Observation of the decay $\Lambda_b^0\rightarrow\chi_{c1}p\pi^-$

The Cabibbo-suppressed decay $\Lambda_b^0\rightarrow\chi_{c1}p\pi^-$ is observed for the first time using data from proton-proton collisions corresponding to an integrated luminosity of 6fb$^{-1}$, collected with the LHCb detector at a centre-of-mass energy of 13TeV. Evidence for the $\Lambda_b^0\rightarrow\chi_{c2}p\pi^-$ decay is also found. Using the $\Lambda_b^0\rightarrow\chi_{c1}pK^-$ decay as normalisation channel, the ratios of branching fractions are measured to be $$\begin{array}{rcl} \frac{ \mathcal{B} (\Lambda_b^0\rightarrow\chi_{c1}p\pi^-)}{\mathcal{B} (\Lambda_b^0\rightarrow\chi_{c1}pK^-)}&=&(6.59 \pm 1.01 \pm 0.22 ) \times 10^{-2} \,, \frac{\mathcal{B} (\Lambda_b^0\rightarrow\chi_{c2}p\pi^-)}{\mathcal{B} (\Lambda_b^0\rightarrow\chi_{c1}p\pi^-)}&=&0.95 \pm 0.30 \pm 0.04 \pm 0.04 \,, \frac{\mathcal{B} (\Lambda_b^0\rightarrow\chi_{c2}pK^-)}{\mathcal{B} (\Lambda_b^0\rightarrow\chi_{c1}pK^-)}&=&1.06 \pm 0.05 \pm 0.04 \pm 0.04 \,,\end{array}$$ where the first uncertainty is statistical, the second is systematic and the third is due to the uncertainties in the branching fractions of $\chi_{c1,2}\rightarrow J/\psi\gamma$ decays.


Introduction
The amplitude analyses of the beauty-baryon decays Λ 0 b → J/ψpK − established the existence of a new class of baryonic resonances in the J/ψp system, hidden-charm pentaquarks, that cannot be described within the simplest pattern of baryon structure consisting of three constituent quarks [1][2][3]. Evidence for a pentaquark contribution in the same J/ψp mass region was obtained in the study of the Cabibbo-suppressed decays Λ 0 b → J/ψpπ − [4]. Recently, further evidence for a new pentaquark candidate in the Ξ − b → J/ψΛK − decay has been reported [5]. Up to now, such hidden-charm pentaquark resonances have been observed only in the J/ψp and J/ψΛ systems. Investigation of such resonances in other decay modes, such as η c p, χ c1 p and χ c2 p could shed light on the nature of these exotic states.
The partial widths of the Λ 0 b → χ c1 pK − and Λ 0 b → χ c2 pK − decays are measured to be almost equal [6]. For beauty mesons a different pattern is observed. The known partial widths for the B → χ c1 K ( * ) and the B → χ c2 K ( * ) decays [7-9] exhibit a large suppression of the decay modes with the χ c2 state with respect to the χ c1 state. Such suppression agrees with expectations from QCD factorisation [10]. More information on the decays of beauty baryons to the χ c1 and χ c2 states is needed to clarify the role of QCD factorisation in baryon decays.
In this paper, a search for the Λ 0 b → χ c1 pπ − and Λ 0 b → χ c2 pπ − decays is reported, where the χ c1 and χ c2 mesons are reconstructed via their radiative decays χ c1,2 → J/ψγ, and the J/ψ mesons are reconstructed in the µ + µ − final state. The Λ 0 b → χ c1 pK − decay mode, which has a similar topology, is used as normalisation channel. The study is based on proton-proton (pp) collision data, corresponding to an integrated luminosity of 6 fb −1 , collected with the LHCb detector at a centre-of-mass energy of 13 TeV. Throughout this paper the inclusion of charge-conjugated processes is implied and the symbol χ cJ is used to denote the χ c1 and χ c2 states collectively.

Detector and simulation
The LHCb detector [11,12] 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 silicon-strip vertex detector surrounding the pp interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes placed downstream of the magnet. The tracking system provides a measurement of the momentum, 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 (RICH) detectors. Photons, electrons and hadrons are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic and a hadronic calorimeter [13]. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers.
The online event selection is performed by a trigger, 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. At the hardware trigger stage, events are required to have a muon with high transverse momentum or dimuon candidates in which a product of the p T of the muons has a high value. In the software trigger, two oppositely charged muons are required to form a good-quality vertex that is significantly displaced from every PV, with a dimuon mass exceeding 2.7 GeV/c 2 .
Simulated events are used to describe signal shapes and to compute the efficiencies needed to determine the branching fraction ratios. In the simulation, pp collisions are generated using Pythia [14] with a specific LHCb configuration [15]. Decays of unstable particles are described by EvtGen [16], in which final-state radiation is generated using Photos [17]. The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [18] as described in Ref. [19]. The transverse momentum and rapidity spectra of the Λ 0 b baryons in simulated samples are adjusted to match those observed in a high-yield low-background sample of reconstructed Λ 0 b → J/ψpK − decays. In the simulation, the Λ 0 b baryon decays are produced according to a phase space decay model. Simulated Λ 0 b → χ cJ pK − decays are corrected to reproduce the pK − mass and cos θ pK − distributions observed in data, where θ pK − is the helicity angle of the pK − system, defined as the angle between the momentum vectors of the kaon and the Λ 0 b baryon in the pK − rest frame. Large calibration samples of low-background decays [20,21] are used to resample the combined detector response used for the identification of protons, kaons and pions. To account for imperfections in the simulation of charged-particle reconstruction, the track reconstruction efficiency determined from simulation is corrected using control channels in data [22].
Muon, proton, pion and kaon candidates are identified combining information from the RICH, calorimeter and muon detectors. They are required to have transverse momenta larger than 550, 500, 200 and 200 MeV/c, respectively. To ensure efficient particle identification, kaons and pions are required to have a momentum between 3.2 and 150 GeV/c, whilst protons must have momentum between 10 and 150 GeV/c. To reduce the combinatorial background due to particles produced in pp interactions, only tracks that are inconsistent with originating from any PV are used.
Pairs of oppositely charged muons consistent with originating from a common vertex are combined to form J/ψ → µ + µ − candidates. The transverse momentum of the dimuon candidate is required to be in excess of 2 GeV/c, and the mass of the µ + µ − system is required to be between 3.020 and 3.135 GeV/c 2 , where the asymmetric mass range around the known J/ψ mass [28] is chosen to account for final-state radiation. The position of the reconstructed dimuon vertex is required to be inconsistent with that of any reconstructed PV.
To create χ cJ candidates, the selected J/ψ candidates are combined with photon candidates that have been reconstructed using clusters in the electromagnetic calorimeter. Only clusters that are not matched to the trajectory of a track extrapolated from the tracking system to the cluster position in the electromagnetic calorimeter are used in the analysis [13]. The transverse energies of the photon candidates are required to exceed 400 MeV. To suppress the large combinatorial background from π 0 → γγ decays, photons that can form a π 0 → γγ candidate with mass within 25 MeV/c 2 of the known π 0 mass [28] are ignored [29,30]. The χ cJ candidates are selected in the J/ψγ mass region between 3.4 and 3.7 GeV/c 2 .
The selected χ cJ candidates are combined with pπ − or pK − pairs to create Λ 0 b → χ cJ pπ − or Λ 0 b → χ cJ pK − candidates, respectively. A kinematic fit [31] that constrains the four charged final-state particles to form a common vertex, the mass of the µ + µ − combination to equal the known J/ψ mass [28] and the Λ 0 b candidate to originate from the associated PV, is performed. Each Λ 0 b candidate is associated with the PV that yields the smallest χ 2 IP , where χ 2 IP is defined as the difference in the vertex-fit χ 2 of a given PV reconstructed with and without the particle under consideration. A good-quality fit is required to further suppress combinatorial background. In addition, the measured decay time of the Λ 0 b candidate, calculated with respect to the associated PV, is required to be greater than 0.1 mm/c to suppress poorly reconstructed candidates and background from particles originating directly from the PV.
To suppress cross-feed from B 0 → χ cJ K + π − decays with the positively charged kaon (negatively charged pion) misidentified as a proton (antiproton) for the signal (normalisation) channel, the Λ 0 b candidate mass recalculated with a kaon (pion) mass hypothesis for the proton is required to be inconsistent with the known B 0 meson mass [28]. In a similar way, Λ 0 b candidates are rejected if the mass of the pπ − (pK − ) combination is consistent with the known φ-meson mass [28] when a kaon mass hypothesis is used for both hadrons. To suppress background from the Λ → pπ − decay, candidates with a pπ − mass that is consistent with the known mass of the Λ baryon [28] are rejected. The contributions from the Λ 0 b → J/ψpπ − and Λ 0 b → J/ψpK − decays combined with random photons are eliminated by the requirement that the mass of the Λ 0 b candidate calculated without a photon is inconsistent with the known mass of the Λ 0 b baryon [6, 28]. Finally, the contributions from wrongly reconstructed B 0 → J/ψK + π − , Λ 0 b → J/ψpK − and B 0 s → J/ψK + K − decays, combined with random photons, are rejected by the requirement that the mass of the Λ 0 b candidate recalculated using different mass hypotheses for the pion, kaon and proton candidates and ignoring the photon in the final state, be inconsistent with the known mass of the corresponding beauty hadron.
To suppress a potentially large combinatorial background, separate BDTG classifiers are used for the Λ 0 b → χ cJ pπ − and Λ 0 b → χ cJ pK − candidates. The classifiers are trained using simulated samples of Λ 0 b → χ c1 pπ − and Λ 0 b → χ c1 pK − decays as signal. The Λ 0 b → χ c1 pπ − and Λ 0 b → χ c1 pK − candidates with the χ c1 pπ − and χ c1 pK − mass in the range 5.65 < m χ c1 pπ − and m χ c1 pK − < 6.00 GeV/c 2 are used as background. The k-fold cross-validation technique [32] with k = 7 is used to avoid introducing a bias in the BDTG output. The BDTG classifier for the Λ 0 b → χ cJ pπ − (Λ 0 b → χ cJ pK − ) candidates is trained on variables related to the reconstruction quality, kinematics and decay time of Λ 0 b candidates, kinematics of particles in the final state and the estimated probabilities that protons and pions (kaons) are correctly identified by the particle identification detectors [20,21]. The requirement on the BDTG output is chosen to maximize the figure-of-merit S/ √ S + B, where S and B are expected signal and background yields, correspondingly. The signal yields are estimated from the simulated samples, normalised to the signal yields observed in data for the loose requirements on the BDTG output, and the background yield B is estimated from the fit to data using a model, described in Sec. 4. After application of the BDTG requirement, 6% of events with Λ 0 b → χ cJ pπ − candidates in the 5.4 < m χ c1 pπ − < 5.8 GeV/c 2 region and 13% of events with Λ 0 b → χ cJ pK − candidates in the 5.3 < m χ c1 pK − < 5.8 GeV/c 2 region contain multiple candidates. These multiple candidates are predominantly caused by the J/ψpπ − or J/ψpK − combination being combined with different photons in the event. A study using simulation shows that the random photons causing multiple candidates typically have lower transverse energy with respect to that of the photons originating from the Λ 0 b baryon decay. Therefore, to reduce multiple candidates for each event, only the Λ 0 b candidate with the highest transverse energy photon is retained.
To improve the Λ 0 b mass resolution, the mass of the Λ 0 b candidates is calculated using a kinematic fit [31], similar to the one described above, but with an additional constraint fixing the mass of the J/ψγ combination to the known χ c1 mass [28]. For the Λ 0 b → χ c1 pπ − and Λ 0 b → χ c1 pK − decays, the mass calculated with such a constraint forms a narrow peak at the known mass of the Λ 0 b baryon, while for the Λ 0 b → χ c2 pπ − and Λ 0 b → χ c2 pK − decays the narrow peak is shifted towards lower values [6,9].

Signal yields and efficiencies
The mass distributions for selected Λ 0 b → χ cJ pπ − and Λ 0 b → χ cJ pK − candidates are shown in Figs. 1 and 2, respectively. The signal yields are determined using unbinned extended maximum-likelihood fits to these distributions. For the Λ 0 b → χ cJ pπ − channel, the fit model consists of two signal components, corresponding to the Λ 0 b → χ c1 pπ − and Λ 0 b → χ c2 pπ − decays, as described below, and a combinatorial background component that is described by the product of an exponential function and a first-order polynomial function, required to be positive in the relevant mass range. For the Λ 0 b → χ cJ pK − channel, the fit model consists of two signal components, corresponding to the Λ 0 b → χ c1 pK − and Λ 0 b → χ c2 pK − decays, a combinatorial background component which is described by a concave third-order positive polynomial function and a component from partially reconstructed Λ 0 b baryon decays, such as Λ 0 b → ψ(2S)pK − with subsequent decays ψ(2S) → J/ψππ, ψ(2S) → J/ψη or ψ(2S) → (χ c1 → J/ψγ) γ, which is described by a Gaussian function. Each of the four signal components is described by the sum of two Crystal Ball (CB) functions [33] with a common mean and power-law tails on both sides. The tail parameters of the CB functions, the ratio of the widths of the two CB functions, and their relative normalisation are fixed to the values obtained from simulation. The widths and the difference in the mean values for the large Λ 0 b → χ c1 pK − and Λ 0 b → χ c2 pK − components are allowed to vary in the fit, while for the small Λ 0 b → χ c1 pπ − and Λ 0 b → χ c2 pπ − components, the difference in the mean values and the ratio of widths are constrained to the values obtained from simulation.

Decay mode
according to the background distributions observed in data. The statistical significance is found to be 9.6 and 3.8 standard deviations for the Λ 0 b → χ c1 pπ − and Λ 0 b → χ c2 pπ − decay modes, respectively.
where N stands for the measured yield, ε denotes the efficiency of the corresponding decay and B(χ cJ → J/ψγ) are the branching fractions of the radiative χ cJ → J/ψγ decays, taken from Ref. [28]. The efficiency is defined as the product of the detector acceptance, reconstruction, selection and trigger efficiencies, where each subsequent efficiency is defined with respect to the previous one. Each of the partial efficiencies is calculated using the appropriately corrected simulation samples. The efficiencies are determined separately for each data-taking period and are combined according to the corresponding luminosity for each period. The ratios of the total efficiencies are determined to be where only the uncertainty that arises from the sizes of the simulated samples is given. The Λ 0 b → χ c1 pπ − decay channel has a much higher combinatorial background level, therefore, the BDTG selection is less efficient with respect to that for the Λ 0 b → χ c1 pK − channel, which is the main factor causing the difference in total efficiencies for these channels. Using these ratios of efficiencies and the measured yields from Table 1, the ratios of the branching fractions are found to be R π/K = (6.59 ± 1.01) × 10 −2 , R π 2/1 = 0.95 ± 0.30 , where the uncertainties are statistical only. Systematic uncertainties are discussed in the next section. Background-subtracted χ c1 p, χ c1 π − and pπ − mass distributions from the Λ 0 b → χ c1 pπ − decay are shown in Fig. 3. The sPlot technique, with the χ c1 pπ − mass as the discriminating variable, is used for background subtraction [35]. The distributions are compared with those obtained from simulated decays generated according to a phase space model and, with the present dataset, no evidence for large contributions from possible exotic states is found.

Systematic uncertainties
Since the Λ 0 b → χ cJ pπ − and Λ 0 b → χ cJ pK − decay channels have similar kinematics and topologies, systematic uncertainties largely cancel in the ratios R defined by Eqs. (1). The remaining contributions to the systematic uncertainties are summarized in Table 2 and discussed below.
The systematic uncertainty related to the signal and background shapes is investigated using alternative parameterisations. For the Λ 0 b → χ c1 pπ − and Λ 0 b → χ c1 pK − components, two alternative models are probed. The first model consists of a sum of a Student's t-distribution [36] and a double-sided Crystal Ball function (CB 2 ) with power-law tails on both sides of the peak [37]. The second alternative model is a sum of a Gaussian and CB 2 functions. For the Λ 0 b → χ c2 pπ − and Λ 0 b → χ c2 pK − components, two other alternative models are probed: a sum of a bifurcated Student's t-distribution with a CB 2 function, and a sum of a skewed Gaussian function [38] with a CB 2 function. The alternative parameterisations for the component from partially reconstructed Λ 0 b decays include a bifurcated Gaussian function and a Student's t-distribution. Two alternative shapes are used for the background parameterisation. The first model consists of a product of an exponential function and a second-order positive polynomial function, while a fourth-order concave positive polynomial function is used as the second alternative model. The systematic uncertainty related to the fit model is estimated by producing pseudoexperiments generated with the baseline fit model and fitted with alternative models. Each pseudoexperiment is approximately 100 times larger than the data sample. The maximal deviations for the ratios of the signal yields with respect to the baseline model are taken as systematic uncertainties in the ratios R. The assigned systematic uncertainties are 2.4%, 3.7% and 3.7% in the ratios R π/K , R π 2/1 and R K 2/1 , respectively. An additional systematic uncertainty in the ratios R arises due to differences between data and simulation. The transverse momentum and rapidity spectra of the Λ 0 b baryons in simulated samples are adjusted to match those observed in a high-yield low-background sample of reconstructed Λ 0 b → J/ψpK − decays. The finite size of this sample causes uncertainty in the obtained Λ 0 b production spectra. The systematic uncertainty in the efficiency ratios, related to the imprecise knowledge of the production Λ 0 b baryon spectra is estimated using the variation of the kinematic spectra of the selected Λ 0 b → J/ψpK − sample within their statistical uncertainty. This systematic uncertainty is found to be smaller than 0.1% in the R π/K ratio and even smaller for the R π 2/1 and R K 2/1 ratios. The simulated Λ 0 b → χ cJ pK − decays are corrected to reproduce the pK − mass and cos θ pK − distributions observed in data. The systematic uncertainty in the ε Λ 0 b →χ c1 pK − and ε Λ 0 b →χ c2 pK − efficiencies, related to the imprecise knowledge of the decay model for the Λ 0 b → χ cJ pK − decays, is estimated using the variation of the pK − mass and cos θ pK − spectra within their uncertainties. The corresponding systematic uncertainties in the R π/K and R K 2/1 ratios are found to be less than 0.1%. There are residual differences in the reconstruction efficiency of charged-particle tracks that do not cancel completely in the ratio due to the different kinematic distributions of the final-state particles. The track-finding efficiencies obtained from simulated samples are corrected using calibration channels [22]. The uncertainties related to the efficiency correction factors, are propagated to the ratios of the total efficiencies using pseudoexperiments and found to be smaller than 0.1% in the ratio R π/K and smaller in the ratios R π 2/1 and R K 2/1 . A small difference between data and simulation for the photon reconstruction is studied using a large sample of B + → J/ψ (K * + → K + (π 0 → γγ)) decays [29,39,40] The associated systematic uncertainty largely cancels in the ratios R.
The combined detector response used for the identification of protons, kaons and pions in simulation is resampled from control channels [21]. The systematic uncertainty obtained through this procedure arises from the kernel shape used in the estimation of the probability density distributions. An alternative combined response is estimated using an alternative kernel estimation with a changed shape and the efficiency models are regenerated [41,42]. The difference between the two estimates for the efficiency ratios is taken as the systematic uncertainty related to hadron identification and is found to be 0.3% in the ratio R π/K . In the ratios R π 2/1 and R K 2/1 this systematic uncertainty cancels as it is assumed to be fully correlated between the modes with χ c1 and χ c2 mesons.
A systematic uncertainty in the ratios related to the knowledge of the trigger efficiencies has been previously studied using high-yield B + → J/ψK + and B + → ψ(2S)K + decays by comparing ratios of trigger efficiencies in data and simulation [43]. Based on these comparisons, a relative uncertainty of 1.1% is assigned to R π/K , while for R π 2/1 and R K 2/1 it is expected to cancel in the ratio due to resemblance of the kinematics of the corresponding decay channels.
The imperfect data description by the simulation due to remaining effects is studied by varying the BDTG selection criteria in ranges that lead to ±20% changes in the measured efficiency. For this study, the high-statistics normalisation channel is used. The resulting difference between the efficiency estimated using data and simulation does not exceed 2.0%, which is taken as a systematic uncertainty in R π/K . This systematic uncertainty in R π 2/1 and R K 2/1 is considered negligible due to the similarity of the kinematics of the corresponding decay channels.
Finally, the uncertainties in the ratios of efficiencies from Eqs.
(2) are 0.4%, 0.6% and 0.7% and are taken as systematic uncertainties due to the finite size of the simulated samples for the R π/K , R π 2/1 and R K 2/1 , respectively. For each choice of the fit model, the statistical significance of the Λ 0 b → χ c2 pπ − signal is calculated from data using Wilks' theorem [34] and confirmed by simulating a large number of pseudoexperiments. The smallest significance found is 3.5 standard deviations, taken as its significance including systematic uncertainties.

Results and summary
A search for the Cabibbo-suppressed decays Λ 0 b → χ cJ pπ − is performed using a data sample collected by the LHCb experiment in proton-proton collisions at a centre-of-mass energy of 13 TeV and corresponding to 6 fb −1 of integrated luminosity. The Λ 0 b → χ c1 pπ − decay is observed for the first time with a yield of 105 ± 16 and a statistical significance above 9 standard deviations. First evidence for the Λ 0 b → χ c2 pπ − decay is obtained with a yield of 51 ± 16 and a significance of 3.5 standard deviations. The ratios of the branching fractions are measured to be = 0.95 ± 0.30 ± 0.04 ± 0.04 , where the first uncertainty is statistical, the second is systematic and the third is related to the uncertainties in the branching fractions of the χ cJ → J/ψγ decays [28]. The ratio R π/K is similar to analogous ratios for other Cabibbo-suppressed decays of the Λ 0 b baryon [25,44]. The expected value for the ratio R π/K , if neglecting the resonance structures in where Φ 3 denotes the full three-body phase space and θ C is the Cabibbo angle [45]. The ratio R K 2/1 agrees well with the previous measurement by the LHCb collaboration of 1.02 ± 0.10 ± 0.02 ± 0.05 [6]. This result has better precision and arises from a statistically independent sample from that of Ref.