EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2018-172 LHCb-PAPER-2018-026 October 18, 2018

First observation of the doubly charmed baryon decay ${{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28932\relax}^{+}_{c}}{{\pi}^{+}}$

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

The doubly charmed baryon decay ${{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28932\relax}^{+}_{c}}{{\pi}^{+}}$ is observed for the first time, with a
statistical significance of $\nobreak{5.9\sigma}$, confirming a recent
observation of the baryon in the ${{\mathchar
28931\relax}^{+}_{c}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$ final state. The data
sample used corresponds to an integrated luminosity of $1.7\mbox{\,fb}^{-1}$,
collected by the LHCb experiment in $pp$ collisions at a center-of-mass energy
of $13\mathrm{\,Te\kern-1.00006ptV}$. The ${\mathchar
28932\relax}^{++}_{{c}{c}}$ mass is measured to be

$\nobreak{3620.6\pm 1.5\mathrm{\,(stat)}\pm 0.4\mathrm{\,(syst)}\pm
0.3\,({{\mathchar
28932\relax}^{+}_{c}}){\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}},$

and is consistent with the previous result. The ratio of branching fractions
between the decay modes is measured to be

$\frac{{\mathcal{B}}({{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28932\relax}^{+}_{c}}{{\pi}^{+}})\times{\mathcal{B}}({{\mathchar
28932\relax}^{+}_{c}}\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}{{\mathcal{B}}({{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}})\times{\mathcal{B}}({{\mathchar
28931\relax}^{+}_{c}}\rightarrow{p}{{K}^{-}}{{\pi}^{+}})}=\nobreak{0.035\pm
0.009\mathrm{\,(stat)}\pm 0.003\mathrm{\,(syst)}}.$

Published in Phys. Rev. Lett. 121, 162002 (2018)

© 2024 CERN for the benefit of the LHCb collaboration. CC-BY-4.0 licence.

The recent observation by the LHCb collaboration [1] of a new state that is
consistent with the doubly charmed baryon ${\mathchar
28932\relax}^{++}_{{c}{c}}$, opens a new field of research studying the
properties of baryons containing two heavy quarks, providing a unique
environment for testing models of quantum chromodynamics (QCD). In studies of
a sample of ${\mathchar 28932\relax}^{++}_{{c}{c}}$ decays to the final state
${{\mathchar 28931\relax}^{+}_{c}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$, with
${{\mathchar 28931\relax}^{+}_{c}}\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$, its
mass was found to be
$3621.40\,\pm\,0.72\mathrm{\,(stat)}\pm\,0.27\,\mathrm{\,(syst)}\pm\,0.14\,{\,({{\mathchar
28931\relax}^{+}_{c}})}$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ [1], and
its lifetime was measured to be
$0.256\,^{+0.024}_{-0.022}\mathrm{\,(stat)}\pm\,0.014\,\mathrm{\,(syst)}$${\mathrm{\,ps}}$
[2].111 The inclusion of charge-conjugate processes is implied throughout.
The measured lifetime firmly establishes its weakly decaying nature. Searching
for new decay modes is the next critical step towards understanding the
dynamics of weak decays of doubly heavy baryons, which may differ
significantly from those of singly heavy hadrons due to interference between
decay amplitudes of the two heavy quarks. The process ${{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28932\relax}^{+}_{c}}{{\pi}^{+}}$ has been predicted to have a sizable
branching fraction [3, 4], making it a promising final state in which to seek
confirmation of the previous observation.

This Letter reports the first observation of the decay ${{{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28932\relax}^{+}_{c}}{{\pi}^{+}}}$, which proceeds predominantly via the tree-
level amplitude represented by the Feynman diagram shown in Fig. 1. The
${\mathchar 28932\relax}^{+}_{c}$ baryon is reconstructed in its Cabibbo-
suppressed decay to ${p}{{K}^{-}}{{\pi}^{+}}$. The data sample used consists
of ${p}{p}$ collisions at a center-of-mass energy of
13$\mathrm{\,Te\kern-1.00006ptV}$ collected by the LHCb experiment in 2016,
corresponding to an integrated luminosity of $1.7$$\mbox{\,fb}^{-1}$. A
measurement of the ${\mathchar 28932\relax}^{++}_{{c}{c}}$ mass with this
sample is presented, and the ratio of the total branching fractions,
${\mathcal{R}({\mathcal{B}})}$, between the decays ${{{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28932\relax}^{+}_{c}}(\rightarrow{p}{{K}^{-}}{{\pi}^{+}})\,{{\pi}^{+}}}$ and
${{{\mathchar 28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}(\rightarrow{p}{{K}^{-}}{{\pi}^{+}})\,{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}}$
is determined.

Figure 1: Dominant Feynman diagram contributing to the decay ${{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28932\relax}^{+}_{c}}{{\pi}^{+}}$.

The LHCb detector [5, 6] 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 [7] surrounding the $pp$
interaction region that allows $c$ and $b$ hadrons to be identified from their
typical long flight distance; a tracking system [8] that provides a
measurement of momentum, $p$, of charged particles; two ring-imaging Cherenkov
detectors [9] that discriminate between different species of charged hadrons;
a calorimeter system consisting of scintillating-pad and preshower detectors,
an electromagnetic calorimeter and a hadronic calorimeter, to identify
photons, electrons and hadrons; a muon system composed of alternating layers
of iron and multiwire proportional chambers [10] to identify muons. The online
event selection is performed by a trigger [11], which consists of a hardware
stage, based on information from the calorimeter and muon systems [12],
followed by a software stage, which applies a full event reconstruction
incorporating real-time alignment and calibration of the detector [13]. The
same alignment and calibration information is propagated to the offline
reconstruction, ensuring consistent and high-quality particle identification
(PID) information between the trigger and offline software. The identical
performance of the online and offline reconstruction offers the opportunity to
perform physics analyses directly using candidates reconstructed in the
trigger which is done in the present analysis.

Simulation is required to model the effects of the detector acceptance and the
imposed selection requirements. In the simulation, $pp$ collisions are
generated using Pythia [14, *Sjostrand:2006za] with a specific LHCb
configuration [16]. A dedicated generator, GenXicc2.0 [17, *Chang:2009va], is
used to simulate ${\mathchar 28932\relax}^{++}_{{c}{c}}$ baryon production.
Decays of hadrons are described by EvtGen [19], in which final-state radiation
is generated using Photos [20]. The interaction of the generated particles
with the detector, and its response, are modelled using the Geant4 toolkit
[21, *Agostinelli:2002hh] as described in Ref. [23].

The selection of ${{{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28932\relax}^{+}_{c}}(\rightarrow{p}{{K}^{-}}{{\pi}^{+}})\,{{\pi}^{+}}}$
decays is designed to be as similar as possible to those of ${{{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}(\rightarrow{p}{{K}^{-}}{{\pi}^{+}})\,{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}}$,
described in Ref. [1]. Three charged particles identified as ${p}$,
${{K}^{-}}$ and ${{\pi}^{+}}$ that form a good-quality vertex are combined to
reconstruct a ${{{\mathchar
28932\relax}^{+}_{c}}\rightarrow{p}{{K}^{-}}{{\pi}^{+}}}$ candidate. The three
particles are required to have transverse momenta in excess of
$500{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ and be inconsistent with originating
from any primary vertex (PV). The ${\mathchar 28932\relax}^{+}_{c}$ vertex is
required to be displaced from any PV by a distance corresponding to a
${\mathchar 28932\relax}^{+}_{c}$ decay time greater than
0.15${\mathrm{\,ps}}$, which corresponds to approximately twice the decay time
resolution. The invariant-mass of each ${\mathchar 28932\relax}^{+}_{c}$
candidate is required to be in the range
2450–2488${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, corresponding to
approximately six times the ${\mathchar 28932\relax}^{+}_{c}$ mass resolution.
An additional positively charged particle, which must be identified as a pion
and have $p_{\mathrm{T}}$ greater than
200${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$, is then combined with the
${{\mathchar 28932\relax}^{+}_{c}}$ candidate to form a ${\mathchar
28932\relax}^{++}_{{c}{c}}$ candidate. The ${{\mathchar
28932\relax}^{+}_{c}}{{\pi}^{+}}$ pair is required to form a vertex that is of
good quality and is upstream of the ${\mathchar 28932\relax}^{+}_{c}$ vertex.
The ${{\mathchar 28932\relax}^{++}_{{c}{c}}}$ candidate must have
$\mbox{$p_{\mathrm{T}}$}>2000{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ and be
consistent with originating from a PV. The candidate is associated with the PV
with respect to which it has the smallest impact parameter $\chi^{2}$
($\chi^{2}_{\text{IP}}$). The $\chi^{2}_{\text{IP}}$ is defined as the
difference in $\chi^{2}$ of the PV fit with and without the particle in
question. To avoid contributions due to duplicate tracks, candidates are
rejected if the angle between any pair of their final-state particles with the
same charge is smaller than $0.5$$\mathrm{\,mrad}$. Specific hardware trigger
requirements are also applied, to increase the signal yield and simplify the
study of the trigger efficiency. Candidates are retained only if the event
contains large transverse energy deposits in the calorimeter arising from the
decay products of the ${\mathchar 28932\relax}^{++}_{{c}{c}}$ candidate, or if
the event contains activity either in the calorimeter or in the muon system
from particles other than these decay products. Simulation shows that the
efficiency for these additional requirements is above 90% for both two-body or
four-body ${\mathchar 28932\relax}^{++}_{{c}{c}}$ decay modes.

A multivariate selector based on the multilayer perceptron algorithm [24,
*TMVA4] is used to further suppress combinatorial backgrounds. To train the
selector, simulated ${{{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28932\relax}^{+}_{c}}(\rightarrow{p}{{K}^{-}}{{\pi}^{+}})\,{{\pi}^{+}}}$
decays are used as a signal sample, and 0.3 million candidates from the upper
sideband with invariant-masses in the range
3800–4000${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ are used as a background
sample. To reduce the effect of the ${\mathchar 28932\relax}^{+}_{c}$ mass
resolution on the invariant-mass of the ${\mathchar
28932\relax}^{++}_{{c}{c}}$ candidates, an alternative evaluation of the
invariant-mass is used, ${m({{\mathchar
28932\relax}^{+}_{c}}{{\pi}^{+}})\equiv M({{\mathchar
28932\relax}^{+}_{c}}{{\pi}^{+}})-M([{p}{{K}^{-}}{{\pi}^{+}}]_{{{\mathchar
28932\relax}^{+}_{c}}})+M_{\mathrm{PDG}}({{\mathchar 28932\relax}^{+}_{c}})}$,
where $M({{\mathchar 28932\relax}^{+}_{c}}{{\pi}^{+}})$ and
$M([{p}{{K}^{-}}{{\pi}^{+}}]_{{{\mathchar 28932\relax}^{+}_{c}}})$ are the
reconstructed masses of the ${\mathchar 28932\relax}^{++}_{{c}{c}}$ and
${\mathchar 28932\relax}^{+}_{c}$ candidates, and
$M_{\mathrm{PDG}}({{\mathchar 28932\relax}^{+}_{c}})$ is the known value of
the ${\mathchar 28932\relax}^{+}_{c}$ mass [26].

The input variables used in the multivariate selector are chosen based on
their discrimination power between signal and background candidates. Three
different types of variables are considered in the training. The first type of
variables are the kinematic information of particles, including the
$p_{\mathrm{T}}$ of each of the four final-state particles and of the
${\mathchar 28932\relax}^{+}_{c}$ and ${\mathchar 28932\relax}^{++}_{{c}{c}}$
candidates; the angle between the ${\mathchar 28932\relax}^{++}_{{c}{c}}$
momentum vector and the displacement vector from the PV to the ${\mathchar
28932\relax}^{++}_{{c}{c}}$ decay vertex. The second type of variables are the
vertex fitting qualities, including the $\chi^{2}$ per degree of freedom of
the ${\mathchar 28932\relax}^{+}_{c}$ and ${\mathchar
28932\relax}^{++}_{{c}{c}}$ vertex fits; the $\chi^{2}$ per degree of freedom
of a kinematic refit [27] of the ${{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28932\relax}^{+}_{c}}(\rightarrow{p}{{K}^{-}}{{\pi}^{+}})\,{{\pi}^{+}}$ decay
chain that requires the ${\mathchar 28932\relax}^{++}_{{c}{c}}$ to originate
from its PV. The third type of variables are related to the lifetime,
including the $\chi^{2}_{\text{IP}}$ of each of the four final-state particles
and of the ${\mathchar 28932\relax}^{+}_{c}$ and ${\mathchar
28932\relax}^{++}_{{c}{c}}$ candidates with respect to their associated PV;
the sum of the $\chi^{2}_{\text{IP}}$ of the four final-state particles; and
the flight distance $\chi^{2}$ of the ${\mathchar 28932\relax}^{+}_{c}$ and
${\mathchar 28932\relax}^{++}_{{c}{c}}$ candidates. The flight distance
$\chi^{2}$ is defined as the $\chi^{2}$ of the hypothesis that the decay
vertex of the candidate coincides with its associated PV.

Candidates are retained only if the multivariate-selector output exceeds a
certain threshold. This threshold is chosen to maximize the expected value of
the figure of merit $\varepsilon/(\frac{5}{2}+\sqrt{N_{\rm B}})$ [28]. Here,
$\varepsilon$ is the estimated signal efficiency and $N_{\rm B}$ is the
expected number of background candidates under the signal peak in the
${{\mathchar 28932\relax}^{++}_{{c}{c}}}$ mass distribution, after the
selection. The quantity $N_{\rm B}$ is determined, assuming an exponential
shape for the background, from the number of ${{\mathchar
28932\relax}^{+}_{c}}{{\pi}^{+}}$ candidates in the mass region of
3800–4000${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, scaled to a signal region
centered at a mass of 3620${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and with
a width of 30${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. This corresponds to
approximately five times the expected ${\mathchar 28932\relax}^{++}_{{c}{c}}$
mass resolution. To test for potential biases in the multivariate selection or
other misreconstruction effects, the same selection criteria are applied to
control samples of data consisting of ${{\mathchar
28932\relax}^{+}_{c}}{{\pi}^{+}}$ candidates in the ${\mathchar
28932\relax}^{+}_{c}$ sideband regions and of wrong-sign combination
${{\mathchar 28932\relax}^{+}_{c}}{{\pi}^{-}}$. No peaking structure is
visible in either samples.

Figure 2 (left) shows the distribution of invariant-masses of ${\mathchar
28932\relax}^{++}_{{c}{c}}$ candidates, $m({{\mathchar
28932\relax}^{+}_{c}}{{\pi}^{+}})$, after applying the complete selection. The
contribution from events containing multiple signal candidates is found to be
less than 1%; all these candidates are included in the fit. A signal is
visible at a mass of approximately
3620${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, in the vicinity of the
previous LHCb ${\mathchar 28932\relax}^{++}_{{c}{c}}$ baryon observation [1].
The mass distribution is fitted with an unbinned extended maximum-likelihood
method to measure the properties of this structure. The peak is described by
an empirical model, consisting of a Gaussian function and a modified Gaussian
function with power-law tails on both sides [29] and with the same mean value.
All tail parameters are fixed to values obtained from a fit to simulated
signal events, while the parameters corresponding to the mass and the mass
resolution are varied in the fit. The background shape is described by an
exponential function. The resulting signal yield is $91\pm 20$ and the mass
value is $\nobreak{3620.7\pm 1.5{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}}$,
where the uncertainties are statistical only. The mass is fully consistent
with the value measured in the ${{{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}}$ decay channel [1], and
the resolution determined by the fit is consistent with expectations based on
known detector performance. The local statistical significance of the signal,
evaluated by taking the likelihood ratio corresponding to fits that include
and exclude the signal component, is found to be $\nobreak{5.9\sigma}$, thus
confirming the observation reported in Ref [1].

The invariant-mass distribution for the reference mode, ${{{{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}}}$, is shown in Fig. 2
(right). The selection used to obtain this sample is identical to that of the
previous analysis [1], except for the additional requirements on the hardware
trigger. An extended unbinned maximum-likelihood fit to the invariant-mass
distribution returns a signal yield of $289\pm 35$ for the reference mode.

Figure 2: Invariant-mass distribution of the ${{{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28932\relax}^{+}_{c}}{{\pi}^{+}}}$ (left) and ${{{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}}$ (right) candidates with
result of the fit overlaid. The black points represent the data, the dotted
(red) line represents the signal contribution, and the dashed (green) line
represents the combinational background.

The branching fraction ratio, ${\mathcal{R}({\mathcal{B}})}$, between the
decays ${{{\mathchar 28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28932\relax}^{+}_{c}}(\rightarrow{p}{{K}^{-}}{{\pi}^{+}})\,{{\pi}^{+}}}$ and
${{{\mathchar 28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}(\rightarrow{p}{{K}^{-}}{{\pi}^{+}})\,{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}}$
is defined as

$\displaystyle{\mathcal{R}({\mathcal{B}})}\equiv\frac{{\mathcal{B}}\left({{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28932\relax}^{+}_{c}}{{\pi}^{+}}\right)\times{\mathcal{B}}\left({{\mathchar
28932\relax}^{+}_{c}}\rightarrow{p}{{K}^{-}}{{\pi}^{+}}\right)}{{\mathcal{B}}\left({{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}\right)\times{\mathcal{B}}\left({{\mathchar
28931\relax}^{+}_{c}}\rightarrow{p}{{K}^{-}}{{\pi}^{+}}\right)}=\frac{r_{N}}{r_{{\varepsilon}}},$
(1)

where $r_{N}$ is the ratio of ${\mathchar 28932\relax}^{++}_{{c}{c}}$ yields
between the signal and reference decay modes, and $r_{{\varepsilon}}$ is the
ratio of total efficiencies between the two modes. In each case, the total
efficiency includes the effects of the geometrical acceptance, trigger,
reconstruction, and selection. Each contribution to the efficiency ratio is
evaluated with simulation, calibrated with data when possible, as described in
the following. The combined efficiency of the reconstruction and the
selection, excluding the hardware-trigger requirement, is determined from
fully simulated signal samples in which the tracking [30] and particle-
identification efficiencies are corrected using control samples. The
correction to the efficiency ratio of the ${{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$ and ${{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28932\relax}^{+}_{c}}{{\pi}^{+}}$ channels is determined to be $0.983\pm
0.007$ for the tracking efficiency, and $1.050\pm 0.020$ for the particle-
identification efficiency. The hardware-trigger efficiency ratio is estimated
from fully simulated signal events, with a $p_{\mathrm{T}}$-dependent
correction derived from data using ${{{{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}(\rightarrow{p}{{K}^{-}}{{\pi}^{+}}){{\pi}^{-}}{{\pi}^{+}}{{\pi}^{-}}}}$
and ${{{{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}(\rightarrow{p}{{K}^{-}}{{\pi}^{+}}){{\pi}^{-}}}}$
decays, which are required to pass the same trigger selection as the
${\mathchar 28932\relax}^{++}_{{c}{c}}$ candidates. These two decay channels
have similar final states and decay topologies as the signal. The total
relative efficiency is determined to be $r_{{\varepsilon}}=0.110\pm 0.002$,
where the uncertainty comes from the limited size of the simulation sample and
is accounted as a systematic uncertainty. To validate this procedure, the
ratio of branching fractions of the decays ${{{{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}(\rightarrow{p}{{K}^{-}}{{\pi}^{+}}){{\pi}^{-}}}}$ and
${{{{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}(\rightarrow{p}{{K}^{-}}{{\pi}^{+}}){{\pi}^{-}}{{\pi}^{+}}{{\pi}^{-}}}}$
is measured using the same data sample, resulting in a value 0.83$\pm$0.05
(statistical uncertainty only) which agrees with the previous LHCb result of
0.70$\pm$0.10 [31].

The main sources of systematic uncertainty that affect the measurements of the
${{\mathchar 28932\relax}^{++}_{{c}{c}}}$ mass are summarized in Table 1.
Samples of ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow{\mu^{+}\mu^{-}}$ and
${{{B}^{+}}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ decays [32, 33] are used to calibrate the reconstructed
momentum of charged particles, which affect the reconstructed mass of signal.
The maximum difference between the correction factors determined with above-
mentioned decays is found to be $0.03\%$, which corresponds to a systematic
uncertainty of $0.38{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ on the measured
${\mathchar 28932\relax}^{++}_{{c}{c}}$ mass. The signal selection efficiency
increases with the ${\mathchar 28932\relax}^{++}_{{c}{c}}$ decay time;
combined with a correlation between the reconstructed mass and the
reconstructed decay time, this induces a positive bias on the masses of both
${{\mathchar 28932\relax}^{++}_{{c}{c}}}$ and ${{\mathchar
28932\relax}^{+}_{c}}$ candidates. The effect is studied with simulation and
the bias on the measured ${\mathchar 28932\relax}^{++}_{{c}{c}}$ mass is found
to be $+0.10\pm 0.10$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, where the
uncertainty is due to the limited size of the simulated samples. A correction
to the ${\mathchar 28932\relax}^{++}_{{c}{c}}$ mass of
$-0.10$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ is therefore applied, and a
systematic uncertainty of $0.10$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$
assigned. The dependence of this bias on the ${\mathchar
28932\relax}^{++}_{{c}{c}}$ lifetime is studied by weighting simulated events
to different lifetime hypotheses; the change is found to be negligible for the
measured ${\mathchar 28932\relax}^{++}_{{c}{c}}$ lifetime [2]. The description
of the final-state radiation in simulation [20] can also cause a bias in the
measured mass, which is estimated with pseudoexperiments. The correction is
determined to be $+0.03$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, with a
negligible uncertainty. The impact of the model used to fit the invariant-mass
distribution on the measured mass is estimated by varying the shape parameters
that are fixed according to simulation, using alternative signal and
background models, and performing the fits over different mass ranges. The
largest variation in the fitted ${{\mathchar 28932\relax}^{++}_{{c}{c}}}$
masses, $0.05{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, is taken as a
systematic uncertainty. The current known value for the ${\mathchar
28932\relax}^{+}_{c}$ mass [26] is used to compute the invariant-mass
$m({{\mathchar 28932\relax}^{+}_{c}}{{\pi}^{+}})$ of the ${{\mathchar
28932\relax}^{++}_{{c}{c}}}$ candidate. Its uncertainty,
$0.30$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, is assigned as a systematic
uncertainty on the ${{\mathchar 28932\relax}^{++}_{{c}{c}}}$ mass.

The systematic uncertainties on the ratio ${\mathcal{R}({\mathcal{B}})}$ are
listed in Table 1 and are described as follows. The alternative fit models
mentioned above result in different values of the ratio $r_{N}$. The largest
relative deviation measured, $5.2\%$, is assigned as a systematic uncertainty
on ${\mathcal{R}({\mathcal{B}})}$. The relative efficiency of the tracking,
particle identification and trigger are estimated using control samples, whose
statistical uncertainties are taken as a systematic uncertainty on
${\mathcal{R}({\mathcal{B}})}$. An additional uncertainty of 4.1% is assigned
on the track-reconstruction efficiency due to uncertainties on the material
budget of the detector and the modelling of hadronic interaction with the
detector material. The particle-identification efficiency is determined in
bins of particle momentum and pseudorapidity using control samples. The size
of the bins is increased or decreased by a factor of two and the largest
deviation on ${\mathcal{R}({\mathcal{B}})}$ is assigned as systematic
uncertainty related to the binning. An additional uncertainty of 4.2% on the
hardware trigger efficiency is determined from the ${\mathchar
28931\relax}^{0}_{b}$ control samples described above, including a statistical
uncertainty from the limited sample size, and an uncertainty that is
determined by testing the procedure in simulation and taking the deviation as
a systematic uncertainty. Combining the systematic uncertainties on the
efficiency mentioned above, a systematic uncertainty of $6.5\%$ on
$\mathcal{R}({\mathcal{B}})$ is assigned. Uncertainties from the ${\mathchar
28932\relax}^{++}_{{c}{c}}$ mass, lifetime and production spectra are
investigated, and 1.2% is assigned as a systematic uncertainty. Different
requirements on the ${\mathchar 28932\relax}^{++}_{{c}{c}}$ $p_{\mathrm{T}}$
are applied to select the ${{{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28932\relax}^{+}_{c}}{{\pi}^{+}}}$ and ${{{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}}$ decays, and this may
cause a bias if the $p_{\mathrm{T}}$ distribution of simulated ${\mathchar
28932\relax}^{++}_{{c}{c}}$ differs from that in data. To assess the size of
this effect, the measurement is repeated applying the same $p_{\mathrm{T}}$
requirement to both modes. The difference in $\mathcal{R}({\mathcal{B}})$ is
found to be $0.7\%$. A separate measurement carried out with a cut-based
selection gives a consistent result.

Table 1:  Systematic uncertainties on the measurement of the ${{\mathchar 28932\relax}^{++}_{{c}{c}}}$ mass and of the ratio of branching fractions $\mathcal{R}({\mathcal{B}})$ between the ${{{\mathchar 28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar 28932\relax}^{+}_{c}}{{\pi}^{+}}}$ and the ${{{\mathchar 28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar 28931\relax}^{+}_{c}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}}$ decay modes.  Source | Mass $[{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}]$ |  ${\cal{R}}({\mathcal{B}})$ [%]
---|---|---
Momentum calibration | 0.38 | —
Selection bias correction | 0.10 | —
Fit model | 0.05 | 5.2
Relative efficiency | — | 6.5
Simulation modelling | — | 1.2
Selection | — | 0.7
Sum in quadrature | 0.40 | 8.5

The value of ${\mathcal{R}({\mathcal{B}})}$ is measured to be
$\nobreak{0.035\pm 0.009\mathrm{\,(stat)}\pm 0.003\mathrm{\,(syst)}}$ and the
${\mathchar 28932\relax}^{++}_{{c}{c}}$ mass is measured to be $3620.6\pm
1.5\mathrm{\,(stat)}\pm 0.4\mathrm{\,(syst)}\pm 0.3\,({{\mathchar
28932\relax}^{+}_{c}}){\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, which is
consistent with the mass measured in the final state ${{\mathchar
28931\relax}^{+}_{c}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$,
$3621.40\,\pm\,0.72\mathrm{\,(stat)}\pm\,0.27\,\mathrm{\,(syst)}\pm\,0.14\,{\,({{\mathchar
28931\relax}^{+}_{c}})}$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ [1].
Averaging over the two measurements, the ${\mathchar
28932\relax}^{++}_{{c}{c}}$ mass is determined to be $3621.24\pm
0.65\mathrm{\,(stat)}\pm
0.31\mathrm{\,(syst)}{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ (see the
Appendix 1 for the comparisons between the measured ${\mathchar
28932\relax}^{++}_{{c}{c}}$ masses and combined result). The combination is
performed using the Best Linear Unbiased Estimate (BLUE) method [34, 35]. In
the combination, the systematic uncertainties are assumed to be uncorrelated
except for the momentum scale calibration.

In summary, a new decay mode of the doubly charmed baryon ${{{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28932\relax}^{+}_{c}}{{\pi}^{+}}}$ is observed with a statistical significance
of $\nobreak{5.9\sigma}$ in a data sample of ${p}{p}$ collisions collected by
the LHCb experiment at a center-of-mass energy of
$\sqrt{s}=13$$\mathrm{\,Te\kern-1.00006ptV}$. The ${\mathchar
28932\relax}^{++}_{{c}{c}}$ mass is consistent with the previous LHCb result
[1] and with most theoretical calculations of the ${\mathchar
28932\relax}^{++}_{{c}{c}}$ mass (see e.g. Ref. [36]). The ratio of the total
branching fractions between this decay (${{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28932\relax}^{+}_{c}}{{\pi}^{+}}$) and the reference mode (${{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$) is consistent with the
prediction of Ref. [4], which, however, has large uncertainties. Therefore,
this measurement provides important information towards an improved
understanding of the decays of doubly charmed baryons.

## Acknowledgements

We thank Chao-Hsi Chang, Cai-Dian Lü, Wei Wang, Xing-Gang Wu, and Fu-Sheng Yu
for frequent and interesting discussions on the production and decays of
double-heavy-flavor baryons. 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); MOST and NSFC (China); CNRS/IN2P3 (France); BMBF,
DFG and MPG (Germany); INFN (Italy); NWO (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 (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);
ANR, Labex P2IO and OCEVU, and Région Auvergne-Rhône-Alpes (France); Key
Research Program of Frontier Sciences of CAS, CAS PIFI, and the Thousand
Talents Program (China); RFBR, RSF and Yandex LLC (Russia); GVA, XuntaGal and
GENCAT (Spain); Herchel Smith Fund, the Royal Society, the English-Speaking
Union and the Leverhulme Trust (United Kingdom); Laboratory Directed Research
and Development program of LANL (USA).

## References

  * [1] LHCb collaboration, R. Aaij et al., _Observation of the doubly charmed baryon ${\mathchar 28932\relax}_{cc}^{++}$_, Phys. Rev. Lett. 119 (2017) 112001, arXiv:1707.01621
  * [2] LHCb collaboration, R. Aaij et al., _Measurement of the lifetime of the doubly charmed baryon ${\mathchar 28932\relax}_{cc}^{++}$_, Phys. Rev. Lett. 121 (2018) 052002, arXiv:1806.02744
  * [3] N. Sharma and R. Dhir, _Estimates of W-exchange contributions to $\Xi_{cc}$ decays_, Phys. Rev. D96 (2017) 113006, arXiv:1709.08217
  * [4] F.-S. Yu et al., _Discovery potentials of doubly charmed baryons_ , Chin. Phys. C42 (2018) 051001, arXiv:1703.09086
  * [5] LHCb collaboration, A. A. Alves Jr. et al., _The LHCb detector at the LHC_, JINST 3 (2008) S08005
  * [6] LHCb collaboration, R. Aaij et al., _LHCb detector performance_ , Int. J. Mod. Phys. A30 (2015) 1530022, arXiv:1412.6352
  * [7] R. Aaij et al., _Performance of the LHCb Vertex Locator_ , JINST 9 (2014) P09007, arXiv:1405.7808
  * [8] R. Arink et al., _Performance of the LHCb Outer Tracker_ , JINST 9 (2014) P01002, arXiv:1311.3893
  * [9] M. Adinolfi et al., _Performance of the LHCb RICH detector at the LHC_, Eur. Phys. J. C73 (2013) 2431, arXiv:1211.6759
  * [10] A. A. Alves Jr. et al., _Performance of the LHCb muon system_ , JINST 8 (2013) P02022, arXiv:1211.1346
  * [11] R. Aaij et al., _The LHCb trigger and its performance in 2011_, JINST 8 (2013) P04022, arXiv:1211.3055
  * [12] F. Archilli et al., _Performance of the muon identification at LHCb_ , JINST 8 (2013) P10020, arXiv:1306.0249
  * [13] G. Dujany and B. Storaci, _Real-time alignment and calibration of the LHCb Detector in Run II_ , J. Phys. Conf. Ser. 664 (2015) 082010
  * [14] T. Sjöstrand, S. Mrenna, and P. Skands, _A brief introduction to PYTHIA 8.1_ , Comput. Phys. Commun. 178 (2008) 852, arXiv:0710.3820
  * [15] T. Sjöstrand, S. Mrenna, and P. Skands, _PYTHIA 6.4 physics and manual_ , JHEP 05 (2006) 026, arXiv:hep-ph/0603175
  * [16] I. Belyaev et al., _Handling of the generation of primary events in Gauss, the LHCb simulation framework_ , J. Phys. Conf. Ser. 331 (2011) 032047
  * [17] C.-H. Chang, J.-X. Wang, and X.-G. Wu, _GENXICC: a generator for hadronic production of the double heavy baryons ${\mathchar 28932\relax}_{{c}{c}}$, ${\mathchar 28932\relax}_{{b}{c}}$ and ${\mathchar 28932\relax}_{{b}{b}}$_, Comput. Phys. Commun. 177 (2007) 467, arXiv:hep-ph/0702054
  * [18] C.-H. Chang, J.-X. Wang, and X.-G. Wu, _GENXICC2.0: an upgraded version of the generator for hadronic production of double heavy baryons ${\mathchar 28932\relax}_{{c}{c}}$, ${\mathchar 28932\relax}_{{b}{c}}$ and ${\mathchar 28932\relax}_{{b}{b}}$_, Comput. Phys. Commun. 181 (2010) 1144, arXiv:0910.4462
  * [19] D. J. Lange, _The EvtGen particle decay simulation package_ , Nucl. Instrum. Meth. A462 (2001) 152
  * [20] P. Golonka and Z. Was, _PHOTOS Monte Carlo: A precision tool for QED corrections in $Z$ and $W$ decays_, Eur. Phys. J. C45 (2006) 97, arXiv:hep-ph/0506026
  * [21] Geant4 collaboration, J. Allison et al., _Geant4 developments and applications_ , IEEE Trans. Nucl. Sci. 53 (2006) 270
  * [22] Geant4 collaboration, S. Agostinelli et al., _Geant4: A simulation toolkit_ , Nucl. Instrum. Meth. A506 (2003) 250
  * [23] M. Clemencic et al., _The LHCb simulation application, Gauss: Design, evolution and experience_, J. Phys. Conf. Ser. 331 (2011) 032023
  * [24] H. Voss, A. Hoecker, J. Stelzer, and F. Tegenfeldt, _TMVA - Toolkit for Multivariate Data Analysis_ , PoS ACAT (2007) 040
  * [25] A. Hoecker et al., _TMVA 4 — Toolkit for Multivariate Data Analysis. Users Guide._ , arXiv:physics/0703039
  * [26] Particle Data Group, M. Tanabashi et al., _Review of particle physics_ , Phys. Rev. D98 (2018) 030001
  * [27] W. D. Hulsbergen, _Decay chain fitting with a Kalman filter_ , Nucl. Instrum. Meth. A552 (2005) 566, arXiv:physics/0503191
  * [28] G. Punzi, _Sensitivity of searches for new signals and its optimization_ , eConf C030908 (2003) MODT002, arXiv:physics/0308063
  * [29] T. Skwarnicki, A study of the radiative cascade transitions between the Upsilon-prime and Upsilon resonances, PhD thesis, Institute of Nuclear Physics, Krakow, 1986, DESY-F31-86-02
  * [30] LHCb collaboration, R. Aaij et al., _Measurement of the track reconstruction efficiency at LHCb_ , JINST 10 (2015) P02007, arXiv:1408.1251
  * [31] LHCb collaboration, R. Aaij et al., _Measurements of the branching fractions for $B_{(s)}\rightarrow D_{(s)}\pi\pi\pi$ and ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{\mathchar 28931\relax}^{+}_{c}}\pi\pi\pi$_, Phys. Rev. D84 (2011) 092001, Erratum ibid. D85 (2012) 039904, arXiv:1109.6831
  * [32] LHCb collaboration, R. Aaij et al., _Measurement of ${b}$-hadron masses_, Phys. Lett. B708 (2012) 241, arXiv:1112.4896
  * [33] LHCb collaboration, R. Aaij et al., _Precision measurement of ${D}$ meson mass differences_, JHEP 06 (2013) 065, arXiv:1304.6865
  * [34] L. Lyons, D. Gibaut, and P. Clifford, _How to combine correlated estimates of a single physical quantity_ , Nucl. Instrum. Meth. A270 (1988) 110
  * [35] A. Valassi, _Combining correlated measurements of several different physical quantities_ , Nucl. Instrum. Meth. A500 (2003) 391
  * [36] C. Alexandrou and C. Kallidonis, _Low-lying baryon masses using $N_{f}=2$ twisted mass clover-improved fermions directly at the physical pion mass_, Phys. Rev. D96 (2017) 034511, arXiv:1704.02647

LHCb collaboration

R. Aaij27, B. Adeva41, M. Adinolfi48, C.A. Aidala73, Z. Ajaltouni5, S. Akar59,
P. Albicocco18, J. Albrecht10, F. Alessio42, M. Alexander53, A. Alfonso
Albero40, S. Ali27, G. Alkhazov33, P. Alvarez Cartelle55, A.A. Alves Jr41, S.
Amato2, S. Amerio23, Y. Amhis7, L. An3, L. Anderlini17, G. Andreassi43, M.
Andreotti16,g, J.E. Andrews60, R.B. Appleby56, F. Archilli27, P. d’Argent12,
J. Arnau Romeu6, A. Artamonov39, M. Artuso61, K. Arzymatov37, E. Aslanides6,
M. Atzeni44, B. Audurier22, S. Bachmann12, J.J. Back50, S. Baker55, V.
Balagura7,b, W. Baldini16, A. Baranov37, R.J. Barlow56, S. Barsuk7, W.
Barter56, F. Baryshnikov70, V. Batozskaya31, B. Batsukh61, V. Battista43, A.
Bay43, J. Beddow53, F. Bedeschi24, I. Bediaga1, A. Beiter61, L.J. Bel27, S.
Belin22, N. Beliy63, V. Bellee43, N. Belloli20,i, K. Belous39, I.
Belyaev34,42, E. Ben-Haim8, G. Bencivenni18, S. Benson27, S. Beranek9, A.
Berezhnoy35, R. Bernet44, D. Berninghoff12, E. Bertholet8, A. Bertolin23, C.
Betancourt44, F. Betti15,42, M.O. Bettler49, M. van Beuzekom27, Ia.
Bezshyiko44, S. Bhasin48, J. Bhom29, S. Bifani47, P. Billoir8, A. Birnkraut10,
A. Bizzeti17,u, M. Bjørn57, M.P. Blago42, T. Blake50, F. Blanc43, S. Blusk61,
D. Bobulska53, V. Bocci26, O. Boente Garcia41, T. Boettcher58, A. Bondar38,w,
N. Bondar33, S. Borghi56,42, M. Borisyak37, M. Borsato41, F. Bossu7, M.
Boubdir9, T.J.V. Bowcock54, C. Bozzi16,42, S. Braun12, M. Brodski42, J.
Brodzicka29, A. Brossa Gonzalo50, D. Brundu22, E. Buchanan48, A. Buonaura44,
C. Burr56, A. Bursche22, J. Buytaert42, W. Byczynski42, S. Cadeddu22, H.
Cai64, R. Calabrese16,g, R. Calladine47, M. Calvi20,i, M. Calvo Gomez40,m, A.
Camboni40,m, P. Campana18, D.H. Campora Perez42, L. Capriotti56, A.
Carbone15,e, G. Carboni25, R. Cardinale19,h, A. Cardini22, P. Carniti20,i, L.
Carson52, K. Carvalho Akiba2, G. Casse54, L. Cassina20, M. Cattaneo42, G.
Cavallero19,h, R. Cenci24,p, D. Chamont7, M.G. Chapman48, M. Charles8, Ph.
Charpentier42, G. Chatzikonstantinidis47, M. Chefdeville4, V. Chekalina37, C.
Chen3, S. Chen22, S.-G. Chitic42, V. Chobanova41, M. Chrzaszcz42, A.
Chubykin33, P. Ciambrone18, X. Cid Vidal41, G. Ciezarek42, P.E.L. Clarke52, M.
Clemencic42, H.V. Cliff49, J. Closier42, V. Coco42, J.A.B. Coelho7, J. Cogan6,
E. Cogneras5, L. Cojocariu32, P. Collins42, T. Colombo42, A. Comerma-
Montells12, A. Contu22, G. Coombs42, S. Coquereau40, G. Corti42, M. Corvo16,g,
C.M. Costa Sobral50, B. Couturier42, G.A. Cowan52, D.C. Craik58, A.
Crocombe50, M. Cruz Torres1, R. Currie52, C. D’Ambrosio42, F. Da Cunha
Marinho2, C.L. Da Silva74, E. Dall’Occo27, J. Dalseno48, A. Danilina34, A.
Davis3, O. De Aguiar Francisco42, K. De Bruyn42, S. De Capua56, M. De Cian43,
J.M. De Miranda1, L. De Paula2, M. De Serio14,d, P. De Simone18, C.T. Dean53,
D. Decamp4, L. Del Buono8, B. Delaney49, H.-P. Dembinski11, M. Demmer10, A.
Dendek30, D. Derkach37, O. Deschamps5, F. Desse7, F. Dettori54, B. Dey65, A.
Di Canto42, P. Di Nezza18, S. Didenko70, H. Dijkstra42, F. Dordei42, M.
Dorigo42,y, A. Dosil Suárez41, L. Douglas53, A. Dovbnya45, K. Dreimanis54, L.
Dufour27, G. Dujany8, P. Durante42, J.M. Durham74, D. Dutta56, R.
Dzhelyadin39, M. Dziewiecki12, A. Dziurda29, A. Dzyuba33, S. Easo51, U.
Egede55, V. Egorychev34, S. Eidelman38,w, S. Eisenhardt52, U. Eitschberger10,
R. Ekelhof10, L. Eklund53, S. Ely61, A. Ene32, S. Escher9, S. Esen27, T.
Evans59, A. Falabella15, N. Farley47, S. Farry54, D. Fazzini20,42,i, L.
Federici25, P. Fernandez Declara42, A. Fernandez Prieto41, F. Ferrari15, L.
Ferreira Lopes43, F. Ferreira Rodrigues2, M. Ferro-Luzzi42, S. Filippov36,
R.A. Fini14, M. Fiorini16,g, M. Firlej30, C. Fitzpatrick43, T. Fiutowski30, F.
Fleuret7,b, M. Fontana22,42, F. Fontanelli19,h, R. Forty42, V. Franco Lima54,
M. Frank42, C. Frei42, J. Fu21,q, W. Funk42, C. Färber42, M. Féo Pereira
Rivello Carvalho27, E. Gabriel52, A. Gallas Torreira41, D. Galli15,e, S.
Gallorini23, S. Gambetta52, Y. Gan3, M. Gandelman2, P. Gandini21, Y. Gao3,
L.M. Garcia Martin72, B. Garcia Plana41, J. García Pardiñas44, J. Garra
Tico49, L. Garrido40, D. Gascon40, C. Gaspar42, L. Gavardi10, G. Gazzoni5, D.
Gerick12, E. Gersabeck56, M. Gersabeck56, T. Gershon50, D. Gerstel6, Ph.
Ghez4, S. Gianì43, V. Gibson49, O.G. Girard43, L. Giubega32, K. Gizdov52, V.V.
Gligorov8, D. Golubkov34, A. Golutvin55,70, A. Gomes1,a, I.V. Gorelov35, C.
Gotti20,i, E. Govorkova27, J.P. Grabowski12, R. Graciani Diaz40, L.A. Granado
Cardoso42, E. Graugés40, E. Graverini44, G. Graziani17, A. Grecu32, R.
Greim27, P. Griffith22, L. Grillo56, L. Gruber42, B.R. Gruberg Cazon57, O.
Grünberg67, C. Gu3, E. Gushchin36, Yu. Guz39,42, T. Gys42, C. Göbel62, T.
Hadavizadeh57, C. Hadjivasiliou5, G. Haefeli43, C. Haen42, S.C. Haines49, B.
Hamilton60, X. Han12, T.H. Hancock57, S. Hansmann-Menzemer12, N. Harnew57,
S.T. Harnew48, T. Harrison54, C. Hasse42, M. Hatch42, J. He63, M. Hecker55, K.
Heinicke10, A. Heister10, K. Hennessy54, L. Henry72, E. van Herwijnen42, M.
Heß67, A. Hicheur2, R. Hidalgo Charman56, D. Hill57, M. Hilton56, P.H.
Hopchev43, W. Hu65, W. Huang63, Z.C. Huard59, W. Hulsbergen27, T. Humair55, M.
Hushchyn37, D. Hutchcroft54, D. Hynds27, P. Ibis10, M. Idzik30, P. Ilten47, K.
Ivshin33, R. Jacobsson42, J. Jalocha57, E. Jans27, A. Jawahery60, F. Jiang3,
M. John57, D. Johnson42, C.R. Jones49, C. Joram42, B. Jost42, N. Jurik57, S.
Kandybei45, M. Karacson42, J.M. Kariuki48, S. Karodia53, N. Kazeev37, M.
Kecke12, F. Keizer49, M. Kelsey61, M. Kenzie49, T. Ketel28, E. Khairullin37,
B. Khanji12, C. Khurewathanakul43, K.E. Kim61, T. Kirn9, S. Klaver18, K.
Klimaszewski31, T. Klimkovich11, S. Koliiev46, M. Kolpin12, R. Kopecna12, P.
Koppenburg27, I. Kostiuk27, S. Kotriakhova33, M. Kozeiha5, L. Kravchuk36, M.
Kreps50, F. Kress55, P. Krokovny38,w, W. Krupa30, W. Krzemien31, W.
Kucewicz29,l, M. Kucharczyk29, V. Kudryavtsev38,w, A.K. Kuonen43, T.
Kvaratskheliya34,42, D. Lacarrere42, G. Lafferty56, A. Lai22, D. Lancierini44,
G. Lanfranchi18, C. Langenbruch9, T. Latham50, C. Lazzeroni47, R. Le Gac6, A.
Leflat35, J. Lefrançois7, R. Lefèvre5, F. Lemaitre42, O. Leroy6, T. Lesiak29,
B. Leverington12, P.-R. Li63, T. Li3, Z. Li61, X. Liang61, T. Likhomanenko69,
R. Lindner42, F. Lionetto44, V. Lisovskyi7, X. Liu3, D. Loh50, A. Loi22, I.
Longstaff53, J.H. Lopes2, G.H. Lovell49, D. Lucchesi23,o, M. Lucio Martinez41,
A. Lupato23, E. Luppi16,g, O. Lupton42, A. Lusiani24, X. Lyu63, F. Machefert7,
F. Maciuc32, V. Macko43, P. Mackowiak10, S. Maddrell-Mander48, O. Maev33,42,
K. Maguire56, D. Maisuzenko33, M.W. Majewski30, S. Malde57, B. Malecki29, A.
Malinin69, T. Maltsev38,w, G. Manca22,f, G. Mancinelli6, D. Marangotto21,q, J.
Maratas5,v, J.F. Marchand4, U. Marconi15, C. Marin Benito7, M. Marinangeli43,
P. Marino43, J. Marks12, P.J. Marshall54, G. Martellotti26, M. Martin6, M.
Martinelli42, D. Martinez Santos41, F. Martinez Vidal72, A. Massafferri1, M.
Materok9, R. Matev42, A. Mathad50, Z. Mathe42, C. Matteuzzi20, A. Mauri44, E.
Maurice7,b, B. Maurin43, A. Mazurov47, M. McCann55,42, A. McNab56, R.
McNulty13, J.V. Mead54, B. Meadows59, C. Meaux6, F. Meier10, N. Meinert67, D.
Melnychuk31, M. Merk27, A. Merli21,q, E. Michielin23, D.A. Milanes66, E.
Millard50, M.-N. Minard4, L. Minzoni16,g, D.S. Mitzel12, A. Mogini8, J. Molina
Rodriguez1,z, T. Mombächer10, I.A. Monroy66, S. Monteil5, M. Morandin23, G.
Morello18, M.J. Morello24,t, O. Morgunova69, J. Moron30, A.B. Morris6, R.
Mountain61, F. Muheim52, M. Mulder27, C.H. Murphy57, D. Murray56, A. Mödden
10, D. Müller42, J. Müller10, K. Müller44, V. Müller10, P. Naik48, T.
Nakada43, R. Nandakumar51, A. Nandi57, T. Nanut43, I. Nasteva2, M. Needham52,
N. Neri21, S. Neubert12, N. Neufeld42, M. Neuner12, T.D. Nguyen43, C. Nguyen-
Mau43,n, S. Nieswand9, R. Niet10, N. Nikitin35, A. Nogay69, N.S. Nolte42, D.P.
O’Hanlon15, A. Oblakowska-Mucha30, V. Obraztsov39, S. Ogilvy18, R.
Oldeman22,f, C.J.G. Onderwater68, A. Ossowska29, J.M. Otalora Goicochea2, P.
Owen44, A. Oyanguren72, P.R. Pais43, T. Pajero24,t, A. Palano14, M.
Palutan18,42, G. Panshin71, A. Papanestis51, M. Pappagallo52, L.L.
Pappalardo16,g, W. Parker60, C. Parkes56, G. Passaleva17,42, A. Pastore14, M.
Patel55, C. Patrignani15,e, A. Pearce42, A. Pellegrino27, G. Penso26, M. Pepe
Altarelli42, S. Perazzini42, D. Pereima34, P. Perret5, L. Pescatore43, K.
Petridis48, A. Petrolini19,h, A. Petrov69, S. Petrucci52, M. Petruzzo21,q, B.
Pietrzyk4, G. Pietrzyk43, M. Pikies29, M. Pili57, D. Pinci26, J. Pinzino42, F.
Pisani42, A. Piucci12, V. Placinta32, S. Playfer52, J. Plews47, M. Plo
Casasus41, F. Polci8, M. Poli Lener18, A. Poluektov50, N. Polukhina70,c, I.
Polyakov61, E. Polycarpo2, G.J. Pomery48, S. Ponce42, A. Popov39, D.
Popov47,11, S. Poslavskii39, C. Potterat2, E. Price48, J. Prisciandaro41, C.
Prouve48, V. Pugatch46, A. Puig Navarro44, H. Pullen57, G. Punzi24,p, W.
Qian63, J. Qin63, R. Quagliani8, B. Quintana5, B. Rachwal30, J.H.
Rademacker48, M. Rama24, M. Ramos Pernas41, M.S. Rangel2, F. Ratnikov37,x, G.
Raven28, M. Ravonel Salzgeber42, M. Reboud4, F. Redi43, S. Reichert10, A.C.
dos Reis1, F. Reiss8, C. Remon Alepuz72, Z. Ren3, V. Renaudin7, S.
Ricciardi51, S. Richards48, K. Rinnert54, P. Robbe7, A. Robert8, A.B.
Rodrigues43, E. Rodrigues59, J.A. Rodriguez Lopez66, M. Roehrken42, A.
Rogozhnikov37, S. Roiser42, A. Rollings57, V. Romanovskiy39, A. Romero
Vidal41, M. Rotondo18, M.S. Rudolph61, T. Ruf42, J. Ruiz Vidal72, J.J.
Saborido Silva41, N. Sagidova33, B. Saitta22,f, V. Salustino Guimaraes62, C.
Sanchez Gras27, C. Sanchez Mayordomo72, B. Sanmartin Sedes41, R.
Santacesaria26, C. Santamarina Rios41, M. Santimaria18, E. Santovetti25,j, G.
Sarpis56, A. Sarti18,k, C. Satriano26,s, A. Satta25, M. Saur63, D.
Savrina34,35, S. Schael9, M. Schellenberg10, M. Schiller53, H. Schindler42, M.
Schmelling11, T. Schmelzer10, B. Schmidt42, O. Schneider43, A. Schopper42,
H.F. Schreiner59, M. Schubiger43, M.H. Schune7, R. Schwemmer42, B. Sciascia18,
A. Sciubba26,k, A. Semennikov34, E.S. Sepulveda8, A. Sergi47,42, N. Serra44,
J. Serrano6, L. Sestini23, A. Seuthe10, P. Seyfert42, M. Shapkin39, Y.
Shcheglov33,†, T. Shears54, L. Shekhtman38,w, V. Shevchenko69, E. Shmanin70,
B.G. Siddi16, R. Silva Coutinho44, L. Silva de Oliveira2, G. Simi23,o, S.
Simone14,d, N. Skidmore12, T. Skwarnicki61, J.G. Smeaton49, E. Smith9, I.T.
Smith52, M. Smith55, M. Soares15, l. Soares Lavra1, M.D. Sokoloff59, F.J.P.
Soler53, B. Souza De Paula2, B. Spaan10, P. Spradlin53, F. Stagni42, M.
Stahl12, S. Stahl42, P. Stefko43, S. Stefkova55, O. Steinkamp44, S. Stemmle12,
O. Stenyakin39, M. Stepanova33, H. Stevens10, A. Stocchi7, S. Stone61, B.
Storaci44, S. Stracka24,p, M.E. Stramaglia43, M. Straticiuc32, U. Straumann44,
S. Strokov71, J. Sun3, L. Sun64, K. Swientek30, V. Syropoulos28, T. Szumlak30,
M. Szymanski63, S. T’Jampens4, Z. Tang3, A. Tayduganov6, T. Tekampe10, G.
Tellarini16, F. Teubert42, E. Thomas42, J. van Tilburg27, M.J. Tilley55, V.
Tisserand5, M. Tobin30, S. Tolk42, L. Tomassetti16,g, D. Tonelli24, D.Y. Tou8,
R. Tourinho Jadallah Aoude1, E. Tournefier4, M. Traill53, M.T. Tran43, A.
Trisovic49, A. Tsaregorodtsev6, G. Tuci24, A. Tully49, N. Tuning27,42, A.
Ukleja31, A. Usachov7, A. Ustyuzhanin37, U. Uwer12, A. Vagner71, V. Vagnoni15,
A. Valassi42, S. Valat42, G. Valenti15, R. Vazquez Gomez42, P. Vazquez
Regueiro41, S. Vecchi16, M. van Veghel27, J.J. Velthuis48, M. Veltri17,r, G.
Veneziano57, A. Venkateswaran61, T.A. Verlage9, M. Vernet5, M. Veronesi27,
N.V. Veronika13, M. Vesterinen57, J.V. Viana Barbosa42, D. Vieira63, M.
Vieites Diaz41, H. Viemann67, X. Vilasis-Cardona40,m, A. Vitkovskiy27, M.
Vitti49, V. Volkov35, A. Vollhardt44, B. Voneki42, A. Vorobyev33, V.
Vorobyev38,w, J.A. de Vries27, C. Vázquez Sierra27, R. Waldi67, J. Walsh24, J.
Wang61, M. Wang3, Y. Wang65, Z. Wang44, D.R. Ward49, H.M. Wark54, N.K.
Watson47, D. Websdale55, A. Weiden44, C. Weisser58, M. Whitehead9, J. Wicht50,
G. Wilkinson57, M. Wilkinson61, I. Williams49, M.R.J. Williams56, M.
Williams58, T. Williams47, F.F. Wilson51,42, J. Wimberley60, M. Winn7, J.
Wishahi10, W. Wislicki31, M. Witek29, G. Wormser7, S.A. Wotton49, K. Wyllie42,
D. Xiao65, Y. Xie65, A. Xu3, M. Xu65, Q. Xu63, Z. Xu3, Z. Xu4, Z. Yang3, Z.
Yang60, Y. Yao61, L.E. Yeomans54, H. Yin65, J. Yu65,ab, X. Yuan61, O.
Yushchenko39, K.A. Zarebski47, M. Zavertyaev11,c, D. Zhang65, L. Zhang3, W.C.
Zhang3,aa, Y. Zhang7, A. Zhelezov12, Y. Zheng63, X. Zhu3, V. Zhukov9,35, J.B.
Zonneveld52, S. Zucchelli15.

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
4Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy,
France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
7LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France
8LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, 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
14INFN Sezione di Bari, Bari, Italy
15INFN Sezione di Bologna, Bologna, Italy
16INFN Sezione di Ferrara, Ferrara, Italy
17INFN Sezione di Firenze, Firenze, Italy
18INFN Laboratori Nazionali di Frascati, Frascati, Italy
19INFN Sezione di Genova, Genova, Italy
20INFN Sezione di Milano-Bicocca, Milano, Italy
21INFN Sezione di Milano, Milano, Italy
22INFN Sezione di Cagliari, Monserrato, Italy
23INFN Sezione di Padova, Padova, Italy
24INFN Sezione di Pisa, Pisa, Italy
25INFN Sezione di Roma Tor Vergata, Roma, Italy
26INFN Sezione di Roma La Sapienza, Roma, Italy
27Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
28Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, Netherlands
29Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
30AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
31National Center for Nuclear Research (NCBJ), Warsaw, Poland
32Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
33Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
34Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
35Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
36Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
37Yandex School of Data Analysis, Moscow, Russia
38Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
39Institute for High Energy Physics (IHEP), Protvino, Russia
40ICCUB, Universitat de Barcelona, Barcelona, Spain
41Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
42European Organization for Nuclear Research (CERN), Geneva, Switzerland
43Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
44Physik-Institut, Universität Zürich, Zürich, Switzerland
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
64School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
65Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
66Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
67Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
68Van Swinderen Institute, University of Groningen, Groningen, Netherlands,
associated to 27
69National Research Centre Kurchatov Institute, Moscow, Russia, associated to
34
70National University of Science and Technology ”MISIS”, Moscow, Russia,
associated to 34
71National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
34
72Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain, associated to 40
73University of Michigan, Ann Arbor, United States, associated to 61
74Los Alamos National Laboratory (LANL), Los Alamos, United States, associated
to 61

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, Vietnam
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
vMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
wNovosibirsk State University, Novosibirsk, Russia
xNational Research University Higher School of Economics, Moscow, Russia
ySezione INFN di Trieste, Trieste, Italy
zEscuela Agrícola Panamericana, San Antonio de Oriente, Honduras
aaSchool of Physics and Information Technology, Shaanxi Normal University
(SNNU), Xi’an, China
abPhysics and Micro Electronic College, Hunan University, Changsha City, China
†Deceased

##  1 Supplementary material for LHCb-PAPER-2018-026

Figure 3 shows the comparison between ${\mathchar 28932\relax}^{++}_{{c}{c}}$
mass measured from ${{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$ and ${{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28932\relax}^{+}_{c}}{{\pi}^{+}}$ channel, and the combined mass value using
these two results.

Figure 3: Measured ${\mathchar 28932\relax}^{++}_{{c}{c}}$ masses obtained
with the decay modes ${{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$ and ${{\mathchar
28932\relax}^{++}_{{c}{c}}}\rightarrow{{\mathchar
28932\relax}^{+}_{c}}{{\pi}^{+}}$, and the combined result. The darker green
band represents the statistical uncertainty on the combination, and the
lighter green band represents the total uncertainty on the combination.