $-1.993\pm 0.044$ |  $-1.642\pm 0.031$
$A_{\rm raw}({{D}^{+}}\rightarrow{{\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}{{\pi}^{+}})$ |  $-0.92\pm 0.17$ |  $-0.83\pm 0.17$ |  $-0.88\pm 0.12$
$A_{D}({{\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}})$ |  $-0.054$ |  $-0.054$ |  $-0.054$
$A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$ |  $-0.11\pm 0.26$ |  $\hphantom{-}0.40\pm 0.26$ |  $\hphantom{-}0.14\pm 0.18$

$2011+2012$ |  MagUp |  MagDown |  Mean
---|---|---|---
$A_{\rm raw}({{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}})$ |  $-1.90\pm 0.12$ |  $-0.01\pm 0.12$ |  $-0.95\pm 0.10$
$A_{\rm raw}({{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}})$ |  $-2.411\pm 0.095$ |  $-1.574\pm 0.090$ |  $-2.005\pm 0.079$
$A_{\rm raw}({{D}^{+}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}})$ |  $-1.411\pm 0.041$ |  $-2.005\pm 0.038$ |  $-1.714\pm 0.031$
$A_{\rm raw}({{D}^{+}}\rightarrow{{\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}{{\pi}^{+}})$ |  $-0.93\pm 0.15$ |  $-0.86\pm 0.14$ |  $-0.89\pm 0.12$
$A_{D}({{\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}})$ |  $-0.053$ |  $-0.053$ |  $-0.053$
$A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$ |  $-0.09\pm 0.22$ |  $\hphantom{-}0.37\pm 0.21$ |  $\hphantom{-}0.14\pm 0.15$

##  4 Systematic uncertainties

Possible systematic shifts of the measured $C\\!P$ asymmetry can be caused by
biases in the determination of individual raw asymmetries and non-cancellation
of detection and production asymmetries. The determination of raw asymmetries
is studied using several suitable alternative signal and background models in
the fit of the mass distributions. Pseudoexperiments are generated based on
the alternative fit results. The baseline model is fitted to the
pseudoexperiment distributions. This is independently done for the four data
categories and all channels. The maximum observed deviations between the
alternative results and the results of the fits to the generated
pseudoexperiment distributions are combined, and a value of $0.025\%$ is
assigned as systematic uncertainty. This strategy allows systematic shifts and
statistical fluctuations to be disentangled.

Partially reconstructed and misidentified three-body charm decays might
produce a peaking background in the $\delta m$ distribution of the Cabibbo-
suppressed decay ${D}^{0}$ $\rightarrow$ ${K}^{-}$ ${K}^{+}$. This background
could therefore contribute to the signal yields obtained with the fit. If
these incorrectly reconstructed decays were to have an asymmetry different
from that of signal decays, the determined signal asymmetry would be shifted.
Simulated events are used to estimate the relative fraction of peaking
background, which is then combined with production and detection asymmetries
measured at LHCb [18, 29] in order to obtain a conservative estimate of the
asymmetry of this background. A value of $0.015\%$ is assigned as systematic
uncertainty.

In order to test the influence of kinematic regions with high asymmetries of
the final state particles in the channels ${D}^{0}$ $\rightarrow$ ${K}^{-}$
${\pi}^{+}$, ${D}^{+}$ $\rightarrow$ ${K}^{-}$ ${\pi}^{+}$ ${\pi}^{+}$ and
${D}^{+}$ $\rightarrow$ ${\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}$
${\pi}^{+}$, such regions are excluded in analogy to the treatment of the soft
pion. The difference in the values for $A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$,
$0.040\%$, is taken as systematic uncertainty.

Possible incomplete cancellation of detection and production asymmetries is
accounted for in several different ways. The weighting procedure is designed
to equalise kinematic distributions, but a perfect agreement cannot be reached
because of binning effects, the sequential rather than simultaneous weighting
and the reduction of large weights. This effect is estimated by repeating the
weighting with alternative configurations, which includes changing the number
of bins, an alternative way of dealing with high weights and weighting in a
reduced set of kinematic variables. For each configuration, the $C\\!P$
asymmetry is determined and the maximum deviation from the baseline result,
$0.062\%$, is propagated as a systematic uncertainty. Additionally, the
kinematic dependence of the raw asymmetries observed in data are modelled with
kinematically dependent detection and production asymmetries assigned to each
particle in the decay. These modelled detection and production asymmetries are
then combined with the weighted kinematic distributions in data to calculate
the raw asymmetries present in the individual channels. The modelled raw
asymmetries are combined to give the final $C\\!P$ asymmetry according to Eq.
1. Since no $C\\!P$ asymmetry in ${{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}}$ is
included in this calculation, an ideal kinematic weighting, corresponding to a
perfect cancellation of all detection and production asymmetries, would result
in this $C\\!P$ asymmetry being zero. The obtained deviation is 0.054% and is
treated as an independent systematic uncertainty.

Charmed mesons produced in the decay of beauty hadrons are suppressed by the
requirement of a small $\chi^{2}_{\text{IP}}$ of the charm meson candidates
with respect to the PV. Nevertheless, a certain fraction of these decay chains
passes the selection. This leads to an effective production asymmetry that
depends on the production asymmetry of the charm mesons, the production
asymmetry of the beauty hadrons and the fraction of secondary charm decays.
The latter is determined for the ${D}^{0}$ decays by a fit to the
$\chi^{2}_{\text{IP}}$ distributions when the selection requirement on this
quantity is removed. This yields an estimated secondary fraction of $4.0\%$
for the channel ${D}^{0}$ $\rightarrow$ ${K}^{-}$ ${K}^{+}$ and $4.9\%$ for
the channel ${D}^{0}$ $\rightarrow$ ${K}^{-}$ ${\pi}^{+}$. For the ${D}^{+}$
decay channels, a conservative estimate of the difference in the fraction of
secondary charm $f_{\rm sec}$ based on these numbers and on a comparison with
simulated events, is made: $f_{\rm
sec}({{D}^{+}}\rightarrow{{K}^{-}}{{K}^{+}}{{\pi}^{+}})-f_{\rm
sec}({{D}^{+}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}{{\pi}^{+}})=4.5\%$. A
combination of these numbers with the production asymmetries measured at LHCb
[29, 30, 31, 32] yields a value of $0.039\%$, which is assigned as a
systematic uncertainty.

The systematic uncertainty on the neutral kaon detection asymmetry is
$0.014\%$. Further sources of systematic uncertainty are investigated by
performing consistency checks. The analysis is repeated using more restrictive
particle identification requirements and the result is found to be compatible
with the baseline result. Additionally, the measurement of the $C\\!P$
asymmetry is repeated splitting the data-taking period into smaller intervals,
and in bins of the momentum of the kaon in the decays ${D}^{0}$ $\rightarrow$
${K}^{-}$ ${\pi}^{+}$ and ${D}^{+}$ $\rightarrow$ ${K}^{-}$ ${\pi}^{+}$
${\pi}^{+}$. No evidence of any dependence is found. All quoted systematic
uncertainties are summarised in Table 3 and added in quadrature to obtain the
overall systematic uncertainty.

Table 3: Systematic uncertainties from the different categories. The quadratic sum is used to compute the total systematic uncertainty.  Category |  Systematic uncertainty[$\%$]
---|---
Determination of raw asymmetries: |
Fit model | $0.025$
Peaking background | $0.015$
Cancellation of nuisance asymmetries: |
Additional fiducial cuts | $0.040$
Weighting configuration | $0.062$
Weighting simulation | $0.054$
Secondary charm meson | $0.039$
Neutral kaon asymmetry | $0.014$
Total | $0.10$

##  5 Summary and combination with previous LHCb measurements

The time-integrated $C\\!P$ asymmetry in
${{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}}$ decays is measured using data
collected by the LHCb experiment and determined to be

$\displaystyle A_{{C\\!P}}({{K}^{-}}{{K}^{+}})=(0.14\pm
0.15\mathrm{\,(stat)}\pm 0.10\mathrm{\,(syst)})\%.$ (9)

This result can be combined with previous LHCb measurements of the same and
related observables. In Ref. [18], $A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$ was
measured to be $A_{{C\\!P}}^{\rm sl}({{K}^{-}}{{K}^{+}})=(-0.06\pm
0.15\mathrm{\,(stat)}\pm 0.10\mathrm{\,(syst)})\%$ for ${D}^{0}$ mesons
originating from semileptonic $b$-hadron decays. Since the same ${D}^{+}$
decay channels were employed for the cancellation of detection asymmetries,
the result is partially correlated with the value presented in this Letter.
The statistical correlation coefficient is calculated as shown in Appendix A,
and is $\rho_{\rm stat}=0.36$ and the systematic uncertainties are
conservatively assumed to be fully correlated. A weighted average results in
the following combined value for the $C\\!P$ asymmetry in the ${D}^{0}$
$\rightarrow$ ${K}^{-}$ ${K}^{+}$ channel

$\displaystyle A_{{C\\!P}}^{\rm comb}({{K}^{-}}{{K}^{+}})=(0.04\pm
0.12\mathrm{\,(stat)}\pm 0.10\mathrm{\,(syst)})\%.$ (10)

The difference in $C\\!P$ asymmetries between ${D}^{0}$ $\rightarrow$
${K}^{-}$ ${K}^{+}$ and ${D}^{0}$ $\rightarrow$ ${\pi}^{-}$ ${\pi}^{+}$
decays, $\Delta A_{{C\\!P}}$, was measured at LHCb using prompt charm decays
[16]. A combination of the measurement of $A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$
presented in this Letter with $\Delta A_{{C\\!P}}$ yields a value for
$A_{{C\\!P}}({{\pi}^{+}}{{\pi}^{-}})$

$\displaystyle
A_{{C\\!P}}({{\pi}^{+}}{{\pi}^{-}})=A_{{C\\!P}}({{K}^{+}}{{K}^{-}})-\Delta
A_{{C\\!P}}=(0.24\pm 0.15\mathrm{\,(stat)}\pm 0.11\mathrm{\,(syst)})\%.$ (11)

The statistical correlation coefficient of the two measurements is $\rho_{\rm
stat}=0.24$, and the systematic uncertainties of the two analyses are assumed
to be fully uncorrelated.

The correlation coefficient between this value and the measurement of
$A_{{C\\!P}}^{\rm sl}({{\pi}^{-}}{{\pi}^{+}})=(-0.19\pm
0.20\mathrm{\,(stat)}\pm 0.10\mathrm{\,(syst)})\%$ using semileptonically-
tagged decays at LHCb [18] is $\rho_{\rm stat}=0.28$. The weighted average of
the values is

$\displaystyle A_{{C\\!P}}^{\rm comb}({{\pi}^{-}}{{\pi}^{+}})=(0.07\pm
0.14\mathrm{\,(stat)}\pm 0.11\mathrm{\,(syst)})\%,$

where, again, the systematic uncertainties are assumed to be fully correlated.

Figure 2: Measurements of $C\\!P$ violation asymmetries in ${D}^{0}$
$\rightarrow$ ${K}^{-}$ ${K}^{+}$ and ${D}^{0}$ $\rightarrow$ ${\pi}^{-}$
${\pi}^{+}$ decays. Alongside the two LHCb measurements, presented in this
Letter (green ellipse) and in Ref.[18] (blue ellipse), and their combination
(red ellipse), the latest value of the Heavy Flavour Averaging Group [1] is
shown (black ellipse). The latter already includes the measurement of $\Delta
A_{{C\\!P}}$ with muon(pion)-tagged ${D}^{0}$ decays, using
$3(1)\,$$\mbox{\,fb}^{-1}$ $pp$ collision data collected with the LHCb
detector [18, 33]. The $68\%$ confidence level contours are displayed where
the statistical and systematic uncertainties are added in quadrature.

When adding the statistical and systematic uncertainties in quadrature, the
values for the $C\\!P$ asymmetries in ${D}^{0}$ $\rightarrow$ ${K}^{-}$
${K}^{+}$ and ${D}^{0}$ $\rightarrow$ ${\pi}^{-}$ ${\pi}^{+}$ have a
correlation coefficient $\rho_{\rm full}=0.61$. Fig. 2 shows the LHCb
measurements of $C\\!P$ asymmetry using both pion- and muon-tagged
${{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}}$ and
${{D}^{0}}\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ decays. Additionally, the latest
combined values of the Heavy Flavour Averaging Group [1] for these quantities
are presented. The time-integrated $C\\!P$ asymmetries can be interpreted in
terms of direct and indirect $C\\!P$ violation as shown in Appendix B.

In conclusion, no evidence of $C\\!P$ violation is found in the Cabibbo-
suppressed decays ${{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}}$ and
${{D}^{0}}\rightarrow{{\pi}^{-}}{{\pi}^{+}}$. These results are obtained
assuming that there is no $C\\!P$ violation in ${D}^{0}$–${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ mixing and no direct $C\\!P$
violation in the Cabibbo-favoured ${{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}$,
${{D}^{+}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$ and
${{D}^{+}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}{{\pi}^{+}}$ decay modes. The
combined LHCb results are the most precise measurements of the individual
time-integrated $C\\!P$ asymmetries $A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$ and
$A_{{C\\!P}}({{\pi}^{-}}{{\pi}^{+}})$ from a single experiment to date.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC
(China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy); FOM
and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES
and FASO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine);
STFC (United Kingdom); NSF (USA). We acknowledge the computing resources that
are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN (Italy),
SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and Yandex
LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID
(Poland) and OSC (USA). We are indebted to the communities behind the multiple
open source software packages on which we depend. Individual groups or members
have received support from AvH Foundation (Germany), EPLANET, Marie
Skłodowska-Curie Actions and ERC (European Union), Conseil Général de Haute-
Savoie, Labex ENIGMASS and OCEVU, Région Auvergne (France), RFBR and Yandex
LLC (Russia), GVA, XuntaGal and GENCAT (Spain), Herchel Smith Fund, The Royal
Society, Royal Commission for the Exhibition of 1851 and the Leverhulme Trust
(United Kingdom).

Appendices

##  Appendix A Calculation of correlations

Since the measurement of $A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$ using semileptonic
$b$-hadron decays employs the same prompt $D^{+}$ calibration channels, it is
correlated to the value obtained from prompt charm decays. Due to different
selection requirements and a different weighting procedure of the candidates,
the asymmetries measured for the ${D}^{+}$ channels are not fully correlated.
The correlation factor $\rho$ between two weighted subsamples $X$ and $Y$ of a
larger data sample $Z$ is given by

$\displaystyle\rho=\sqrt{\frac{\left(\sum_{Z}\omega_{X}\omega_{Y}\right)^{2}}{\sum_{X}\omega_{X}^{2}\sum_{Y}\omega_{Y}^{2}}},$
(12)

where $\omega_{X}$ and $\omega_{Y}$ are the weights of candidates in the X and
Y subsamples. Whereas the four ${D}^{+}$ $\rightarrow$
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ ${\pi}^{+}$ data samples have
correlation factors $\rho_{{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\pi}$
between $0.64$ and $0.70$, the correlation factors of the ${D}^{+}$
$\rightarrow$ ${{K}^{-}}$${\pi}^{+}$ ${\pi}^{+}$ samples, $\rho_{K\pi\pi}$,
are in the range $0.07$ to $0.08$. The main reason for these small
correlations is the prescaling of the ${D}^{+}$ $\rightarrow$ $K$${\pi}^{+}$
${\pi}^{+}$ data in the semileptonic analysis which was removed in the prompt
case. From these numbers, for each data category the correlation
$\rho_{A_{{C\\!P}}}$ of the values for $A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$ are
calculated as

$\displaystyle\rho_{A_{{C\\!P}}}=\frac{1}{\sigma_{A_{{C\\!P}}}^{\mathrm{prompt}}\sigma_{A_{{C\\!P}}}^{\mathrm{sl}}}\left[\rho_{{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\pi}\sigma_{{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\pi}^{\mathrm{prompt}}\sigma_{{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\pi}^{\mathrm{sl}}+\rho_{K\pi\pi}\sigma_{K\pi\pi}^{\mathrm{prompt}}\sigma_{K\pi\pi}^{\mathrm{sl}}\right].$
(13)

Here, $\sigma$ represents the statistical uncertainty of the measured
asymmetry of the respective channel. This results in correlation factors
between $0.34$ and $0.37$ for the four data categories. When combining these
correlations in a similar way to Eq. 13, the statistical correlation
$\rho_{\mathrm{stat}}$ between the semileptonic and prompt measurements of
$A_{{C\\!P}}({{K}^{+}}{{K}^{-}})$ is obtained to be
$\rho_{\mathrm{stat}}=0.36$.

The other correlation factors presented in Sec. 5 are obtained using a similar
strategy.

##  Appendix B Mean decay times

The time-integrated $C\\!P$ asymmetry $A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$ is not
only sensitive to direct $C\\!P$ violation, but also has a contribution from
indirect $C\\!P$ violation. This contribution depends on the mean decay time
in units of the lifetime of the ${D}^{0}$ mesons, $\left\langle
t(hh)\right\rangle/\tau({{D}^{0}})$, as

$A_{{C\\!P}}\approx a_{{C\\!P}}^{\rm dir}-A_{\Gamma}\frac{\left\langle
t(hh)\right\rangle}{\tau({{D}^{0}})}\ ,$ (14)

where $a_{{C\\!P}}^{\rm dir}$ is the direct $C\\!P$ violation term,
$\tau$(${D}^{0}$) the ${D}^{0}$ lifetime and $A_{\Gamma}$ a measure of
indirect $C\\!P$ violation. More details about the method and the systematic
uncertainties considered can be found in [16], [18].

When calculating $A_{{C\\!P}}({{\pi}^{-}}{{\pi}^{+}})$ from
$A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$ and $\Delta A_{{C\\!P}}$, a difference of
the mean decay time of the ${{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}}$ samples
used for measuring $A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$ and $\Delta A_{{C\\!P}}$
leads to an additional contribution which is proportional to this difference
and the size of indirect $C\\!P$ violation. This can be accounted for by
adding this difference to the mean decay time of the
${{D}^{0}}\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ sample used in the $\Delta
A_{{C\\!P}}$ measurement. In Table 4 this modified mean decay time is labelled
by $A_{{C\\!P}}({{K}^{-}}{{K}^{+}})-\Delta A_{{C\\!P}}$.

Table 4: Summary of the mean decay times of the ${{D}^{0}}\rightarrow h^{-}h^{+}$ candidates used in the measurements of $\Delta A_{{C\\!P}}$ and $A_{{C\\!P}}$ using prompt and semileptonic ${D}^{0}$ decays, and their combined values. The first uncertainty of the results is statistical, and the second one accounts for the systematics. Tag | Mode | Measurement | $\left\langle t(hh)\right\rangle/\tau({{D}^{0}})$ | Ref.
---|---|---|---|---
Prompt |  ${K}^{-}$ ${K}^{+}$ | $\Delta A_{{C\\!P}}$ | $2.1524\pm 0.0005\pm 0.0162$ | [16]
Prompt |  ${\pi}^{-}$ ${\pi}^{+}$ | $\Delta A_{{C\\!P}}$ | $2.0371\pm 0.0005\pm 0.0151$ | [16]
Prompt |  ${K}^{-}$ ${K}^{+}$ | $A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$ | $2.2390\pm 0.0007\pm 0.0187$ | –
Prompt |  ${\pi}^{-}$ ${\pi}^{+}$ |  $A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$ $-$$\Delta A_{{C\\!P}}$ | $2.1237\pm 0.0008\pm 0.0375$ | –
Semileptonic |  ${K}^{-}$ ${K}^{+}$ | $\Delta A_{{C\\!P}}$ | $1.082\pm 0.001\pm 0.004$ | [18]
Semileptonic |  ${\pi}^{-}$ ${\pi}^{+}$ | $\Delta A_{{C\\!P}}$ | $1.068\pm 0.001\pm 0.004$ | [18]
Semileptonic |  ${K}^{-}$ ${K}^{+}$ | $A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$ | $1.051\pm 0.001\pm 0.004$ | [18]
Semileptonic |  ${\pi}^{-}$ ${\pi}^{+}$ | $A_{{C\\!P}}({{K}^{-}}{{K}^{+}})-\Delta A_{{C\\!P}}$ | $1.0370\pm 0.0011\pm 0.0089$ | –
Pr. + sl. |  ${\pi}^{-}$ ${\pi}^{+}$ | $A_{{C\\!P}}({{K}^{-}}{{K}^{+}})-\Delta A_{{C\\!P}}$ | $1.7121\pm 0.0007\pm 0.0267$ | –
Pr. + sl. |  ${K}^{-}$ ${K}^{+}$ | $A_{{C\\!P}}({{K}^{-}}{{K}^{+}})$ | $1.6111\pm 0.0007\pm 0.0109$ | –

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LHCb collaboration

R. Aaij40, B. Adeva39, M. Adinolfi48, Z. Ajaltouni5, S. Akar6, J. Albrecht10,
F. Alessio40, M. Alexander53, S. Ali43, G. Alkhazov31, P. Alvarez Cartelle55,
A.A. Alves Jr59, S. Amato2, S. Amerio23, Y. Amhis7, L. An41, L. Anderlini18,
G. Andreassi41, M. Andreotti17,g, J.E. Andrews60, R.B. Appleby56, F.
Archilli43, P. d’Argent12, J. Arnau Romeu6, A. Artamonov37, M. Artuso61, E.
Aslanides6, G. Auriemma26, M. Baalouch5, I. Babuschkin56, S. Bachmann12, J.J.
Back50, A. Badalov38, C. Baesso62, S. Baker55, W. Baldini17, R.J. Barlow56, C.
Barschel40, S. Barsuk7, W. Barter40, M. Baszczyk27, V. Batozskaya29, B.
Batsukh61, V. Battista41, A. Bay41, L. Beaucourt4, J. Beddow53, F. Bedeschi24,
I. Bediaga1, L.J. Bel43, V. Bellee41, N. Belloli21,i, K. Belous37, I.
Belyaev32, E. Ben-Haim8, G. Bencivenni19, S. Benson43, J. Benton48, A.
Berezhnoy33, R. Bernet42, A. Bertolin23, F. Betti15, M.-O. Bettler40, M. van
Beuzekom43, Ia. Bezshyiko42, S. Bifani47, P. Billoir8, T. Bird56, A.
Birnkraut10, A. Bitadze56, A. Bizzeti18,u, T. Blake50, F. Blanc41, J.
Blouw11,†, S. Blusk61, V. Bocci26, T. Boettcher58, A. Bondar36,w, N.
Bondar31,40, W. Bonivento16, A. Borgheresi21,i, S. Borghi56, M. Borisyak35, M.
Borsato39, F. Bossu7, M. Boubdir9, T.J.V. Bowcock54, E. Bowen42, C.
Bozzi17,40, S. Braun12, M. Britsch12, T. Britton61, J. Brodzicka56, E.
Buchanan48, C. Burr56, A. Bursche2, J. Buytaert40, S. Cadeddu16, R.
Calabrese17,g, M. Calvi21,i, M. Calvo Gomez38,m, A. Camboni38, P. Campana19,
D. Campora Perez40, D.H. Campora Perez40, L. Capriotti56, A. Carbone15,e, G.
Carboni25,j, R. Cardinale20,h, A. Cardini16, P. Carniti21,i, L. Carson52, K.
Carvalho Akiba2, G. Casse54, L. Cassina21,i, L. Castillo Garcia41, M.
Cattaneo40, Ch. Cauet10, G. Cavallero20, R. Cenci24,t, M. Charles8, Ph.
Charpentier40, G. Chatzikonstantinidis47, M. Chefdeville4, S. Chen56, S.-F.
Cheung57, V. Chobanova39, M. Chrzaszcz42,27, X. Cid Vidal39, G. Ciezarek43,
P.E.L. Clarke52, M. Clemencic40, H.V. Cliff49, J. Closier40, V. Coco59, J.
Cogan6, E. Cogneras5, V. Cogoni16,40,f, L. Cojocariu30, G. Collazuol23,o, P.
Collins40, A. Comerma-Montells12, A. Contu40, A. Cook48, S. Coquereau38, G.
Corti40, M. Corvo17,g, C.M. Costa Sobral50, B. Couturier40, G.A. Cowan52, D.C.
Craik52, A. Crocombe50, M. Cruz Torres62, S. Cunliffe55, R. Currie55, C.
D’Ambrosio40, F. Da Cunha Marinho2, E. Dall’Occo43, J. Dalseno48, P.N.Y.
David43, A. Davis59, O. De Aguiar Francisco2, K. De Bruyn6, S. De Capua56, M.
De Cian12, J.M. De Miranda1, L. De Paula2, M. De Serio14,d, P. De Simone19,
C.-T. Dean53, D. Decamp4, M. Deckenhoff10, L. Del Buono8, M. Demmer10, D.
Derkach35, O. Deschamps5, F. Dettori40, B. Dey22, A. Di Canto40, H.
Dijkstra40, F. Dordei40, M. Dorigo41, A. Dosil Suárez39, A. Dovbnya45, K.
Dreimanis54, L. Dufour43, G. Dujany56, K. Dungs40, P. Durante40, R.
Dzhelyadin37, A. Dziurda40, A. Dzyuba31, N. Déléage4, S. Easo51, M. Ebert52,
U. Egede55, V. Egorychev32, S. Eidelman36,w, S. Eisenhardt52, U.
Eitschberger10, R. Ekelhof10, L. Eklund53, Ch. Elsasser42, S. Ely61, S.
Esen12, H.M. Evans49, T. Evans57, A. Falabella15, N. Farley47, S. Farry54, R.
Fay54, D. Fazzini21,i, D. Ferguson52, V. Fernandez Albor39, A. Fernandez
Prieto39, F. Ferrari15,40, F. Ferreira Rodrigues1, M. Ferro-Luzzi40, S.
Filippov34, R.A. Fini14, M. Fiore17,g, M. Fiorini17,g, M. Firlej28, C.
Fitzpatrick41, T. Fiutowski28, F. Fleuret7,b, K. Fohl40, M. Fontana16,40, F.
Fontanelli20,h, D.C. Forshaw61, R. Forty40, V. Franco Lima54, M. Frank40, C.
Frei40, J. Fu22,q, E. Furfaro25,j, C. Färber40, A. Gallas Torreira39, D.
Galli15,e, S. Gallorini23, S. Gambetta52, M. Gandelman2, P. Gandini57, Y.
Gao3, L.M. Garcia Martin68, J. García Pardiñas39, J. Garra Tico49, L.
Garrido38, P.J. Garsed49, D. Gascon38, C. Gaspar40, L. Gavardi10, G. Gazzoni5,
D. Gerick12, E. Gersabeck12, M. Gersabeck56, T. Gershon50, Ph. Ghez4, S.
Gianì41, V. Gibson49, O.G. Girard41, L. Giubega30, K. Gizdov52, V.V.
Gligorov8, D. Golubkov32, A. Golutvin55,40, A. Gomes1,a, I.V. Gorelov33, C.
Gotti21,i, M. Grabalosa Gándara5, R. Graciani Diaz38, L.A. Granado Cardoso40,
E. Graugés38, E. Graverini42, G. Graziani18, A. Grecu30, P. Griffith47, L.
Grillo21,40,i, B.R. Gruberg Cazon57, O. Grünberg66, E. Gushchin34, Yu. Guz37,
T. Gys40, C. Göbel62, T. Hadavizadeh57, C. Hadjivasiliou5, G. Haefeli41, C.
Haen40, S.C. Haines49, S. Hall55, B. Hamilton60, X. Han12, S. Hansmann-
Menzemer12, N. Harnew57, S.T. Harnew48, J. Harrison56, M. Hatch40, J. He63, T.
Head41, A. Heister9, K. Hennessy54, P. Henrard5, L. Henry8, J.A. Hernando
Morata39, E. van Herwijnen40, M. Heß66, A. Hicheur2, D. Hill57, C. Hombach56,
H. Hopchev41, W. Hulsbergen43, T. Humair55, M. Hushchyn35, N. Hussain57, D.
Hutchcroft54, M. Idzik28, P. Ilten58, R. Jacobsson40, A. Jaeger12, J.
Jalocha57, E. Jans43, A. Jawahery60, F. Jiang3, M. John57, D. Johnson40, C.R.
Jones49, C. Joram40, B. Jost40, N. Jurik61, S. Kandybei45, W. Kanso6, M.
Karacson40, J.M. Kariuki48, S. Karodia53, M. Kecke12, M. Kelsey61, I.R.
Kenyon47, M. Kenzie49, T. Ketel44, E. Khairullin35, B. Khanji21,40,i, C.
Khurewathanakul41, T. Kirn9, S. Klaver56, K. Klimaszewski29, S. Koliiev46, M.
Kolpin12, I. Komarov41, R.F. Koopman44, P. Koppenburg43, A. Kozachuk33, M.
Kozeiha5, L. Kravchuk34, K. Kreplin12, M. Kreps50, P. Krokovny36,w, F.
Kruse10, W. Krzemien29, W. Kucewicz27,l, M. Kucharczyk27, V. Kudryavtsev36,w,
A.K. Kuonen41, K. Kurek29, T. Kvaratskheliya32,40, D. Lacarrere40, G.
Lafferty56, A. Lai16, D. Lambert52, G. Lanfranchi19, C. Langenbruch9, T.
Latham50, C. Lazzeroni47, R. Le Gac6, J. van Leerdam43, J.-P. Lees4, A.
Leflat33,40, J. Lefrançois7, R. Lefèvre5, F. Lemaitre40, E. Lemos Cid39, O.
Leroy6, T. Lesiak27, B. Leverington12, Y. Li7, T. Likhomanenko35,67, R.
Lindner40, C. Linn40, F. Lionetto42, B. Liu16, X. Liu3, D. Loh50, I.
Longstaff53, J.H. Lopes2, D. Lucchesi23,o, M. Lucio Martinez39, H. Luo52, A.
Lupato23, E. Luppi17,g, O. Lupton57, A. Lusiani24, X. Lyu63, F. Machefert7, F.
Maciuc30, O. Maev31, K. Maguire56, S. Malde57, A. Malinin67, T. Maltsev36, G.
Manca7, G. Mancinelli6, P. Manning61, J. Maratas5,v, J.F. Marchand4, U.
Marconi15, C. Marin Benito38, P. Marino24,t, J. Marks12, G. Martellotti26, M.
Martin6, M. Martinelli41, D. Martinez Santos39, F. Martinez Vidal68, D.
Martins Tostes2, L.M. Massacrier7, A. Massafferri1, R. Matev40, A. Mathad50,
Z. Mathe40, C. Matteuzzi21, A. Mauri42, B. Maurin41, A. Mazurov47, M.
McCann55, J. McCarthy47, A. McNab56, R. McNulty13, B. Meadows59, F. Meier10,
M. Meissner12, D. Melnychuk29, M. Merk43, A. Merli22,q, E. Michielin23, D.A.
Milanes65, M.-N. Minard4, D.S. Mitzel12, A. Mogini8, J. Molina Rodriguez62,
I.A. Monroy65, S. Monteil5, M. Morandin23, P. Morawski28, A. Mordà6, M.J.
Morello24,t, J. Moron28, A.B. Morris52, R. Mountain61, F. Muheim52, M.
Mulder43, M. Mussini15, D. Müller56, J. Müller10, K. Müller42, V. Müller10, P.
Naik48, T. Nakada41, R. Nandakumar51, A. Nandi57, I. Nasteva2, M. Needham52,
N. Neri22, S. Neubert12, N. Neufeld40, M. Neuner12, A.D. Nguyen41, C. Nguyen-
Mau41,n, S. Nieswand9, R. Niet10, N. Nikitin33, T. Nikodem12, A. Novoselov37,
D.P. O’Hanlon50, A. Oblakowska-Mucha28, V. Obraztsov37, S. Ogilvy19, R.
Oldeman49, C.J.G. Onderwater69, J.M. Otalora Goicochea2, A. Otto40, P. Owen42,
A. Oyanguren68, P.R. Pais41, A. Palano14,d, F. Palombo22,q, M. Palutan19, J.
Panman40, A. Papanestis51, M. Pappagallo14,d, L.L. Pappalardo17,g, W.
Parker60, C. Parkes56, G. Passaleva18, A. Pastore14,d, G.D. Patel54, M.
Patel55, C. Patrignani15,e, A. Pearce56,51, A. Pellegrino43, G. Penso26, M.
Pepe Altarelli40, S. Perazzini40, P. Perret5, L. Pescatore47, K. Petridis48,
A. Petrolini20,h, A. Petrov67, M. Petruzzo22,q, E. Picatoste Olloqui38, B.
Pietrzyk4, M. Pikies27, D. Pinci26, A. Pistone20, A. Piucci12, S. Playfer52,
M. Plo Casasus39, T. Poikela40, F. Polci8, A. Poluektov50,36, I. Polyakov61,
E. Polycarpo2, G.J. Pomery48, A. Popov37, D. Popov11,40, B. Popovici30, S.
Poslavskii37, C. Potterat2, E. Price48, J.D. Price54, J. Prisciandaro39, A.
Pritchard54, C. Prouve48, V. Pugatch46, A. Puig Navarro41, G. Punzi24,p, W.
Qian57, R. Quagliani7,48, B. Rachwal27, J.H. Rademacker48, M. Rama24, M. Ramos
Pernas39, M.S. Rangel2, I. Raniuk45, G. Raven44, F. Redi55, S. Reichert10,
A.C. dos Reis1, C. Remon Alepuz68, V. Renaudin7, S. Ricciardi51, S.
Richards48, M. Rihl40, K. Rinnert54, V. Rives Molina38, P. Robbe7,40, A.B.
Rodrigues1, E. Rodrigues59, J.A. Rodriguez Lopez65, P. Rodriguez Perez56,†, A.
Rogozhnikov35, S. Roiser40, A. Rollings57, V. Romanovskiy37, A. Romero
Vidal39, J.W. Ronayne13, M. Rotondo19, M.S. Rudolph61, T. Ruf40, P. Ruiz
Valls68, J.J. Saborido Silva39, E. Sadykhov32, N. Sagidova31, B. Saitta16,f,
V. Salustino Guimaraes2, C. Sanchez Mayordomo68, B. Sanmartin Sedes39, R.
Santacesaria26, C. Santamarina Rios39, M. Santimaria19, E. Santovetti25,j, A.
Sarti19,k, C. Satriano26,s, A. Satta25, D.M. Saunders48, D. Savrina32,33, S.
Schael9, M. Schellenberg10, M. Schiller40, H. Schindler40, M. Schlupp10, M.
Schmelling11, T. Schmelzer10, B. Schmidt40, O. Schneider41, A. Schopper40, K.
Schubert10, M. Schubiger41, M.-H. Schune7, R. Schwemmer40, B. Sciascia19, A.
Sciubba26,k, A. Semennikov32, A. Sergi47, N. Serra42, J. Serrano6, L.
Sestini23, P. Seyfert21, M. Shapkin37, I. Shapoval45, Y. Shcheglov31, T.
Shears54, L. Shekhtman36,w, V. Shevchenko67, A. Shires10, B.G. Siddi17,40, R.
Silva Coutinho42, L. Silva de Oliveira2, G. Simi23,o, S. Simone14,d, M.
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1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
10Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
11Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
12Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
13School of Physics, University College Dublin, Dublin, Ireland
14Sezione INFN di Bari, Bari, Italy
15Sezione INFN di Bologna, Bologna, Italy
16Sezione INFN di Cagliari, Cagliari, Italy
17Sezione INFN di Ferrara, Ferrara, Italy
18Sezione INFN di Firenze, Firenze, Italy
19Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
20Sezione INFN di Genova, Genova, Italy
21Sezione INFN di Milano Bicocca, Milano, Italy
22Sezione INFN di Milano, Milano, Italy
23Sezione INFN di Padova, Padova, Italy
24Sezione INFN di Pisa, Pisa, Italy
25Sezione INFN di Roma Tor Vergata, Roma, Italy
26Sezione INFN di Roma La Sapienza, Roma, Italy
27Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
28AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
29National Center for Nuclear Research (NCBJ), Warsaw, Poland
30Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
31Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
32Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
33Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
34Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
35Yandex School of Data Analysis, Moscow, Russia
36Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
37Institute for High Energy Physics (IHEP), Protvino, Russia
38ICCUB, Universitat de Barcelona, Barcelona, Spain
39Universidad de Santiago de Compostela, Santiago de Compostela, Spain
40European Organization for Nuclear Research (CERN), Geneva, Switzerland
41Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
42Physik-Institut, Universität Zürich, Zürich, Switzerland
43Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
44Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
45NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
46Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
47University of Birmingham, Birmingham, United Kingdom
48H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
49Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
50Department of Physics, University of Warwick, Coventry, United Kingdom
51STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
52School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
53School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
54Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
55Imperial College London, London, United Kingdom
56School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
57Department of Physics, University of Oxford, Oxford, United Kingdom
58Massachusetts Institute of Technology, Cambridge, MA, United States
59University of Cincinnati, Cincinnati, OH, United States
60University of Maryland, College Park, MD, United States
61Syracuse University, Syracuse, NY, United States
62Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
63University of Chinese Academy of Sciences, Beijing, China, associated to 3
64Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
65Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
66Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
67National Research Centre Kurchatov Institute, Moscow, Russia, associated to
32
68Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC,
Valencia, Spain, associated to 38
69Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 43

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bLaboratoire Leprince-Ringuet, Palaiseau, France
cP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
dUniversità di Bari, Bari, Italy
eUniversità di Bologna, Bologna, Italy
fUniversità di Cagliari, Cagliari, Italy
gUniversità di Ferrara, Ferrara, Italy
hUniversità di Genova, Genova, Italy
iUniversità di Milano Bicocca, Milano, Italy
jUniversità di Roma Tor Vergata, Roma, Italy
kUniversità di Roma La Sapienza, Roma, Italy
lAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
mLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
nHanoi University of Science, Hanoi, Viet Nam
oUniversità di Padova, Padova, Italy
pUniversità di Pisa, Pisa, Italy
qUniversità degli Studi di Milano, Milano, Italy
rUniversità di Urbino, Urbino, Italy
sUniversità della Basilicata, Potenza, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità di Modena e Reggio Emilia, Modena, Italy
vIligan Institute of Technology (IIT), Iligan, Philippines
wNovosibirsk State University, Novosibirsk, Russia
†Deceased