Observation of the doubly Cabibbo-suppressed decay Ξ + c → pφ

The doubly Cabibbo-suppressed decay Ξ + c → pφ with φ → K + K − is observed for the ﬁrst time, with a statistical signiﬁcance of more than ﬁfteen standard deviations. The data sample used in this analysis corresponds to an integrated luminosity of 2 fb − 1 recorded with the LHCb detector in pp collisions at a centre-of-mass energy of 8 TeV. The ratio of branching fractions between the decay Ξ + c → pφ and the singly Cabibbo-suppressed decay Ξ + c → pK − π + is measured to be


Introduction
The flavour structure of the weak interaction between quarks is described by the Cabibbo-Kobayashi-Maskawa (CKM) matrix [1].In particular, the tree-level decays of charmed particles depend on the matrix elements V ud , V us , V cd and V cs .The hierarchy of the CKM matrix elements becomes evident using the approximate Wolfenstein parametrisation, which is based on the expansion in powers of the small parameter λ ≈ 0.23 with [2,3].Tree-level decays depending on both V us and V cd matrix elements are known as doubly Cabibbo-suppressed (DCS) decays.They have small branching fractions compared to the Cabibbo-favoured (CF) and the singly Cabibbo-suppressed (SCS) decays [4].A systematic study of the relative contributions of DCS and CF diagrams to decays of charm baryons could shed light onto the role of the nonspectator quark, and in particular Pauli interference [5].Such studies would be helpful for a better understanding of the lifetime hierarchy of charm baryons [5][6][7][8].So far only one DCS charm-baryon decay, Λ + c → pK + π − , has been observed [9,10].This article reports the first observation of the DCS decay Ξ + c → pφ with φ → K + K − , hereafter referred to as the signal decay channel. 1 The leading-order diagram for the Ξ + c → pφ decay is shown in Fig. 1.The branching fraction of the signal decay channel is measured relative to the branching fraction of the SCS decay channel Ξ + c → pK − π + , The measurement is based on a data sample of pp collisions collected in 2012 with the LHCb detector at the centre-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 2 fb −1 .
three stations of silicon-strip detectors and straw drift tubes [14] 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 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 [15].Photons, electrons, and hadrons are identified by a system consisting of scintillating-pad and preshower detectors, an electromagnetic and a hadronic calorimeter.
Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers [16].The online event selection is performed by a trigger [17], which consists of a hardware stage, based on information from the calorimeter and the muon systems, followed by a software stage, which applies a full event reconstruction.
At the hardware trigger stage, the events are required to have a muon with high p T or a hadron, photon or electron with high transverse energy in the calorimeters.The software trigger requires a two-, three-or four-track secondary vertex with a significant displacement from any primary pp interaction vertex.At least one charged particle must have a transverse momentum p T > 1.6 GeV/c and be inconsistent with originating from any PV.
Simulation is used to evaluate detection efficiencies for the signal and the normalisation decay channels.In the simulation, pp collisions are generated using Pythia [18] with the specific LHCb configuration [19].Decays of hadronic particles are described by EvtGen [20], in which the final-state radiation is generated using Photos [21].The interaction of the generated particles with the detector and its response are implemented using the Geant4 toolkit [22] as described in Ref. [23].

Selection of candidates
The candidates for the Ξ + c → pK − h + decays, where h + = {π + , K + }, are formed using three charged tracks with p T > 250 MeV/c.Hadrons used for the reconstruction of the Ξ + c baryons should not be produced at the PV.Only pions, protons, and kaons with an impact parameter χ 2 IP in excess of 9 with respect to all reconstructed PVs are taken into consideration for subsequent analysis.The χ 2 IP quantity is calculated as the difference in χ 2 of the PV fit with and without the particle in question.The momenta of the reconstructed final-state particles are required to be in the range 3.2 -150 GeV/c for the mesons, and in the range 10 -100 GeV/c for the proton.The reconstructed tracks must pass particle-identification (PID) requirements based on information from the RICH detectors, the calorimeter, and the muon stations [24].The PID requirements are loose for mesons and much tighter for protons, to suppress π + and K + misidentified as protons.The three tracks must form a common vertex.The selected Ξ + c candidates must have the rapidity (y) and transverse momentum 2.0 < y < 4.5 and 4 < p T < 16 GeV/c.Additional requirements are introduced to suppress the contribution from D + and D + s decays with pions or kaons misidentified as protons.Such background manifests itself as narrow peaking structures in the mass spectrum of the three hadrons if the mass hypothesis for the track identified as a proton is changed to a pion or kaon.Candidates with a mass within ±10 MeV/c 2 (approximately ±2.5σ) of the known values are rejected.
The candidate is associated to the PV with the smallest value of χ 2 IP .In order to evaluate the candidate Ξ + c decay time and the two-body masses for the particles in the final state, a constrained fit is performed, requiring the candidate to be originated from its associated PV and have a mass equal to its known value [25].The proper decay time is required to be between 0.55 and 1.5 ps to reduce the fraction of baryons coming from b-hadron decays.The b-hadron component is also suppressed by the requirement on the χ 2 IP value of the reconstructed baryon to be less than 32.The masses of the pK − h + combinations are calculated without the mass constraint.They are required to be in the range 2.42 to 2.51 GeV/c 2 for the Ξ + c candidates.In the offline selection, trigger objects are associated with reconstructed particles [17].Selection requirements can therefore be made on the trigger selection itself and on whether the decision was due to the signal decay candidate (Trigger On Signal, TOS category), or to other particles produced in the pp collision (Trigger Independent of Signal, TIS category) or to a combination of both.The selected candidates must belong to the TIS category of the hardware-trigger and to the TOS category of the two levels of the software-trigger.
Only Ξ + c → pK − K + candidates from the φ → K + K − region, i.e. candidates with a K − K + mass (M K − K + ) less than 1.07 GeV/c 2 , are used.A very small fraction of Ξ + c → pφ events leaks into the M K − K + > 1.07 GeV/c 2 region.In the R pφ measurement this effect is taken into account using the distribution observed in simulated events.Figures 2 (left) and 3 show the mass distribution of the selected candidates for the Ξ + c → pK − K + and Ξ + c → pK − π + decay channels, respectively.Clear peaks can be seen in both distributions.The studies of the underlying background events suggest no peaking contributions for the signal and normalisation decay channels.
In parallel to Ξ + c selections, samples of Λ + c → pK − h + decays are also selected.The candidates for the Λ + c decays are used to calibrate resolutions and trigger efficiencies and to perform other cross-checks.

Fit model and yields of signal and normalisation candidates
The yields of the selected Ξ + c → pK − h + decays are determined from unbinned extended maximum-likelihood fits to the corresponding pK − K + or pK − π + mass spectra.The probability density function consists of a Gaussian core and exponential tails.The following distribution is used as the Ξ + c model: where M is the candidate mass, µ is the peak position, σ reflects the core-peak width, κ is an asymmetry parameter, and β characterises the exponential tails [26].The value of is −1 for M ≤ µ and +1 for M > µ.The parameter β is fixed in the fit of the Ξ + c → pK − K + mass distribution to the value obtained from the fits of the normalisation and of the Λ + c → pK − K + decay channels.The background is modelled by an exponential function.The results of the fits for the Ξ + c → pK − K + and Ξ + c → pK − π + decay channels are presented in Figs. 2 and 3, respectively.The yields are N pKK = 3790 ± 120 for the ) LHCb LHCb Ξ + c → pK − K + decay channel and N pKπ = (324.7 ± 0.8) × 10 3 for the normalisation decay channel.
To separate the φ and non-φ contributions to the signal decay channel, the K − K + mass distribution after background substraction using the sPlot technique [27] is analysed.The M K − K + observable is evaluated with the Ξ + c mass constraint and is almost independent from the M pK − K + discriminating variable.The effect of the correlation is small and is taken into account in the systematic uncertainty of the measurement.
The fraction of the φ contribution (f φ ) in the selected Ξ + c → pK − K + candidates is determined by a binned nonextended maximum-likelihood fit to the M K − K + spectrum.A P -wave relativistic Breit-Wigner distribution with Blatt-Weisskopf form factor [28] is used to describe the φ → K + K − lineshape.The barrier radius is set to 3.5 GeV −1 in natural units.This distribution is convolved with a Gaussian function to model the experimental resolution.The parameters of the resolution function are fixed using the Λ + c → pK − K + sample.For the non-φ contribution, the Flatté parameterisation [29] is used in the form where m 0 refers to the mass of the f 0 (980) resonance, g 1 and g 2 are coupling constants, and ρ ππ and ρ KK are the Lorentz-invariant phase-space factors.The term g 2 ρ KK accounts for the opening of the kaon threshold.The values m 0 g 1 = 0.165 ± 0.018 GeV 2 and g 2 /g 1 = 4.21 ± 0.33 have been determined by the BES collaboration [30].The choice of the Flatté parametrisation is suggested by the K − K + mass distribution in the Λ + c → pK − K + data sample.The φ contribution dominates in the K − K + mass spectrum with a measured fraction f φ = (90.0± 2.7)%.
As a cross-check of the result obtained with the sPlot approach, an extended twodimensional likelihood fit to the M pK − K + and M K − K + distributions is performed.Four two-dimensional terms are considered.The M pK − K + dependency for the φ and non- ) LHCb φ terms for the Ξ + c decay component are described by Eq. 2. Two additional φ and non-φ terms are introduced for the M pK − K + background description.These terms are independent linear distributions in the M pK − K + spectrum.A second-order polynomial is used to describe the K − K + mass distribution of the non-Ξ + c non-φ background.The results of the two-dimensional fit are in agreement with the sPlot-based procedure.
The statistical uncertainty of the f φ parameter is determined by a simulation generated according to the alternative two-dimensional (M pK − K + vs. M K − K + ) model described above.The statistical significance of the observation of the Ξ + c → pφ decay is well above 15σ.The fit to the M K − K + distribution results in an evidence of a non-φ contribution to the DCS Ξ + c → pK − K + decay.A statistical significance of 3.9σ is obtained under the assumption of normal distributions for the uncertainties.

Efficiencies and branching fractions ratio
The total detection efficiencies for both the signal and the normalisation decays can be factorised as where acc denotes the geometrical acceptance of the LHCb detector, rec&sel|acc corresponds to the efficiency of reconstruction and selection of the candidates within the geometrical acceptance, hardware|software and software|rec&sel are the trigger efficiencies for the selected candidates of the hardware and software levels, respectively, and PID is the PID efficiency.
Since the hardware trigger level accepts events independently of the reconstructed candidates, i.e. the events belong to the TIS category, the efficiency hardware|software is assumed to cancel in the ratio of the signal and normalisation efficiencies.All other efficiencies except PID are determined from simulation.The simulated sample of Ξ + c → pK − K + events with the intermediate φ resonance is used to determine efficiencies for the signal decay channel.The simulated sample for the Ξ + c → pK − π + decay was produced according to a phase-space distribution.It is corrected to reproduce the Dalitz plot distribution observed with data.An additional correction is introduced for both simulated samples to account for the difference in the tracking efficiencies between data and simulation [31].
The PID efficiencies for the hadrons are determined from large samples of protons, kaons, and pions [24].These samples are binned in momentum and pseudorapidity of the hadron, as well as in the charged particle multiplicity of the event.The PID efficiency for the Ξ + c candidates are determined on an event-by-event basis.The weights for each candidate are taken from the calibration histograms using trilinear interpolation.The efficiency PID is determined as the ratio of Ξ + c yields obtained from maximum-likelihood fits of the M pK − h + distributions from the weighted and unweighted samples.
The ratio between the total efficiencies of the signal and the normalisation decay channels is determined in bins of p T and y of the Ξ + c baryon.This procedure accounts for kinematic features of the Ξ + c production, which could be poorly modelled in the simulation.Averaged over the (p T , y) bins this ratio is determined to be (91.1 ± 3.6)%, including systematic uncertainties.
To reduce the effect of the dependence of the efficiency on the Ξ + c kinematics, the mass fits are repeated in seven nonoverlapping (p T , y) bins, which cover the LHCb fiducial volume.The fit procedure is the same as described above, except that the σ parameter of the signal distribution in Eq. 2 is fixed to the value of the normalisation decay channel, scaled by a factor obtained from a fit to the Λ + c → pK − K + and Λ + c → pK − π + mass distributions in the same (p T , y) bins.The ratios of the yields of the signal and normalisation decay channels are corrected by the ratios of the total efficiencies.The branching fraction ratios are evaluated for each (p T , y) bin as The known value of B(φ → K + K − ) = 0.492 ± 0.005 is used [3].The weighted average of the branching fraction ratios evaluated for the (p T , y) bins is R pφ = (19.8± 0.7) × 10 −3 , where the uncertainty reflects the statistical uncertainty of the Ξ + c yields and f φ .The alternative two-dimensional fitting procedure gives R pφ = (19.8± 0.8) × 10 −3 , which is in excellent agreement with the result determined using the sPlot technique.

Systematic uncertainties
The list of systematic uncertainties for the measured ratio R pφ is presented in Table 1.The total uncertainty is obtained as the quadratic sum of all contributions.
In order to estimate the systematic uncertainties for the yields of the Ξ + c → pK − K + and the normalisation decay channels, various hypotheses are tested for the description of the signal and background shapes.When the signal parameterisations in the M pK − K + and M pK − π + spectra are changed to a modified Novosibirsk function [32], no significant deviation from the nominal fit model is found.The change of the function for the non-φ component to a two-body phase space model in the fit to the M K − K + distribution leads to a systematic uncertainty of 0.5%, which is considered as the signal fit-model uncertainty.
The background-model parameterisation is tested by replacing of polynomial function with a product of polynomial and exponential functions.The uncertainty related to the sPlot method is studied with two samples of 500 pseudoexperiments each, in which the samples are generated according to the M pK − K + -M K − K + model described in Sec. 4. In one set of pseudoexperiments the effect of the residual correlation between M pK − K + and M K − K + is introduced.The systematic uncertainty of the sPlot technique is assigned from the deviations of the results of these tests from the nominal ones.
The cancellation of the hardware-trigger efficiencies in the ratio of the signal and the normalisation decay channels is studied with the Λ + c control samples.A technique based on the partial overlap of the TIS and TOS subsamples [17] is used to evaluate hardware efficiencies for the Λ + c → pK − h + decay channels.The data are consistent with the hypothesis of equal hardware-trigger efficiencies for the signal and normalisation decay channels.The precision achieved by means of these studies, limited by the statistics in the overlap between the TIS and TOS subsamples, is used as a systematic uncertainty for the hardware-trigger efficiency ratio.
For the software-trigger, the systematic uncertainty is assessed using simulation.The large variation of software-trigger requirements demonstrates the stability of the ratio of software-trigger efficiencies for the signal and normalisation decay channels at the 1% to 2% level.The overall systematic uncertainty for both hardware-and software-trigger efficiencies is reported in Table 1.
The main source of uncertainty of the PID efficiency is related to the difference between results obtained with different calibration samples for the protons.The Λ + c → pK − π + sample is used as default in the analysis, while results obtained with the Λ → pπ − calibration sample are used to assign a systematic uncertainty.For determination of PID efficiencies the calibration samples are binned according to proton, pion, or kaon kinematics.The associated systematic uncertainty is studied by comparing the results with different binning and interpolation schemes.The uncertainty related to the finite size of the calibration samples is considered to be fully correlated between the signal and normalisation decay channels and to cancel in the ratio.
The dominant uncertainty on the tracking efficiency correction arises from the different track reconstruction efficiency for kaons and pions due to different hadronic cross-sections with the detector material.Half of the K − π + detection asymmetry measured by LHCb [33] is assigned as systematic uncertainty.Another source of uncertainty due to tracking efficiency is related to the binning of the tracking correction histogram.The difference between the results using interpolated and binned values of the efficiency is assigned as systematic uncertainty.
The uncertainty due to the selected (p T , y)-bins to determine R pφ is obtained from studies carried out with an alternative binning.There is an uncertainty of 0.7% from the size of the simulation sample.The obtained value of R pφ is stable within 0.8% against a variation of selection requirements.This value is taken as the uncertainty due to the selection requirements.

Conclusions
The first observation of the DCS Ξ + c → pφ decay is presented, using pp collision data collected with the LHCb detector at a centre-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 2 fb −1 .The ratio of the branching fractions with respect to the SCS Ξ + c → pK − π + decay channel is measured to be R pφ = (19.8± 0.7 ± 0.9 ± 0.2) where the first uncertainty is statistical, the second systematic and the third due to the knowledge of the φ → K + K − branching fraction.An evidence of the 3.5σ, including systematic uncertainties, for a non-φ contribution to the DCS Ξ + c → pK − K + decay is also found.

Figure 2 :
Figure 2: (Left) Fit results for the Ξ + c → pK − K + decay.The candidates are selected in the φ meson region, i.e. with the requirement of M K − K + < 1.07 GeV/c 2 .The red dotted line corresponds to the signal component, the black dashed line reflects the background distribution, and the blue solid line is their sum.(Right) Background subtracted K − K + mass distribution for the Ξ + c → pK − K + decay.The red dotted line shows the Ξ + c → pφ contribution, the black dashed line represents the non-φ contribution, and the solid blue line is the total fit function.

Figure 3 :
Figure 3: Fit results for the Ξ + c → pK − π + decay.The red dotted line corresponds to the signal component, the black dashed line reflects the background distribution and the blue solid line is their sum.

a
Universidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil b Laboratoire Leprince-Ringuet, Palaiseau, France c P.N.Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia d Università di Bari, Bari, Italy e Università di Bologna, Bologna, Italy f Università di Cagliari, Cagliari, Italy g Università di Ferrara, Ferrara, Italy h Università di Genova, Genova, Italy i Università di Milano Bicocca, Milano, Italy j Università di Roma Tor Vergata, Roma, Italy k Università di Roma La Sapienza, Roma, Italy l AGH -University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Kraków, Poland m LIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain n Hanoi University of Science, Hanoi, Vietnam o Università di Padova, Padova, Italy p Università di Pisa, Pisa, Italy q Università degli Studi di Milano, Milano, Italy r Università di Urbino, Urbino, Italy s Università della Basilicata, Potenza, Italy t Scuola Normale Superiore, Pisa, Italy u Università di Modena e Reggio Emilia, Modena, Italy v H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom w MSU -Iligan Institute of Technology (MSU-IIT), Iligan, Philippines x Novosibirsk State University, Novosibirsk, Russia y Sezione INFN di Trieste, Trieste, Italy z School of Physics and Information Technology, Shaanxi Normal University (SNNU), Xi'an, China aa Physics and Micro Electronic College, Hunan University, Changsha City, China ab Lanzhou University, Lanzhou, China † Deceased

Table 1 :
Systematic uncertainties relative to the central value of the ratio R pφ .