First observation of the decay $\Lambda_b^0 \to \eta_c(1S) p K^-$

The decay $\Lambda_b^0 \to \eta_c(1S) p K^-$ is observed for the first time using a data sample of proton-proton collisions, corresponding to an integrated luminosity of 5.5 $fb^{-1}$, collected with the LHCb experiment at a centre-of-mass energy of 13 TeV. The branching fraction of the decay is measured, using the $\Lambda_b^0 \to J/\psi p K^-$ decay as a normalisation mode, to be $\mathcal{B}(\Lambda_b^0 \to \eta_c(1S) p K^-)=(1.06\pm0.16\pm0.06^{+0.22}_{-0.19})\times10^{-4}$, where the quoted uncertainties are statistical, systematic and due to external inputs, respectively. A study of the $\eta_c(1S) p$ mass spectrum is performed to search for the $P_c(4312)^+$ pentaquark state. No evidence is observed and an upper limit of \begin{equation*} \frac{\mathcal{B}(\Lambda_b^0 \to P_c(4312)^+ K^-)\times \mathcal{B}(P_c(4312)^+ \to \eta_c(1S) p)}{\mathcal{B}(\Lambda_b^0 \to \eta_c(1S) p K^-)}<0.24 \end{equation*} is obtained at 95% confidence level.

The yet-unobserved Λ 0 b → η c pK − decay, where η c refers to the η c (1S) meson, can provide a unique approach to search for new pentaquarks, and to study the observed states. It has been predicted that a DΣ c molecular state, with a mass of around 4265 MeV/c 2 , can contribute to the decay Λ 0 b → η c pK − via η c p final-state interactions [26]. The observed P c (4312) + state could be such a molecular state [27], since its mass is close to the DΣ c threshold [5].
The study of the Λ 0 b → η c pK − decay provides a new way to test the binding mechanism of pentaquark states, as the predicted ratio of the branching fractions for a pentaquark decaying into η c p compared to the J/ψ p final states depends on the pentaquark model. The branching fraction of P c (4312) + → η c p is predicted to be three times larger than that of the J/ψ p decay mode if the P c (4312) + state is a DΣ c molecule [13][14][15].
This Letter presents the first observation of the Λ 0 b → η c pK − decay, with the η c meson reconstructed using the η c → pp decay mode. The analysis uses the decay Λ 0 b → J/ψ pK − as a normalisation channel, where the J/ψ meson decays to pp. The data sample used in this analysis corresponds to an integrated luminosity of 5.5 fb −1 , collected with the LHCb experiment in proton-proton collisions at √ s =13 TeV between 2016 and 2018. In the B-meson sector, Heavy Quark Effective Theory (HQET) [28,29] predicts that the decay rates of the B → η c X and B → J/ψ X channels are of the same order of magnitude. Experimental results are in good agreement with this expectation [30]. Studying the branching fraction ratio between the Λ 0 b → η c pK − and Λ 0 b → J/ψ pK − decays will provide the first comparison of b-baryon decay rates to the η c X and J/ψ X final states, and help to test whether the presence of an additional spectator quark modifies the final-state interactions in a nonnegligible way.
The LHCb detector is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, and is described in detail in Refs. [31,32]. The detector includes a silicon-strip vertex detector surrounding the proton-proton interaction region, tracking stations on either side of a dipole magnet, ring-imaging Cherenkov (RICH) detectors, calorimeters and muon chambers. The online event selection is performed by a trigger [33], 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 requires a two-, three-or four-track secondary vertex with a significant displacement from any primary vertex (PV) that is consistent with originating from the decay of a b hadron [34].
Simulated data samples as described in Refs. [35][36][37][38][39][40], are used to optimize the event selection, determine the efficiency of the reconstruction and event selection, and to constrain the fit model which determines the signal yield. The simulated Λ 0 b → η c pK − and Λ 0 b → J/ψ pK − decays are generated based on a uniform phase-space model. The simulated decays are also weighted to match the Λ 0 b momentum spectrum and Dalitz-plot distribution in the data, as described later in this Letter.
The Λ 0 b → η c (→ pp)pK − , and Λ 0 b → J/ψ (→ pp)pK − candidates are reconstructed and selected using the same selection criteria, with a pp mass window of [2800, 3200] MeV/c 2 that covers both the η c and J/ψ mass regions. In the following, the notation [cc] will be used to refer to both the η c and the J/ψ candidates from Λ 0 b baryon decays. Particle identification (PID) variables in the simulation are calibrated using large data samples of kinematically identified protons and kaons, originating from The offline event selection is performed using a preselection, followed by a requirement on the response of a Boosted Decision Tree (BDT) classifier [41,42]. In the preselection, each track is required to be of good quality. Kaons and protons are both required to have p T > 300 MeV/c, where p T is the component of the momentum transverse to the beam. Protons are also required to have a momentum larger than 10 GeV/c 2 , such that the kaons and protons can be distinguished by the RICH detectors. The sum of the p T of the proton and kaon from the Λ 0 b baryon is required to be larger than 900 MeV/c. The [cc] candidate is required to have a good-quality vertex.
The Λ 0 b candidate must have a good-quality decay vertex that is significantly displaced from every PV, and have χ 2 IP < 25 with respect to the associated PV. Here, χ 2 IP is defined as the χ 2 difference between the vertex fit of a PV reconstructed with or without the particle in question, and the associated PV is the one with the smallest χ 2 IP value. The angle between the reconstructed momentum vector of the Λ 0 b candidate and the line connecting the associated PV and the Λ 0 b decay vertex, where a kaon or pion is misidentified as a proton, is removed by applying strict particle identification requirements on candidates with a mass within ±50 MeV/c 2 around the known B 0 s or B 0 mass [30] after assigning a kaon or pion mass hypothesis to the proton. Backgrounds from φ(1020) → K + K − and D 0 → K + K − decays, where one of the kaons is misidentified as a proton and the Λ 0 b candidate is formed by combining the particles with a [cc] candidate from elsewhere in the event, are also observed. These contributions are removed by placing stricter particle-identification requirements on candidates with a pK − mass within ±10 MeV/c 2 (±20 MeV/c 2 ) of the known φ(1020) (D 0 ) mass, after assigning a kaon mass hypothesis [30] to the proton.
After the preselection, further separation between the signal and combinatorial backgrounds originating from a random combination of final-state particles is achieved by using a BDT classifier. The classifier uses the following input variables: the p T of the Λ 0 b candidate, and of the kaon and proton directly from the Λ 0 b decay; the χ 2 IP of the Λ 0 b candidate, the [cc] candidate, and the kaon and proton directly from the Λ 0 b decay; the smallest values of both the p T and χ 2 IP of the [cc] decay products; the significance of the displacement of the Λ 0 b vertex with respect to the associated PV; the vertex-fit χ 2 of the Λ 0 b candidate; the θ Λ 0 b angle; and the PID information of the final-state particles. The BDT is trained using simulated Λ 0 b → η c pK − decays for the signal, and the data candidates in the pppK − invariant-mass sideband above 5800 MeV/c 2 for the background. The requirement on the BDT response is optimized by maximizing the figure of merit sig /(a/2 + N bkg ) [43], where sig is the BDT selection efficiency estimated using the simulated Λ 0 b → η c pK − sample, a = 5 is the target significance for the signal in standard deviations, and N bkg is the expected yield of background with pp and pppK − masses in the ranges m(pp) ∈ [2951.4, 3015.4] MeV/c 2 and m(pppK − ) ∈ [5585, 5655] MeV/c 2 , respectively. The background yields are estimated using the pppK − and pp invariant-mass sidebands in the data. The BDT response requirement provides about 70% signal efficiency and suppresses the background by a factor of approximately 100. After the BDT selection, a background in the normalisation channel is observed due to swapping the proton from the Λ 0 b decay with a proton from the J/ψ decay. This contribution is removed by requiring the invariant mass of system formed by the proton from the Λ 0 b baryon and the antiproton from the J/ψ meson to be inconsistent with the known J/ψ mass [30]. The pppK − and pp invariant-mass spectra of the selected data are displayed in Fig. 1.
A two-dimensional unbinned maximum-likelihood fit to the pppK − and pp invariantmass distributions is performed to determine the signal yield. The pppK − mass spectra of the signal and normalisation channels are described using the same model, sharing the shape parameters. The signal is modelled by the sum of two Crystal Ball (CB) functions [44] with common peak positions. The tail parameters of the CB functions are determined from simulation, while the mean and width of the Gaussian cores are freely varying in the fit to the data. The pp mass spectrum is described with a relativistic Breit-Wigner function [45] convolved with a Gaussian resolution function for the η c , and is described with the sum of two CB functions with common peak positions for the J/ψ decay.
When modelling the m(pp) spectrum, the correlation between m(pppK − ) and m(pp) needs to be taken into account. The width (peak) parameter of the resolution function of the signal channel, and the width (peak) parameters of the Gaussian cores for the normalisation channel, are parameterized as second-order (first-order) polynomial functions of m(pppK − ); the coefficients of these polynomial functions are calibrated using simulated samples.
For the two-dimensional mass spectrum of the background components, it is assumed that m(pppK − ) and m(pp) are uncorrelated, which is corroborated using the backgrounddominated data sample before the BDT selection is applied. For background from Λ 0 b → pppK − decays but with the pp pair not originating from a η c or J/ψ resonance, the m(pp) spectrum is described using an exponential function, and the m(pppK − ) spectrum is described using the same model as the signal but the parameters of the distribution are allowed to take different values in the fit. For background with a [cc] → pp process but not from a Λ 0 b decay, the m(pppK − ) distribution is described using an exponential function, and the m(pp) spectrum is modelled by Breit-Wigner functions that are each convolved with a separate Gaussian function to describe the η c and J/ψ resonances. In the fit, a Gaussian constraint of 31.9 ± 0.7 MeV/c 2 [30] is applied to the natural width of the η c meson for both the signal and background components. For combinatorial backgrounds, both the m(pppK − ) and m(pp) spectra are described using exponential functions. The background shape due to swapping the two protons in the Λ 0 b → η c (→ pp)pK − decay shares the same shape in m(pppK − ) as the signal channel, while the m(pp) shape, and the relative yield with respect to the signal component of the signal channel, are determined from simulation. Given the limited yield of Λ 0 b → η c pK − decays expected in this data sample, the interference between the Λ 0 b → η c pK − and nonresonant Λ 0 b → pppK − decays is not considered. An amplitude analysis of a larger data set is needed to have sensitivity  to such interference effects. The m(pppK − ) and m(pp) distributions of the selected candidates are presented in Fig. 1, with the one-dimensional projections of the fit overlaid. The yields of the signal and normalisation modes are N (Λ 0 b → η c pK − ) = 173 ± 25 and N (Λ 0 b → J/ψ pK − ) = 804 ± 31, respectively, where the uncertainties are statistical only. To estimate the signal significance, a two-dimensional fit without the contribution from the Λ 0 b → η c pK − decay is performed. The difference in log-likelihood between this and the nominal fit is found to be 29.4. Based on the assumption of a χ 2 distribution with one degree of freedom, the statistical significance of the Λ 0 b → η c pK − decay with respect to the background-only hypothesis, expressed in Gaussian standard deviations, is 7.7σ.
The branching fraction of the Λ 0 b → η c pK − decay is given by where N represents the yield of the decay given in the parentheses, determined from a fit to the invariant-mass spectrum and the efficiency accounting for the detector geometrical acceptance, reconstruction and event selection. The known values of the branching fractions, B, of the Λ 0 b → J/ψ pK − , J/ψ → pp [30] and η c → pp decays [46] are used as external inputs.
The efficiencies of the detector geometrical acceptance, reconstruction and event selections are determined from simulation. The agreement between data and simulation is improved by weighting the two-dimensional (p, p T ) distribution of the Λ 0 b baryons in simulation. The weights are obtained using a comparison between a large sample of data and simulated events from Λ 0 b → J/ψ pK − decays, where the J/ψ meson is reconstructed through its decay J/ψ → µ + µ − . The distributions of m(pK − ) and m([cc]p) in the simulation for signal and normalisation channels are also weighted to match the corresponding distributions observed in data, where the data distributions are obtained using the sPlot technique [47] with m(pppK − ) and m(pp) as the discriminating variables. The ratio between the overall efficiencies of the signal and normalisation channels is 0.95 ± 0.02, where the uncertainty accounts only for the finite yields of the simulated events.
Sources of systematic uncertainty on the Λ 0 b → η c pK − branching fraction arise from the fitting procedure and limited knowledge of the efficiencies. Pseudoexperiments are used to estimate the effects due to parameters determined from simulation. Systematic uncertainties on the fit model are evaluated by using alternative fit models where: the exponential functions are replaced by Chebyshev polynomials; the contributions from genuine Λ 0 b decays in the m(pppK − ) spectrum are modelled by the Hypatia distribution [48]; the resolution of the η c peaking structure in m(pp) spectrum is replaced by the average resolution of the CB functions describing the J/ψ peak; the shape parameters of the Λ 0 b peak in the Λ 0 b → pppK − decay without the η c or J/ψ resonances are fixed to be the same as those of the signal and the normalisation decays. Pseudoexperiments are used to estimate the potential bias of the fit yields, which is found to be negligible compared to the statistical uncertainties. Based on each alternative fit model described above, the significance of the Λ 0 b → η c pK − is re-estimated. The smallest significance found is approximately 7.7σ. This is the first observation of this decay mode.
Uncertainties on the efficiency ratio between the signal and normalisation channels are largely cancelled due to the similarity of these two decay modes. For the estimation of systematic uncertainties related to the weighting procedure of m([cc]p), m(pK − ) and (p, p T ) of the Λ 0 b decays in simulation, pseudoexperiments are used to propagate the uncertainties of single-event weights, originating from the finite yield of the samples used to obtain the weights, to the uncertainty of the overall efficiency ratio; an alternative binning scheme is used to estimate the uncertainty due to the choice of binning in the weighting procedure; and the negative weights, given by the sPlot technique due to statistical fluctuations, are set to zero to recalculate the overall efficiency ratio. A systematic uncertainty is also assigned for the finite size of the simulated samples used for the efficiency estimation.
The total systematic uncertainty of the Λ 0 b → η c pK − branching fraction measurement is obtained by adding the above contributions in quadrature, leading to a value of 5.8%, and details are given in Table 1. The dominant contribution is the uncertainty related to the fit model. The limited knowledge of the branching fractions of the Λ 0 b → J/ψ pK − , J/ψ → pp and η c → pp decays [30] is also considered as an external source that contributes Table 1: Summary of the uncertainties on the branching fraction ratio B(Λ 0 b → η c pK − )/B(Λ 0 b → J/ψ pK − ). The total systematic uncertainty is obtained by summing the individual contributions in quadrature.

Source
Uncertainty (%) to the total uncertainty.
The background-subtracted data distributions of m([cc]p) for the signal and normalisation channels are shown in Fig. 2, with the distributions of simulated events overlaid. The background subtraction is based on the sPlot technique [47], with m(pppK − ) and m(pp) as the discriminating variables. No significant peaking structures are seen. The fractions of the P c (4312) + , P c (4440) + and P c (4457) + contributions to the Λ 0 b → J/ψ pK − decays are only roughly 0.3%, 1.1% and 0.5%, respectively [5], and given the limited Λ 0 b → J/ψ pK − yields of this analysis, it is not surprising that these P c contributions are not observed.
A weighted unbinned maximum-likelihood fit [49] is applied to the backgroundsubtracted η c p mass spectrum in order to search for the P c (4312) + state. The P c (4312) + resonance is modelled using a relativistic Breit-Wigner function [45], with parameters obtained from Ref. [5], and is convolved with the sum of two Gaussian resolution functions whose shape parameters are determined from simulation. The contribution from Λ 0 b → η c pK − decays with a non-resonant η c p system is modelled using simulated events generated based on a uniform phase-space model. The fit projection is shown in Fig. 2 (a).
The yield of the P c (4312) + state is determined to be 16 +12 − 9 (stat.) ± 4 (syst.), corresponding to a fraction of 0.09 +0.06 −0.05 (stat.) ± 0.02 (syst.) of the signal yield. The systematic uncertainty on the yield is estimated by using alternative models to describe the Λ 0 b component without η c p resonances, and varying the mass and width of the P c (4312) + state based on their uncertainties from Ref. [5]. From the profile likelihood distribution, an upper limit of 0.24 at 95% confidence level is set on the fraction of the P c (4312) + contribution.
In summary, the first observation of the decay Λ 0 b → η c pK − is reported using protonproton collision data collected with the LHCb experiment, corresponding to an integrated luminosity of 5.5 fb −1 . The significance of this observation, over the background-only hypothesis, is 7.7 standard deviations. The branching fraction ratio between the Λ 0 b → η c pK − and Λ 0 b → J/ψ pK − decays is measured to be where the first uncertainty is statistical, the second is systematic, and the last is due to the uncertainty on the branching fractions of the η c → pp and J/ψ → pp decays. Using this ratio, the branching fraction of the Λ 0 b → η c pK − decay is determined to be where the third uncertainty also depends on the branching fraction of the Λ 0 b → J/ψ pK − decay.
The observation of this decay opens up a new line of investigation in searching for pentaquarks in the η c p system, which could shed light on the binding mechanism of the recently observed pentaquark states [5]. If the P c (4312) + state is a DΣ c molecule and the predictions of Refs. [13][14][15] are accurate, the contribution from the P c (4312) + state to the Λ 0 b → η c pK − decay rate is expected to be around 10 times larger than that to the Λ 0 b → J/ψ pK − decay rate. No signal is seen in the data and an upper limit of 24% at 95% confidence level is placed on the value of B(Λ 0 b → P c (4312) + K − ) × B(P c (4312) + → η c p)/B(Λ 0 b → η c pK − ).