Observation of the decays $\Lambda_b^0 \to \chi_{c1} p K^-$ and $\Lambda_b^0 \to \chi_{c2} p K^-$

TL;DR

This paper reports the first observation of specific Lambda_b^0 baryon decays involving chi_c states, measuring their branching ratios and the baryon mass with high precision using LHCb data.

Contribution

It provides the first observation and measurement of branching ratios for Lambda_b^0 decays to chi_c1 and chi_c2 states, and determines the baryon mass with improved accuracy.

Findings

First observation of these decay modes.

Measured branching fraction ratios with uncertainties.

Precise Lambda_b^0 mass measurement.

Abstract

The first observation of the decays $\Lambda_b^0 \to \chi_{c1} p K^-$ and $\Lambda_b^0 \to \chi_{c2} p K^-$ is reported using a data sample corresponding to an integrated luminosity of $3.0$ fb$^{-1}$, collected by the LHCb experiment in $pp$ collisions at centre-of-mass energies of 7 and 8 TeV. The following ratios of branching fractions are measured \begin{eqnarray*} \frac{{\cal B}(\Lambda_b^0 \to \chi_{c1} p K^-)}{{\cal B}(\Lambda_b^0 \to J/\psi p K^-)} = 0.242 \pm 0.014 \pm 0.013 \pm 0.009, \frac{{\cal B}(\Lambda_b^0 \to \chi_{c2} p K^-)}{{\cal B}(\Lambda_b^0 \to J/\psi p K^-)} = 0.248 \pm 0.020 \pm 0.014 \pm 0.009, \frac{{\cal B}(\Lambda_b^0 \to \chi_{c2} p K^-)}{{\cal B}(\Lambda_b^0 \to \chi_{c1} p K^-)} = 1.02 \pm 0.10 \pm 0.02 \pm 0.05, \end{eqnarray*} where the first uncertainty is statistical, the second systematic and the third due to the uncertainty on the branching fractions of the $\chi_{c1}\to J/\psi\gamma$ and $\chi_{c2} \to J/\psi\gamma$ decays. Using both decay modes, the mass of the $\Lambda_b^0$ baryon is also measured to be $m_{\Lambda_b^0} = 5619.44 \pm 0.28 \pm 0.26$ MeV/$c^2$, where the first and second uncertainties are statistical and systematic, respectively.

Figures

Equations

$$\frac{\mathcal{B}({\text{mathchar}28931}_b^0\to {\chi }_{c1}p{K}^{-})}{\mathcal{B}({\text{mathchar}28931}_b^0\to J/\psi p{K}^{-})}=0.242\pm 0.014\pm 0.013\pm 0.009,$$

$$\frac{\mathcal{B}({\text{mathchar}28931}_b^0\to {\chi }_{c2}p{K}^{-})}{\mathcal{B}({\text{mathchar}28931}_b^0\to J/\psi p{K}^{-})}=0.248\pm 0.020\pm 0.014\pm 0.009,$$

$$\frac{\mathcal{B}({\text{mathchar}28931}_b^0\to {\chi }_{c2}p{K}^{-})}{\mathcal{B}({\text{mathchar}28931}_b^0\to {\chi }_{c1}p{K}^{-})}=1.02\pm 0.10\pm 0.02\pm 0.05,$$

$$R_{1(2)}$$

$$R_{2/1}$$

$$R_1$$

$$R_2$$

$$R_{2/1}$$

$$\mathcal{B}\left({\text{mathchar}28931}_b^0\to {\chi }_{c1}p{K}^{-}\right)$$

$$\mathcal{B}\left({\text{mathchar}28931}_b^0\to {\chi }_{c2}p{K}^{-}\right)$$

Full text

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

​​​

CERN-EP-2017-073

LHCb-PAPER-2017-011

August 9, 2017

Observation of the decays ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\chi_{c1}{p}{{K}^{-}}$ and ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\chi_{c2}{p}{{K}^{-}}$

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

The first observation of the decays ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\chi_{c1}{p}{{K}^{-}}$ and ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\chi_{c2}{p}{{K}^{-}}$ is reported using a data sample corresponding to an integrated luminosity of $3.0\mbox{\,fb}^{-1}$, collected by the LHCb experiment in $pp$ collisions at centre-of-mass energies of 7 and 8 TeV. The following ratios of branching fractions are measured

[TABLE]

where the first uncertainty is statistical, the second systematic and the third due to the uncertainty on the branching fractions of the ${\chi_{{c}1}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{\gamma}$ and ${\chi_{{c}2}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{\gamma}$ decays. Using both decay modes, the mass of the ${\mathchar 28931\relax}^{0}_{b}$ baryon is also measured to be

$m_{{\mathchar 28931\relax}^{0}_{b}}=5619.44\pm 0.28\pm 0.26{\mathrm{\,Me\kern-1.00006ptV\!/}c^{2}}\,,$

where the first and second uncertainties are statistical and systematic, respectively.

Published as Phys. Rev. Lett. 119, 062001 (2017)

© CERN on behalf of the LHCb collaboration, licence CC-BY-4.0.

Since the birth of the quark model, it has been speculated that hadrons could be formed from multiquark states beyond the well-studied quark-antiquark (meson) and three-quark (baryon) combinations [1, 2, 3]. Using a six-dimensional amplitude analysis of the ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{p}{{K}^{-}}$ decay mode, the LHCb collaboration observed the $P_{c}(4380)^{+}$ and $P_{c}(4450)^{+}$ states [4, 5], which are consistent with $uudc\overline{c}$ hidden-charm pentaquarks decaying to ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{p}$. Many phenomenological models describing the dynamics of these states have been proposed, including meson-baryon molecules [6, 7, 8], compact pentaquarks [9, 10, 11] and kinematic rescattering effects [12, 13, 14, 15, 16]. In particular, the authors of Ref. [12] noted the closeness of the $P_{c}(4450)^{+}$ mass to the $\chi_{c1}p$ threshold and proposed that, if the $P_{c}(4450)^{+}$ state is a rescattering effect, then it would not appear as an enhancement near the $\chi_{c1}p$ threshold in the ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\chi_{c1}p{{K}^{-}}$ decay mode, an approach recently challenged in Ref. [17]. This Letter presents an initial stage in the investigation of this hypothesis by making the first observation of ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{\chi_{{c}1}}{p}{{K}^{-}}$ and ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{\chi_{{c}2}}{p}{{K}^{-}}$ decays and measurements of their branching fractions relative to the ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{p}{{K}^{-}}$ decay. Throughout this Letter, the inclusion of charge-conjugated processes is implied and the symbol $\chi_{cJ}$ is used to denote the ${\chi_{{c}1}}$ and ${\chi_{{c}2}}$ states collectively. All ${{\mathchar 28931\relax}^{0}_{b}}$ decay modes considered here proceed via the same quark-level process, whose dominant contribution is shown in Fig. 1. A measurement of the ${\mathchar 28931\relax}^{0}_{b}$ baryon mass is also presented.

Previous measurements of the branching fractions of ${B}\rightarrow\chi_{cJ}K$ decays [18, 19, 20] have shown that the $\chi_{c2}$ mode is suppressed relative to the $\chi_{c1}$ mode, in agreement with the predictions from the factorisation approach [21], although the suppression appears to be lessened when additional particles are present in the final state [22]. Studying the production of $\chi_{cJ}$ mesons in ${\mathchar 28931\relax}^{0}_{b}$ baryon decays will help to further test the factorisation approach, as the additional spectator quark in the baryon decay may play an important role in modifying final-state interactions.

The measurements described in this Letter are based on a data sample corresponding to 1.0$\mbox{\,fb}^{-1}$ of integrated luminosity collected by the LHCb experiment in $pp$ collisions at a centre-of-mass energy of 7$\mathrm{\,Te\kern-1.00006ptV}$ in 2011, and 2.0$\mbox{\,fb}^{-1}$ at 8$\mathrm{\,Te\kern-1.00006ptV}$ in 2012. The LHCb detector [23, 24] 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 surrounding the $pp$ interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about $4{\mathrm{\,Tm}}$, and three stations of silicon-strip detectors and straw drift tubes placed downstream of the magnet. The tracking system provides a measurement of momentum, $p$, of charged particles with a relative uncertainty that varies from $0.5\,\%$ at low momentum to $1.0\,\%$ at 200${\mathrm{\,Ge\kern-1.00006ptV\!/}c}$. The minimum distance of a track to a primary vertex (PV), the impact parameter (IP), is measured with a resolution of (15+29/\mbox{p_{\mathrm{T}}}){\,\upmu\mathrm{m}}, where $p_{\mathrm{T}}$ is the component of the momentum transverse to the beam, in ${\mathrm{\,Ge\kern-1.00006ptV\!/}c}$. Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov detectors. Photons, electrons and hadrons are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic calorimeter and a hadronic calorimeter. 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. The software trigger selects events that contain a pair of oppositely charged muons that form a vertex that is significantly separated from all PVs.

In the simulation, $pp$ collisions are generated using Pythia 8 [25, *Sjostrand:2007gs] with a specific LHCb configuration [27]. Decays of hadronic particles are described by EvtGen [28], in which final-state radiation is generated using Photos [29]. The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [30, *Agostinelli:2002hh] as described in Ref. [32]. The products of the ${{\mathchar 28931\relax}^{0}_{b}}$ decays are generated uniformly within the available phase space.

The ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\chi_{cJ}p{{K}^{-}}$ and ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p{{K}^{-}}$ candidates are reconstructed via the decays $\chi_{cJ}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\gamma$ and ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rightarrow\mu^{+}\mu^{-}$. To separate signal from background, an offline selection is applied after the trigger, consisting of a loose preselection followed by a multivariate classifier based on a gradient-boosted decision tree (GBDT) [33].

The ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ candidates are formed from two oppositely charged particles with \mbox{p_{\mathrm{T}}}>550{\mathrm{\,Me\kern-1.00006ptV\!/}c}, identified as muons and consistent with originating from a common vertex, but inconsistent with originating from any PV. The invariant mass of the $\mu^{+}\mu^{-}$ pair is required to be in the range $[3000,3170]{\mathrm{\,Me\kern-1.00006ptV\!/}c^{2}}$. The $\chi_{cJ}$ candidates are formed from a ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ candidate and a photon with \mbox{p_{\mathrm{T}}}>700{\mathrm{\,Me\kern-1.00006ptV\!/}c}. Photons that are consistent with originating from a $\pi^{0}$ meson when combined with any other photon in the event are removed. The invariant mass of the $\mu^{+}\mu^{-}\gamma$ combination is required to be in the range $[3400,3700]{\mathrm{\,Me\kern-1.00006ptV\!/}c^{2}}$. In the following, the notation $[c\overline{c}]$ will be used to refer to the initial ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ or $\chi_{cJ}$ candidate from the ${\mathchar 28931\relax}^{0}_{b}$ baryon decay, while the notation $m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}X)$ or $m(\chi_{cJ}X)$ denotes an invariant mass that has been calculated with a mass constraint applied to the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ or $\chi_{cJ}$ candidate.

The ${\mathchar 28931\relax}^{0}_{b}$ candidates are formed from a $[c\overline{c}]$ candidate and two good-quality oppositely charged tracks each with \mbox{p_{\mathrm{T}}}>200{\mathrm{\,Me\kern-1.00006ptV\!/}c}, identified as a proton and kaon. Both tracks are required to be significantly displaced from any PV. A kinematic fit [34] is applied to the ${\mathchar 28931\relax}^{0}_{b}$ candidate, with the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\chi_{c1}$ masses constrained to their known values [35], and the ${\mathchar 28931\relax}^{0}_{b}$ candidate constrained to point back to a PV. This has the effect of producing separated peaks for the two decay modes. The mass resolution for ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\chi_{c2}p{{K}^{-}}$ decays is lower compared to that for ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\chi_{c1}p{{K}^{-}}$ decays due to the wrong mass hypothesis of the $[c\overline{c}]$ candidate.

Contributions from ${{B}^{0}}\rightarrow[c\overline{c}]{{K}^{+}}\pi^{-}$ (${{B}^{0}_{s}}\rightarrow[c\overline{c}]\phi$, $\phi\rightarrow{{K}^{+}}{{K}^{-}}$) decays, where the $\pi^{-}$ (${{K}^{-}}$) is misidentified as an antiproton, are suppressed by placing tighter particle identification requirements on the misidentified hadron for candidates with an invariant mass within 30${\mathrm{\,Me\kern-1.00006ptV\!/}c^{2}}$ of the ${B}^{0}$ (${B}^{0}_{s}$) mass [35] when evaluated using ${{\pi}^{-}}$ or ${{K}^{-}}$ mass assignments for the antiproton candidates. Typical mis-identification probabilities are $5-15$ %, dependent on the particle momentum [36]. In the ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\chi_{cJ}p{{K}^{-}}$ samples, small contributions from ${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{+}}\pi^{-}$ or ${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ decays, where in addition to the misidentification the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson is combined with a random photon in the event, are removed by the requirement that $m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{+}}{{\pi}^{-}})$ or $m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{+}}{{K}^{-}})$ are within 30${\mathrm{\,Me\kern-1.00006ptV\!/}c^{2}}$ of the ${B}^{0}$ or ${B}^{0}_{s}$ mass. Additionally, $\phi\rightarrow{{K}^{+}}{{K}^{-}}$ decays are vetoed by removing all candidates where the invariant mass of the $p{{K}^{-}}$ combination is within 12${\mathrm{\,Me\kern-1.00006ptV\!/}c^{2}}$ of the known $\phi$ meson mass when the kaon mass is used instead of the proton mass. Further misreconstructed backgrounds are studied using a fast simulation package [37] and are found to have no peaking components in the invariant mass window of interest.

The GBDT is used to further suppress the combinatorial background. It is trained on a simulated sample of ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\chi_{c1}p{{K}^{-}}$ decays for the signal and candidates from data with $m(\chi_{c1}p{{K}^{-}})$ in the range $[5700,5800]{\mathrm{\,Me\kern-1.00006ptV\!/}c^{2}}$ for the background. Twelve variables are used as input. The first of these is the $\chi^{2}$ value obtained from a kinematic fit with the ${{\mathchar 28931\relax}^{0}_{b}}$ candidate constrained to point back to a PV and a mass constraint applied to the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$. In addition, for the signal mode, ${\chi_{{c}1}}$ or ${\chi_{{c}2}}$ mass constraints are applied, with the smaller $\chi^{2}$ values being used; note that this differs from the fit used to separate the mass peaks, which does not include a ${\chi_{{c}2}}$ constraint. The remaining variables are the $p_{\mathrm{T}}$ of the ${{\mathchar 28931\relax}^{0}_{b}}$, proton and kaon; the ${{\mathchar 28931\relax}^{0}_{b}}$ decay-length significance; the cosine of the angle between the momentum of the ${{\mathchar 28931\relax}^{0}_{b}}$ candidate and its displacement from the PV; the proton and kaon $\chi^{2}_{\text{IP}}$, defined as the difference in the vertex-fit $\chi^{2}$ of the PV when reconstructed with and without the considered particle; and the estimated probabilities that the two muons, kaon and proton are correctly identified by the particle identification detectors.

Prior to the training, several modifications are made to the simulated samples to better match the kinematic distributions observed in data. First, the simulated ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p{{K}^{-}}$ events are weighted according to the six-dimensional amplitude model developed in Ref. [4]. Second, a multidimensional gradient-boosting algorithm [38] is used to weight the simulated ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p{{K}^{-}}$ decays such that the distributions of ${\mathchar 28931\relax}^{0}_{b}$ pseudorapidity, the number of tracks in the event and the GBDT training variables (apart from those related to particle identification) match those observed in the preselected background-subtracted ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p{{K}^{-}}$ data sample. These weights are also applied to the simulated ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\chi_{cJ}p{{K}^{-}}$ samples. Finally, the simulated distributions of the particle identification variables for the muon, proton and kaon candidates are resampled from data calibration samples (${{D}^{*+}}\rightarrow{D}{{\pi}^{+}}$, ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rightarrow\mu^{+}\mu^{-}$, ${\mathchar 28931\relax}\rightarrow p\pi^{-}$ and ${{\mathchar 28931\relax}^{+}_{c}}\rightarrow p{{K}^{-}}{{\pi}^{+}}$ decays) in bins of track $p$, $p_{\mathrm{T}}$ and the number of tracks.

The optimal working point for the GBDT response is chosen by maximising a figure of merit, $S/\sqrt{S+B}$, where $S=S_{0}\epsilon$ and $B$ are the expected signal and background yields within $\pm 20{\mathrm{\,Me\kern-1.00006ptV\!/}c^{2}}$ of the known ${\mathchar 28931\relax}^{0}_{b}$ baryon mass [35], $S_{0}$ is the signal yield determined from data without any cut on the GBDT response, and $\epsilon$ is the relative efficiency of the GBDT selection, evaluated using the simulated sample. The ${\mathchar 28931\relax}^{0}_{b}$ mass sidebands from the data are used to estimate $B$. The same GBDT and working point are used for the ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p{{K}^{-}}$ normalisation mode. The GBDT selection efficiencies are $78\,\%$, $75\,\%$ and $68\,\%$ for the ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\chi_{c1}p{{K}^{-}}$, ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\chi_{c2}p{{K}^{-}}$ and ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p{{K}^{-}}$ channels, respectively.

After applying the GBDT requirement, $(2.9\pm 0.4)\,\%$ of the selected events contain multiple ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\chi_{cJ}p{{K}^{-}}$ candidates. In approximately $80\,\%$ of these cases, the same ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p{{K}^{-}}$ combination is combined with an additional, unrelated, photon in the event. The results reported in this Letter retain all candidates and the reported branching fractions are corrected to account for this. The correction factor is $0.993\pm 0.006$ ($0.986\pm 0.009$) for ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{\chi_{{c}1}}p{{K}^{-}}$ (${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{\chi_{{c}2}}p{{K}^{-}}$) decays, which is evaluated using a combination of the simulated samples and pseudoexperiments. The larger width of the ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\chi_{c2}p{{K}^{-}}$ component leads to the larger uncertainty on the correction factor. For the selected ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p{{K}^{-}}$ sample, $(0.75\pm 0.05)\,\%$ of the events have multiple candidates.

Extended unbinned maximum-likelihood fits are performed to the distributions of $m(\chi_{c1}{p}{{K}^{-}})$ and $m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{p}{{K}^{-}})$ for the signal and normalisation modes, respectively. The fit models consist of signal components, each described by the sum of two Crystal Ball (CB) functions [39] with a common mean and power-law tails on both sides, and a linear combinatorial background component. Due to the small $\chi_{c0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\gamma$ branching fraction [35] the contribution from the $\chi_{c0}$ mode is negligible. Several parameters of the signal shapes are determined from fits to simulated samples. These include the tail parameters of the CB functions, the ratio of the widths of the two CB functions, and their relative normalisations. The ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{\chi_{{c}2}}{p}{{K}^{-}}$ signal component is shifted to a lower mass in $m(\chi_{c1}{p}{{K}^{-}})$ due to the ${\chi_{{c}1}}$ mass constraint. The signal and background yields, the gradient of the background shape and the mean of each signal component are free parameters in the fit to data. In addition, the widths of the $\chi_{c1}$ and $\chi_{c2}$ components in the fit to $m(\chi_{c1}{p}{{K}^{-}})$ are allowed to differ from simulation by a common scaling factor, while the width of the narrower CB function in the ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{p}{{K}^{-}}$ signal component is a free parameter in the fit to data. The results of these fits are shown in Fig. 2. The measured yields are $453\pm 25$, $285\pm 23$ and $29\,815\pm 178$ for the ${\chi_{{c}1}}$, ${\chi_{{c}2}}$ and ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ modes, respectively. The significance of each of the signal components in the fit to $m(\chi_{c1}{p}{{K}^{-}})$ is calculated using Wilks’ theorem [40]. This gives statistical significances of $29$ and $17$ standard deviations for the decay modes with $\chi_{c1}$ and $\chi_{c2}$, respectively.

Simulated samples are used to determine, for each decay mode, the reconstruction and selection efficiency as a function of the Dalitz plot coordinates [41], $m^{2}({p}{{K}^{-}})$ and $m^{2}([c\overline{c}]{p})$. This approach focuses on the dimensions where the efficiency variation is expected to be largest whilst averaging over other dimensions in the phase space of ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow[c\overline{c}]p{{K}^{-}}$ decays. This assumption is treated as a source of systematic uncertainty. The efficiency of each mode, $\epsilon_{[c\overline{c}]}$, is due to geometric acceptance, reconstruction and selection including the GBDT. The ratios of the phase-space-averaged values of these efficiencies are $0.182\pm 0.005$ for $\epsilon_{{\chi_{{c}1}}}/\epsilon_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}$, and $0.196\pm 0.005$ for $\epsilon_{{\chi_{{c}2}}}/\epsilon_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}$, where the uncertainties are due to the size of the simulated samples. This includes a correction factor for the $\chi_{cJ}$ decay modes to account for differences in the photon reconstruction efficiency between data and simulation [20, 42].

An efficiency-corrected, background-subtracted yield is determined for each decay mode as $N^{\rm corr}([c\overline{c}]{p}{{K}^{-}})=\sum_{i}w_{i}/\epsilon_{[c\overline{c}],i}$, where the index $i$ runs over all candidates in the fit range. The $w_{i}$ are weights determined using the sPlot background-subtraction technique [43], which project out the signal component from the combined signal plus background densities using the $[c\overline{c}]{p}{{K}^{-}}$ invariant mass as discriminating variable. The corrected yields are found to be about $99\,700\pm 5300$, $57\,800\pm 4400$ and $1\,213\,500\pm 7300$ for the ${\chi_{{c}1}}$, ${\chi_{{c}2}}$ and ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ decay modes, respectively, where the uncertainties are determined from the sum in quadrature of the event weights. Since these weights are determined from a fit in which all shape parameters are fixed, following the sPlot prescription, the effect on the yield uncertainty due to the statistical uncertainties on these parameters is not included. To quantify this, the unweighted fit is performed with the shape parameters fixed and then free, and the difference in quadrature of the uncertainties is found to be 1.5 % of the yield for ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\chi_{c1}{p}{{K}^{-}}$ decays and 2.1 % for ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\chi_{c2}{p}{{K}^{-}}$. A corresponding uncertainty is added in quadrature to that on the efficiency-corrected yield. The effect is negligible for the much larger ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{p}{{K}^{-}}$ signal.

The ratios of branching fractions are determined as

[TABLE]

where the branching fraction of the ${\chi_{{c}1}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\gamma$ $({\chi_{{c}2}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\gamma)$ decay is taken to be $(33.9\pm 1.2)\,\%$ ($(19.2\pm 0.7)\,\%$) [35]. Figure 3(a) shows the distribution of $\Delta m+m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}$, where $\Delta m$ is $m(\mu^{+}\mu^{-}\gamma)-m(\mu^{+}\mu^{-})$ and $m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}$ is the known mass of the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson [35], while Fig. 3(b) shows $\Delta m+m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}$ for background-subtracted ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\chi_{cJ}{p}{{K}^{-}}$ candidates. Both distributions show clear enhancements at the known masses of the $\chi_{cJ}$ mesons.

The ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow\chi_{cJ}{p}{{K}^{-}}$ data sample is also used to make a measurement of the ${{\mathchar 28931\relax}^{0}_{b}}$ mass, $m_{{{\mathchar 28931\relax}^{0}_{b}}}$. The momenta of the particles are scaled to account for known miscalibration of the detector [44]. In addition, the separation between the ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{\chi_{{c}1}}{p}{{K}^{-}}$ and ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{\chi_{{c}2}}{p}{{K}^{-}}$ components in the $m(\chi_{c1}{p}{{K}^{-}})$ spectrum is fixed to the known mass difference between the $\chi_{c1}$ and $\chi_{c2}$ mesons [35], to obtain a single measurement of $m_{{{\mathchar 28931\relax}^{0}_{b}}}$ using both decay modes. The mass fit is repeated after these changes, yielding $m_{{{\mathchar 28931\relax}^{0}_{b}}}=5619.44\pm 0.28{\mathrm{\,Me\kern-1.00006ptV\!/}c^{2}}$.

Systematic uncertainties on the ratios of branching fractions are assigned due to imperfect knowledge of the trigger efficiency and data/simulation discrepancies in the photon reconstruction as well as for uncertainties on the corrections applied to the simulated data (kinematic reweighting, phase-space weighting and particle identification resampling), the treatment of multiple candidates, the limited size of simulated data samples, and the models for the signal and background components in the fits. The per-candidate efficiencies as a function of the Dalitz plot coordinates are also replaced by phase-space-averaged efficiencies, and the difference with the nominal result is assigned as a systematic uncertainty.

The systematic uncertainties due to the trigger and photon reconstruction are taken from previous LHCb studies [20, 45, 42]. The uncertainties assigned due to the kinematic weighting are evaluated by repeating the analysis with alternative efficiency histograms that make use of a simplified three-dimensional weighting procedure with only the ${\mathchar 28931\relax}^{0}_{b}$ pseudorapidity, ${\mathchar 28931\relax}^{0}_{b}$ $p_{\mathrm{T}}$ and event track-multiplicity. The uncertainty on the correction for multiple candidates is assigned as a systematic uncertainty. The uncertainty from the size of the simulated samples is determined from pseudoexperiments by varying the efficiency in each bin of each efficiency histogram within its uncertainties. The signal and background components of the invariant mass fits are replaced with the sum of two Gaussian functions and an exponential function, respectively, to estimate systematic uncertainties due to the choice of models.

The largest systematic uncertainties on $R_{1}$ and $R_{2}$ come from the photon reconstruction (both 4.0 %) and kinematic weighting of the simulated samples (2.2 % and 2.0 %, respectively). For $R_{2/1}$, the largest systematic uncertainties are due to the size of the simulated samples (1.2 %) and the treatment of multiple candidates (1.1 %). The total systematic uncertainties on $R_{1}$, $R_{2}$ and $R_{2/1}$ are 5.2 %, 5.4 % and 2.0 %, respectively.

For the ${{\mathchar 28931\relax}^{0}_{b}}$ mass measurement, systematic uncertainties are assigned due to the uncertainty on the momentum scale for charged-particle tracks, uncertainties on the $\chi_{cJ}$ and kaon masses, energy loss in the material, miscalibration of the electromagnetic calorimeter, and the models for the signal and background components in the fit. The total systematic uncertainty ($0.26{\mathrm{\,Me\kern-1.00006ptV\!/}c^{2}}$) is dominated by the uncertainty on the momentum scale ($0.24{\mathrm{\,Me\kern-1.00006ptV\!/}c^{2}}$), the effect of which is determined by repeating the analysis with the momentum scaling parameter varied up and down by one standard deviation [44]. The uncertainty from the miscalibration of the electromagnetic calorimeter [46] is found to be small due to the mass constraints that are applied, as is the uncertainty on the energy loss in material, which is taken from a previous LHCb study [47].

In conclusion, the ratios of branching fractions are found to be

[TABLE]

where the first uncertainty is statistical, the second systematic and the third due to the uncertainty on the branching fractions of the $\chi_{cJ}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{\gamma}$ decays. The values of $R_{1}$ and $R_{2}$ may be combined with existing measurements of ${\cal B}\left({{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{p}{{K}^{-}}\right)/{\cal B}\left({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{*}}(892)^{0}\right)$ [48] and ${\cal B}\left({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{*}}(892)^{0}\right)$ [49] to obtain absolute branching fraction measurements. As the result in Ref. [49] assumes equal production of ${{{B}^{+}}}{{{B}^{-}}}$ and ${{B}^{0}}{{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}$ pairs at the ${\mathchar 28935\relax{(4S)}}$ resonance, a correction is applied using the current world average value of ${\cal B}({\mathchar 28935\relax{(4S)}}\rightarrow{{{B}^{+}}}{{{B}^{-}}})/{\cal B}({\mathchar 28935\relax{(4S)}}\rightarrow{{B}^{0}}{{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}})=1.058\pm 0.024$ [35], yielding ${\cal B}\left({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{*}}(892)^{0}\right)=(1.22\pm 0.08)\times 10^{-3}$ and ${\cal B}\left({{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{p}{{K}^{-}}\right)=(3.01\pm 0.21\,^{+0.43}_{-0.26})\times 10^{-4}$, where the second uncertainty is due to the ratio of fragmentation fractions, $f_{{{\mathchar 28931\relax}^{0}_{b}}}/f_{d}$ [50, 51], and the first incorporates all other sources. This gives

[TABLE]

where the third uncertainty is due to uncertainties on the $\chi_{cJ}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{\gamma}$, ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{p}{{K}^{-}}$ and ${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{*}}(892)^{0}$ branching fractions and the fourth is due to $f_{{{\mathchar 28931\relax}^{0}_{b}}}/f_{d}$ [50, 51]. These results show no suppression of the $\chi_{{c}2}$ mode relative to the $\chi_{{c}1}$ mode in ${\mathchar 28931\relax}^{0}_{b}$ baryon decays, which is different to what is observed in ${B}\rightarrow\chi_{cJ}K$ decays [18, 19, 20]. These decays will be useful for future investigations into the nature of the two pentaquark candidates observed by the LHCb collaboration and provide further information on the applicability of the factorisation approach in describing $b$-hadron decays to final states containing charmonium.

The ${{\mathchar 28931\relax}^{0}_{b}}$ mass has also been measured and is found to be $5619.44\pm 0.28\pm 0.26{\mathrm{\,Me\kern-1.00006ptV\!/}c^{2}}$, where the first uncertainty is statistical and the second systematic. This result is combined with previous LHCb measurements from ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow[c\overline{c}]X$ decays [52, 53, 47] assuming that systematic uncertainties on the momentum scale and energy loss are fully correlated between the measurements while other sources of systematic uncertainties are uncorrelated. The procedure for the combination is the same as that used in Ref. [47]. This yields a new average value of $5619.62\pm 0.16\pm 0.13{\mathrm{\,Me\kern-1.00006ptV\!/}c^{2}}$, which supersedes previous combinations of these results.

Acknowledgements

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 (The 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 (The 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), Conseil Général de Haute-Savoie, Labex ENIGMASS and OCEVU, Région Auvergne (France), RFBR and Yandex LLC (Russia), GVA, XuntaGal and GENCAT (Spain), Herchel Smith Fund, The Royal Society, Royal Commission for the Exhibition of 1851 and the Leverhulme Trust (United Kingdom).