Search for the doubly charmed baryon Ωcc+

A search for the doubly charmed baryon Ωcc+ with the decay mode Ωcc+ → Ξc+K−π+ is performed using proton-proton collision data at a centre-of-mass energy of 13 TeV collected by the LHCb experiment from 2016 to 2018, corresponding to an integrated luminosity of 5.4 fb−1. No significant signal is observed within the invariant mass range of 3.6 to 4.0GeV/c2. Upper limits are set on the ratio R of the production cross-section times the total branching fraction of the Ωcc+ → Ξc+K−π+ decay with respect to the Ξcc++→Λc+K−π+π+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Xi _{cc}^{ + + } \to \Lambda _c^ + {K^ - }{\pi ^ + }{\pi ^ + }$$\end{document} decay. Upper limits at 95% credibility level for R in the range 0.005 to 0.11 are obtained for different hypotheses on the Ωcc+ mass and lifetime in the rapidity range from 2.0 to 4.5 and transverse momentum range from 4 to 15 GeV/c.


Introduction
The quark model [1][2][3] predicts the existence of multiplets of baryon states with a structure containing three valence quarks, two charm quarks and a light quark (u, d or s).There are three doubly charmed, weakly decaying states expected: a Ξ cc isodoublet (ccu, ccd) and an Ω + cc isosinglet (ccs), each with spin-parity J P = 1/2 + .Theoretical models [4][5][6][7] predict that the light quark moves with a large relative velocity with respect to the bound (cc)-diquark inside the baryon and experiences a short-range of QCD potential.
The Ξ ++ cc baryon with mass 3620.6 ± 1.6 MeV/c 2 was first observed by the LHCb collaboration in the Λ + c K − π + π + decay 1 [8], and confirmed in the Ξ + c π + decay [9].The search for Ξ + cc via its decay to Λ + c K − π + was updated recently by the LHCb collaboration, and no significant signal was found [10].The Ω + cc mass is predicted to be in the range 3.6 − 3.9 GeV/c 2 [6,[11][12][13][14][15][16][17][18][19][20] and its lifetime is predicted to be 75 − 180 fs [6,[21][22][23][24][25][26].Due to destructive Pauli interference [21], the Ξ ++ cc and Ω + cc baryons have a larger lifetime than that of the Ξ + cc baryon which is shortened by the contribution from W boson exchange between the charm and down quarks.In proton-proton (pp) collisions at a centre-of-mass energy of 13 TeV, the production cross-section of the doubly charmed baryons is predicted to be within the range of 60 − 1800 nb [5,7,[26][27][28][29][30], which is between 10 −4 and 10 −3 times that of the total charm quark production [31].The production cross-section of the Ω + cc baryon is expected to be about 1/3 of those of the Ξ + cc and Ξ ++ cc baryons due to the presence of an s quark [32].A discovery of the Ω + cc baryon and measurements of its properties would validate the aforementioned theoretical predictions, and deepen our understanding on the dynamics in the production and decays of the doubly charmed baryons.In this paper, a search for the Ω + cc baryon via the Ω + cc → Ξ + c K − π + decay, which is predicted to have a relatively large branching fraction [33,34], is presented.The data are collected by the LHCb experiment in pp collisions at a centre-of-mass energy of 13 TeV in the period from 2016 to 2018.A possible Feynman diagram for this decay is shown in Fig. 1.

𝑠
In order to avoid experimenters' bias, the results of the analysis were not examined until the full procedure had been finalised.Two different selections are developed: selection A is optimised to maximise the hypothetical signal sensitivity and selection B is optimised for the production ratio measurement.The analysis strategy is defined as follows: selection A is first used to search for Ω + cc signal and evaluate its significance as a function of Ω + cc 1 Inclusion of charge-conjugated processes is implied throughout this paper.
mass.If evidence for a signal with a global significance above 3 standard deviations after considering the look-elsewhere effect would be found, the mass would be measured and Selection B would be employed to measure the production cross-section of the Ω + cc baryon; else, upper limits on the production ratio R as a function of the Ω + cc mass for different lifetime hypotheses would be set.The production ratio R, relative to the where σ is the baryon production cross-section and B is the branching fraction of the corresponding decays.Both the Ω + cc and Ξ ++ cc baryons are required to be in the rapidity range of 2.0 to 4.5 and have transverse momentum between 4 and 15 GeV/c.
The production ratio is evaluated as where ε sig and ε norm refer to the efficiencies of the Ω + cc signal and the Ξ ++ cc normalisation decay mode, respectively, N sig and N norm are the corresponding yields, and α is the single-event sensitivity.The lifetime of the Ω + cc baryon is unknown and strongly affects the selection efficiency, hence upper limits on R are quoted as a function of the Ω + cc baryon mass for a discrete set of lifetime hypotheses.

Detector and simulation
The LHCb detector [35,36] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of particles containing b or c quarks.The detector includes a high-precision tracking system consisting of a siliconstrip vertex detector surrounding the pp interaction region [37], a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes [38,39] placed downstream of the magnet.The tracking system provides a measurement of the momentum, p, of charged particles with a relative uncertainty that varies from 0.5% at low momentum to 1.0% at 200 GeV/c.The minimum distance of a track to a primary pp-collision vertex (PV), the impact parameter (IP), is measured with a resolution of (15 + 29/p T ) µm, where p T is the component of the momentum transverse to the beam, in GeV/c.Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov detectors [40].The online event selection is performed by a trigger [41], which consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, which applies a full event reconstruction.
Simulated samples are required to develop the event selection and to estimate the detector acceptance and the efficiency of the imposed selection requirements.Simulated pp collisions are generated using Pythia [42] with a specific LHCb configuration [43].A dedicated generator, GenXicc2.0[44], is used to simulate the doubly charmed baryon production.Decays of unstable particles are described by EvtGen [45], in which finalstate radiation is generated using Photos [46].The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [47] as described in Ref. [48].The Ω + cc →Ξ + c K − π + decay is assumed to proceed according to a uniform phase-space model.The Ω + cc baryon and Ξ ++ cc baryon are assumed to have no polarization.Unless otherwise stated, simulated events are generated with an Ω + cc (Ξ ++ cc ) mass of 3738 MeV/c 2 (3621 MeV/c 2 ) and a lifetime of 160 fs (256 fs).

Reconstruction and selection
The Ω + cc signal mode is reconstructed by combining a Ξ + c candidate with kaon and pion candidates coming from the same vertex.The Ξ + c candidates are firstly formed by combining three tracks originating from the same vertex, displaced with respect to the PV; at least one track is required to satisfy an inclusive software trigger based on a multivariate classifier [49,50], and the three tracks must satisfy particle identification (PID) requirements to be compatible with a pK − π + hypothesis.Then the Ξ + c candidates with good vertex quality and invariant mass within the region of 2450 to 2486 MeV/c 2 are combined with two extra tracks, identified as K − and π + , to reconstruct a Ω + cc candidate.The Ξ + c mass region is defined as 2468 ± 18 MeV/c 2 where the mean value is the known Ξ + c mass [51] and the width is corresponding to three times the mass resolution.
To improve further the Ω + cc signal purity, a multivariate classifier based on a boosted decision tree (BDT) [52,53] is developed to suppress combinatorial background.The classifier is trained using simulated Ω + cc events as signal and wrong-sign Ξ + c K − π − combinations in data with mass in the interval 3600 to 4000 MeV/c 2 to represent background.
For selection A, no specific trigger requirement is applied.A multivariate selection is trained with two sets of variables which show good discrimination between Ω + cc signal and background.The first set contains variables related to the reconstructed Ω + cc candidates, including the Ω + cc decay vertex-fit quality, such as χ 2 IP , the pointing angle and the flightdistance χ 2 .Here χ 2 IP is the difference in χ 2 of the PV reconstructed with and without the Ω + cc candidate, the pointing angle is the three-dimensional angle between the Ω + cc candidate momentum direction and the vector joining the PV and the reconstructed Ω + cc decay vertex, while the flight-distance χ 2 is defined as the χ 2 of the hypothesis that the decay vertex of the candidate coincides with its associated PV.The second set adds variables related to the decay products (p, K − and π + from the Ξ + c decay, and K − and π + from the Ω + cc decay), including momentum, transverse momentum, χ 2 IP and PID variables.The threshold of the multivariate output is determined by maximising the figure of merit ε/ 5/2 + √ N B [54], where ε is the estimated MVA selection efficiency, 5/2 corresponds to 5 standard deviations in a Gaussian significance test, and N B is the expected number of background candidates in the signal region, estimated with the wrong-sign Ξ + c K − π − combinations in the mass region of ±12.5 MeV/c 2 around the Ω + cc mass of 3738 MeV/c 2 used in the simulation, taking into account the difference of the background level for the signal sample and the wrong-sign sample.
After the multivariate selection, the reconstructed Ω + cc candidates could suffer from background from candidates reconstructed with clone tracks, i.e. reconstructed tracks sharing a large portion of their detector hits.Clone tracks could be included in a Ω + cc candidate, when one is used for the π + candidate from the Ξ + c decay and its clone for the π + candidate from the Ω + cc decay.To avoid that, candidates with the angle between each pair of identically charged tracks smaller than 0.5 mrad are removed.The Ω + cc candidates could also be formed by the same five final tracks but with two tracks interchanged, e.g. the K − (π + ) candidate from the Ξ + c decay is swapped with the K − (π + ) candidate from the Ω + cc decay.In this case, only one candidate is chosen randomly.For selection B, the multivariate selection is similar to selection A except that the PID variables of the K − and π + candidates from the Ω + cc decay are not used in the training to ease the efficiency determination.Furthermore, an additional hardware trigger requirement is imposed on candidates for both the signal and the normalisation modes to minimise differences between data and simulation.The data sets are split into two disjoint subsamples.One subsample is triggered on signals associated with one of the reconstructed Ξ + c candidates with high transverse energy deposits in the calorimeters (TOS), and the other is triggered on signals exclusively unrelated to the Ω + cc candidate (exTIS).
The reconstruction and selection requirements of the Ξ ++ cc normalisation mode are similar to those in the Ξ + cc search [10,31].Both Ω + cc and Ξ ++ cc candidates are required to be in the fiducial region of rapidity 2.0 < y < 4.5 and transverse momentum 4 < p T < 15 GeV/c.

Yield measurements
After applying selection A to the full data sample, the invariant mass distribution m(Ξ + c K − π + ) of selected Ω + cc candidates is shown in Fig. 2. To improve the mass resolution, the variable m(Ξ + c K − π + ) is defined as the difference of the reconstructed mass of the Ω + cc and Ξ + c candidates plus the known Ξ + c mass [51].The m(Ξ + c K − π + ) distribution is fitted with a sum of signal and background components, where the signal component is described by the sum of two Crystal Ball functions [55] and the background component by a second-order Chebyshev function.The parameters of the signal shape are fixed from simulation, where the width is found to be around 5.5 MeV/c 2 .The parameters of background shape are obtained from a fit to the wrong-sign Ξ + c K − π − combinations.An unbinned maximum likelihood fit is performed with the peak position varied in steps of   2 MeV/c 2 , and the largest signal contribution is found for an Ω + cc mass of 3876 MeV/c 2 .The local significance of the signal peak is quantified with a p-value, which is calculated as the likelihood ratio of the background plus signal hypothesis and the backgroundonly hypothesis [56,57].The local p-value is plotted in Fig. 3 as a function of mass, m(Ξ + c K − π + ), showing a dip around 3876 MeV/c 2 , which has the largest local significance, corresponding to 3.2 standard deviations.The global significance is evaluated with pseudoexperiments, by taking into account the look-elsewhere effect [58] in the mass range from 3600 MeV/c 2 to 4000 MeV/c 2 , and is estimated to be 1.8 standard deviations.As no excess above 3 standard deviations is observed, upper limits on the production ratios are set by using selection B. The invariant mass distribution of Ω + cc candidates is shown in Fig. 4 with the fit under the background-only hypothesis.The measured production ratio is a function of single-event sensitivity α and N sig , as shown in Eq. 2. The parameter α is calculated using the yield of the normalisation mode N norm multiplied by the efficiency ratio between the normalisation and signal modes, while N sig is extracted by fitting the data of the signal mode.
The Ξ ++ cc yields, N norm , are determined by performing an extended unbinned maximum likelihood fit to the invariant mass in the two trigger categories.The invariant mass distribution m(Λ + c K − π + π + ) is defined as the difference of the reconstructed mass of the Ξ ++ cc and Λ + c candidates plus the known Λ + c mass [51].For illustration, the m(Λ + c K − π + π + ) distributions for the 2018 data set are shown in Fig. 5 together with the associated fit projections.The mass shapes of the normalisation mode are a sum of a Gaussian function and a modified Gaussian function with power-law tails on both sides for signal and a second-order Chebyshev polynomial for background, which is the same as used in the Ξ + cc search [31].The Ξ ++ cc yields are summarised in Table 1, where the TOS refers to the trigger on signal and the exTIS refers to exclusive trigger independently of signal.

Efficiency ratio estimation
The efficiency ratio between the Ξ ++ cc mode and Ω + cc mode, defined as ε norm /ε sig , is determined from simulation.The distributions of the transverse momentum, rapidity of the doubly charmed baryons, and the event multiplicity in simulated samples are weighted according to the differences between simulation and data seen for the Ξ ++ cc baryon.The ) states are corrected to match those in data.The tracking and PID efficiencies for both normalisation and signal modes are corrected using calibration data samples [59][60][61].The efficiency ratios of both trigger categories for different data-taking periods are summarised in Table 2. Since there is an additional track in the Ξ ++ cc decay when compared to the Ω + cc decay, the reconstruction and selection efficiency of Ξ ++ cc candidates is significantly lower.The increase in the efficiency ratio for the 2017 and 2018 data is due to the optimisation of the Ξ ++ cc online selection, following the observation of the Ξ ++ cc baryon [8].In order to take into account the dependence of the selection efficiency upon the unknown value of the Ω + cc lifetime, simulated Ω + cc events are weighted to reproduce different exponential decay time distributions corresponding to lifetimes of 40, 80, 120, 160, and 200 fs.This method is used to estimate the change in the efficiency.The single-event sensitivities are calculated by the ratio of Ξ ++ cc efficiency to the Ω + cc efficiency with different lifetime hypotheses, as shown in Tables 3 and 4, for both trigger categories.
The Ω + cc mass is also unknown.To test the effects of different mass hypotheses, two simulated samples are generated with m(Ω + cc ) = 3638 MeV/c 2 and m(Ω + cc ) = 3838 MeV/c 2 .These samples are used to weight the p T distributions of final states in the Ω + cc decay to match those in the other mass hypotheses, and the efficiency is recalculated with the weighted samples.When varying the Ω + cc mass, it is found that the efficiency is constant; therefore, the Ω + cc mass dependence is neglected in the evaluation of the single-event sensitivities.

Systematic uncertainties
The sources of systematic uncertainties on the production ratio R are listed in Table 5, where individual sources are assumed to be independent and summed in quadrature to compute the total systematic uncertainty.The choice of the mass models used to fit the invariant mass distribution affects the normalisation yields and therefore affects the calculation of single-event sensitivities.The related systematic uncertainty is studied by using alternative functions to describe the signal and background shapes of the Ξ ++ cc mode.The sum of two Gaussian functions is chosen as an alternative signal model and a second-order polynomial function is chosen to substitute the background model.The difference in the signal yields obtained by changing models is assigned as the systematic uncertainty.
The systematic uncertainty associated with the trigger efficiency is evaluated using a tag-and-probe method [41].The size of the normalisation sample is insufficient to derive this systematic uncertainty.Instead, b-flavoured hadrons decaying with similar final-state topologies are used.For the TOS category, Λ 0 b →Λ + c π + π − π − and Λ 0 b →Λ + c π − candidates can be triggered by the energy deposit in the calorimeter by one of the Λ + c decay products, which are similar to the Ξ ++ cc → Λ + c K − π + π + and Ω + cc → Ξ + c K − π + decays.The efficiency ratio of these two Λ 0 b modes is estimated and the difference of the ratio between data and simulation is assigned as a systematic uncertainty.For the exTIS category, the B + c →J/ψ π + decay, which has two heavy-flavour particles (b-and c-hadrons) and is similar to the signal topology, is used to study the trigger efficiency with particle candidates that are independent and unrelated to the signal.The systematic uncertainty for the exTIS trigger category is assigned as the difference in the efficiency ratio of Λ 0 b →Λ + c π + π − π − mode to B + c →J/ψ π + mode in data and in simulation.The tracking efficiency is corrected with calibration data samples [59], and is affected by three sources of systematic uncertainties.First, the inaccuracy of the simulation in terms of detector occupancy, which is assigned as 1.5% and 2.5% for kaons and pions, does not cancel in the ratio.An additional systematic uncertainty arises from the calibration method which provides a 0.8% uncertainty per track [59].The third uncertainty is due to the limited size of the calibration samples and studied by pseudoexperiments.The tracking efficiency is corrected by the pseudoexperiments and the Gaussian width of the newly obtained distribution of the efficiency ratio is assigned as the systematic uncertainty.
The PID efficiency is determined in intervals of particle momentum, pseudorapidity and event multiplicity using calibration data samples.The corresponding sources of  [62], which is propagated to the systematic uncertainty in the efficiency.
As the agreeemnt between data and simulation is limited, a difference of 5.0% is found among different periods of data-taking, which is taken as systematic uncertainty.

Results
Upper limits on the production ratio R are set with a simultaneous fit to the m(Ξ + c K − π + ) distributions of different trigger categories for all the data sets from 2016 to 2018, following the strategy described in Sec. 4 for the normalisation mode.The upper limit values are calculated by setting different Ω + cc mass hypotheses in the fit within the m(Ξ + c K − π + ) mass range from 3600 to 4000 MeV/c 2 with a step of 2 MeV/c 2 , for five different lifetime hypotheses, 40, 80, 120, 160, and 200 fs.
For each Ω + cc mass and lifetime hypothesis, the likelihood profile is determined as a function of R. It is then convolved with a Gaussian distribution whose width is equal to the square root of the quadratic combination of the statistical and systematic uncertainties on the single-event sensitivity.The upper limit at 95% credibility level is defined as the value of R at which the integral of the profile likelihood equals 95% of the total area.Figure 6 shows the 95% credibility level upper limits at different mass hypotheses for five different lifetimes.The upper limits on R decrease when increasing the Ω + cc lifetime.Considering the whole explored mass range, the highest upper limit on R is 0.11 obtained under lifetime hypothesis of 40 fs while the lowest is 0.5 × 10 −2 obtained under lifetime hypothesis of 200 fs.

Conclusion
A search for the Ω + cc baryon through the Ξ + c K − π + decay is performed, using pp collision data collected by the LHCb experiment from 2016 to 2018 at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 5.4 fb −1 .No significant signal is observed in the mass range of 3.6 to 4.0 GeV/c 2 .Upper limits are set at 95% credibility  level on the ratio of the Ω + cc production cross-section times the branching fraction to that of the Ξ ++ cc baryon as a function of the Ω + cc mass and for different lifetime hypotheses, in the rapidity range of 2.0 to 4.5 and the transverse momentum range of 4 to 15 GeV/c.The upper limits are set assuming that the Ω + cc →Ξ + c K − π + decay proceeds according to a uniform phase-space model.The upper limits depend strongly on the mass and lifetime hypotheses of the Ω + cc , and vary from 1.1 × 10 −1 to 0.5 × 10 −2 for 40 fs to 200 fs, respectively.Future searches by the LHCb experiment with upgraded detectors, improved trigger conditions, additional Ω + cc decay modes, and larger data samples will further increase the Ω + cc signal sensitivity.

Figure 2 :
Figure 2: Invariant mass m(Ξ + c K − π + ) distribution of selected Ω + cc candidates from (black points) selection A, with (blue solid line) the fit with the largest local significance at the mass of 3876 MeV/c 2 superimposed.

Figure 3 :
Figure 3: Local p-value at different m(Ω + cc ) values evaluated with the likelihood ratio test.Lines indicating one, two and three standard deviations (σ) of local significance are also shown.

Figure 4 :
Figure 4: Invariant mass m(Ξ + c K − π + ) distribution of selected Ω + cc candidates (black points) with selection B, only background fit is shown.

Figure 5 :
Figure 5: Distribution of invariant mass m(Λ + c K − π + π + ) for selected Ξ ++ cc candidates in different categories: (a) triggered by one of the Λ + c decay products and (b) triggered exclusively by particles unrelated to the Ξ ++ cc decay products, in the 2018 data set.The fit results are superimposed.

Figure 6 :
Figure 6: Upper limits on the production ratio R at 95% credibility level as a function of m(Ξ + c K − π + ) at √ s = 13 TeV, for five Ω + cc lifetime hypotheses.

Table 1 :
Signal yields for the Ξ ++ cc → Λ + c K − π + π + normalisation mode N norm for both trigger categories and different data-taking periods with the corresponding integrated luminosity L. The uncertainties are statistical only.

Table 2 :
Efficiency ratios ε norm /ε sig between normalisation and signal modes for both trigger categories for different data-taking periods, where the TOS refers to the trigger on signal and the exTIS refers to exclusive trigger independently of signal.The uncertainties are statistical only.

Table 3 :
Single-event sensitivity α(Ξ ++ cc ) [10 −2 ] of the Ξ ++ cc normalisation mode triggered by one of the Ξ + c (Λ + c ) products for different lifetime hypotheses of the Ω + cc baryon for different data-taking periods.The uncertainties are due to the limited size of the simulated samples and the statistical uncertainties on the measured Ξ ++ cc baryon yields.

Table 4 :
Single-event sensitivity α(Ξ ++ cc ) [10 −2 ] of the Ξ ++ cc normalisation mode triggered exclusively by particles unrelated to the Ω + cc (Ξ ++ cc ) decay products for different lifetime hypotheses of the Ω + cc baryon in the different data-taking periods.The uncertainties are due to the limited size of the simulated samples and the statistical uncertainty on the measured Ξ ++ cc baryon yield.

Table 5 :
Systematic uncertainties on the production ratio R.
Università di Bologna, Bologna, Italy e Università di Cagliari, Cagliari, Italy f Università di Ferrara, Ferrara, Italy g Università di Firenze, Firenze, Italy h Università di Genova, Genova, Italy i Università degli Studi di Milano, Milano, Italy j Università di Milano Bicocca, Milano, Italy k Università di Modena e Reggio Emilia, Modena, Italy l Università di Padova, Padova, Italy m Scuola Normale Superiore, Pisa, Italy n Università di Pisa, Pisa, Italy o Università della Basilicata, Potenza, Italy p Università di Roma Tor Vergata, Roma, Italy q Università di Siena, Siena, Italy r Università di Urbino, Urbino, Italy s MSU -Iligan Institute of Technology (MSU-IIT), Iligan, Philippines t AGH -University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Kraków, Poland u P.N.Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia v Novosibirsk State University, Novosibirsk, Russia w Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden x Hanoi University of Science, Hanoi, Vietnam d