Measurement of the lifetime of the doubly charmed baryon $\Xi_{cc}^{++}$

The first measurement of the lifetime of the doubly charmed baryon $\Xi_{cc}^{++}$ is presented, with the signal reconstructed in the final state $\Lambda_c^+ K^- \pi^+ \pi^+$. The data sample used corresponds to an integrated luminosity of $1.7\,\mathrm{fb}^{-1}$, collected by the LHCb experiment in proton-proton collisions at a centre-of-mass energy of $13\mathrm{\,Te\kern -0.1em V}$. The $\Xi_{cc}^{++}$ lifetime is measured to be $0.256\,^{+0.024}_{-0.022}{\,\rm (stat)\,} \pm 0.014 {\,\rm(syst)}\mathrm{\,ps}$.

The quark model of hadrons predicts the existence of weakly decaying baryons that contain two beauty or charm quarks, and are therefore referred to as doubly heavy baryons.Such states provide a unique system for testing models of quantum chromodynamics (QCD), the theory that describes the strong interaction.In the quark model, the doubly charmed baryon Ξ cc forms an isodoublet, consisting of the Ξ ++ cc and Ξ + cc baryons with quark content ccu and ccd, respectively.Predictions for the Ξ + cc lifetime span the range from 50 to 250 fs, while the Ξ ++ cc lifetime is expected to be three to four times larger, from 200 to 1050 fs [1][2][3][4][5][6][7][8][9][10].The predicted larger Ξ ++ cc lifetime is due to the destructive Pauli interference of the charm-quark decay products and the valence (up) quark in the initial state, whereas the Ξ + cc lifetime is shortened due to an additional contribution from W -exchange between the charm and down quarks [1][2][3][4][5][6][7][8][9][10].Charge-conjugate processes are implied throughout this Letter.
The SELEX collaboration [11,12] reported the observation of the Ξ + cc baryon in the final states Λ + c K − π + and pD + K − , with a measured mass of 3518.7 ± 1.7 MeV/c 2 .Its lifetime was found to be less than 33 fs at the 90% confidence level.However, the signal has not been confirmed in searches performed at the FOCUS [13], BaBar [14], Belle [15], and LHCb [16] experiments.Recently, the LHCb collaboration observed a resonance in the Λ + c K − π + π + mass spectrum at a mass of 3621.40 ± 0.78 MeV/c 2 [17], which is consistent with expectations for the Ξ ++ cc baryon (e.g.Ref. [18]).The difference in masses between the two reported states, 103 ± 2 MeV/c 2 , is much larger than the few MeV/c 2 expected by the breaking of isospin symmetry [19][20][21], and that is observed in all other isodoublets.While the resonance seen in the Λ + c K − π + π + mass spectrum by LHCb is consistent with being the Ξ ++ cc baryon, a measurement of its lifetime is critical to establish its nature.The lifetime is also a necessary ingredient for theoretical predictions of branching fractions of Ξ cc decays, and can offer insight into the interplay between strong and weak interactions in these decays.
This Letter reports the first measurement of the Ξ ++ cc lifetime, with the Ξ ++ cc baryon reconstructed through the decay chain The data sample used, the same as in Ref. [17], corresponds to an integrated luminosity of 1.7 fb −1 , collected by the LHCb experiment in proton-proton collisions at a centre-of-mass energy of 13 TeV.Since the combined reconstruction and selection efficiency varies as a function of the decay time, the decay-time distribution is measured relative to that of a control mode with similar topology and known lifetime [22,23], Λ 0 b → Λ + c π − π + π − .This technique, used in a number of lifetime measurements at LHCb [22,[24][25][26][27][28][29][30][31], leads to a reduced systematic uncertainty as it is only sensitive to the ratio of the decay-time acceptances.
The LHCb detector [32,33] 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 elements that are particularly relevant to this analysis are: a silicon-strip vertex detector [34] surrounding the pp interaction region that allows c and b hadrons to be identified from their characteristically long flight distance; a tracking system [35], placed upstream and downstream of a dipole magnet, that provides a measurement of momentum, p, of charged particles; and two ring-imaging Cherenkov detectors [36] that are able to discriminate between different species of charged hadrons.The magnetic field polarity can be reverted periodically throughout the data-taking.The online event-selection is performed by a trigger [37], which consists of a hardware stage, based on information from the calorimeter and muon systems [38,39], followed by a software stage, which applies a full event reconstruction incorporating near-real-time alignment and calibration of the detector [40].The output of the reconstruction performed in the software trigger [41] is used as input to the present analysis.
Samples of 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 production of the Ξ ++ cc baryon.Decays of hadrons are described by EvtGen [45], in which final-state radiation is simulated 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].
Candidate Ξ ++ cc → Λ + c K − π + π + decays are reconstructed and selected with a multivariate selector following the same procedure as used in the previous analysis [17], except for two additional selection criteria.The first requires that the events are selected, at the hardware-trigger level, either by large transverse energy deposits in the calorimeter from the decay products of the Ξ ++ cc candidate or by activity in the calorimeter or muon system from particles other than the Ξ ++ cc decay products.This requirement removes events for which the efficiency can not be determined precisely.The second is a requirement on the reconstructed decay time of the Ξ ++ cc candidates, t, which must lie in the range 0.1-2.0ps, where the lower limit on t is imposed to avoid biases from resolution effects.Candidate Λ 0 b → Λ + c π − π + π − decays are reconstructed and selected in exactly the same way as Ξ ++ cc decays, except that the allowed invariant-mass range is centred around the Λ 0 b mass and both negatively charged Λ 0 b decay products are required to be identified as pions.The same hardware and software trigger criteria are applied to both Ξ ++ cc and Λ 0 b candidates.To obtain better resolution, the invariant mass of a candidate is calculated as where ) is the invariant mass of the Λ + c candidate, and M PDG (Λ + c ) is the known value of the Λ + c mass [23].The distributions of the mass m of selected Λ + c K − π + π + and Λ + c π − π + π − candidates are shown in Fig. 1.Unbinned extended maximum-likelihood fits to these distributions are performed as in Ref. [17], with the signal described by the sum of a Gaussian function and a double-sided Crystal Ball function [49], and the background parameterised by a second-order Chebyshev  polynomial.The same fit models are used for both the Ξ ++ cc and Λ 0 b samples, but with different resolution parameters.Signal yields of 304 ± 35 Ξ ++ cc and 3397 ± 119 Λ 0 b decays are obtained.The small decrease in the Ξ ++ cc yield compared with the value of 313 ± 33 reported in Ref. [17] is due to the two additional selection requirements described above.
The decay time of Ξ ++ cc or Λ 0 b candidates is computed with a kinematic fit [50] in which the momentum vector of the candidate is required to be aligned with the line joining the production and decay vertices.The decay-time resolution, determined from simulation, is 63 fs (32 fs) for the Ξ ++ cc (Λ 0 b ) decay, which is much less than the Ξ ++ cc (Λ 0 b ) lifetime and has negligible dependence on the decay time within the current precision.The normalised decay-time distributions of the Ξ ++ cc and Λ 0 b baryons are shown in Fig. 2, where the background contributions have been subtracted according to the fit results shown in Fig. 1 using the sPlot technique [51].
The decay-time acceptance is defined as the ratio between the reconstructed and the generated decay-time distributions, and is determined with samples of simulated events containing Ξ ++ cc (Λ 0 b ) decays, in which the Ξ ++ cc (Λ 0 b ) lifetime is set to 0.333 ps (1.451 ps), as shown in Fig. 3.This decay-time acceptance, which is described by a histogram in this analysis, takes into account the reconstruction efficiency, as well as the bin migration effect caused by the decay-time resolution.A potential bias in the relative decay-time acceptance due to the assumed lifetimes is considered as a source of systematic uncertainty.The simulated Ξ ++ cc and Λ 0 b decays are weighted to match their observed transverse-momentum distributions in data.The difference between the Ξ ++ cc or Λ 0 b decay-time acceptances is mainly due to the larger Λ 0 b mass, which results in higher momentum of the decay products and larger opening angles in the decay.An exponential function is fitted to the background-subtracted and acceptance-corrected decay-time distribution of Λ 0 b candidates, and a lifetime of 1.474 ± 0.077 ps is obtained, where the uncertainty is statistical only.This is consistent with the known value 1.470 ± 0.010 ps [23], and validates that the detector simulation correctly reproduces the decay-time acceptance.
The Ξ ++ cc lifetime is measured by performing a weighted, unbinned maximum-likelihood fit [52] to the decay-time distribution of the selected Ξ ++ cc sample.Each candidate is assigned a signal weight for background subtraction, which is computed using its invariant mass m as the discriminating variable following the sPlot technique [51].The probability density function describing the decay-time distribution of the Ξ ++ cc signal candidates, denoted by f Ξ ++ cc (t), is defined as where H Λ 0 b (t) is the background-subtracted decay-time distribution of the Λ 0 b control channel, Ξ ++ cc (t) and Λ 0 b (t) are the decay-time acceptance distributions for the Ξ ++ cc and Λ 0 b decays, and τ (Λ 0 b ) = 1.470 ± 0.010 ps is the known value [23] of the Λ 0 b lifetime [22].Here H Λ 0 b (t), Ξ ++ cc (t), and Λ 0 b (t) are the histograms shown in Figs. 2 and 3.The binning scheme is chosen to minimize the systematic uncertainty on the lifetime due to the finite bin width.The background-subtracted Ξ ++ cc decay-time distribution is shown in Fig. 4 with the fit result superimposed.The only free parameter of the fit is the Ξ ++ cc lifetime, which is measured to be τ (Ξ ++ cc ) = 0.256 +0.024 −0.022 ps.Here the uncertainties are statistical only, and include contributions due to the limited sizes of the simulated samples (0.007 ps) and of the Λ 0 b sample (0.006 ps).These contributions are estimated with a bootstrapping method [53], where candidates are randomly selected from the original simulated or Λ 0 b samples to form statistically independent samples of pseudodata.The standard deviations of the lifetime measurements obtained in these samples are then taken as the corresponding statistical uncertainty.
Sources of systematic uncertainty on the Ξ ++ cc lifetime are summarised in Table 1 and described below.The effects of the choice of signal and background models are studied by using alternative mass shapes, namely a sum of two Gaussian functions for signal and an exponential function for background.The change in the measured lifetime, 0.005 ps, is assigned as a systematic uncertainty.In the baseline fit, the signal and background mass shapes are assumed to be independent of the decay time.The effect of this assumption is investigated by fitting the invariant-mass distribution of the Ξ ++ cc and Λ 0 b samples in four independent intervals of decay time and recalculating the signal weights based on these fit results.Using these weights in the fit, the Ξ ++ cc lifetime changes by 0.004 ps, which is taken as the systematic uncertainty due to the correlation between the mass and decay time.It is found that the measured lifetime depends slightly upon the binning scheme.With the nominal binning, a difference of 0.001 ps with respect to the input lifetime is measured, which is taken as a systematic uncertainty.
The kinematic distributions of the Ξ ++ cc and Λ 0 b signals in the simulation are generally found to be in good agreement with those in data.However, some differences are observed in the output distribution of the multivariate selector.To assess the impact of such differences, the simulation is weighted to match this output distribution in data and the decay-time acceptance is recomputed.The difference between the result from this procedure and the original one is 0.004 ps, which is assigned as the corresponding systematic uncertainty.The simulated Ξ ++ cc → Λ + c K − π + π + and Λ 0 b → Λ + c π − π + π − samples are generated assuming that the decay products are distributed uniformly across the available phase space.The possible effect of intermediate resonances is evaluated by weighting the simulated invariant mass distributions of the three hadrons, i.e.M (K − π + π + ) for Ξ ++ cc and M (π − π + π − ) for Λ 0 b candidates, to match the distributions seen in data.The resulting difference in the measured lifetime, 0.011 ps, is assigned as a systematic uncertainty.
The transverse-energy threshold in the calorimeter hardware trigger varied during data taking, and this variation is not fully described by the simulation.To investigate the influence of this difference, the hardware trigger requirement is applied to the data with a higher (uniform) threshold.The measurement is repeated and the change in the measured lifetime, 0.002 ps, is taken as a systematic uncertainty.The input lifetime used in the simulation for the Ξ ++ cc baryon is 0.333 ps.The simulated events are weighted to be distributed according to the measured lifetime and the decay-time acceptance is recomputed.The resulting difference in the measured lifetime, 0.002 ps, is taken as a systematic uncertainty.The Λ 0 b lifetime is precisely known [22,23].An alternative fit in which τ (Λ 0 b ) is allowed to vary within its uncertainty leads to a change in the measured Ξ ++ cc lifetime of less than 0.001 ps, which is assigned as a systematic uncertainty.Other systematic effects, including the threshold applied to the multivariate selector, the decay-time resolution, and the uncertainty on the length scale of the vertex detector, are studied and found to be negligible; no systematic uncertainties are assigned for these effects.As further checks, the measured lifetime is compared between subsets of the data, including Ξ ++ cc versus Ξ −− cc , opposite LHCb magnet polarities, and different numbers of  1, are added in quadrature, and the total systematic uncertainty on the measured Ξ ++ cc lifetime is found to be 0.014 ps.
In summary, the Ξ ++ cc lifetime is measured using a data sample corresponding to an integrated luminosity of 1.7 fb −1 , collected by the LHCb experiment in pp collisions at a centre-of-mass energy of 13 TeV, and is found to be

Figure 4 :
Figure 4: Background-subtracted decay-time distribution of selected Ξ ++ cc → Λ + c K − π + π + candidates.The rate-averaged fit result across each decay-time bin is shown as the continuous line.

Table 1 :
Summary of systematic uncertainties.and is found to be stable.A separate measurement carried out with an alternative method, in which both the Ξ ++ cc and Λ 0 b decay-time distributions are binned, gives a consistent result.All sources of systematic uncertainty, listed in Table