Search for the rare decay $\Lambda_{c}^{+} \to p\mu^+\mu^-$

A search for the flavor-changing neutral-current decay $\Lambda_{c}^{+} \to p\mu^+\mu^-$ is reported using a data set corresponding to an integrated luminosity of $3.0\rm fb^{-1}$ collected by the LHCb collaboration. No significant signal is observed outside of the dimuon mass regions around the $\phi$ and $\omega$ resonances and an upper limit is placed on the branching fraction of $\mathcal{B} (\Lambda_{c}^{+} \to p\mu^+\mu^-)<7.7~(9.6)\times 10^{-8}~{\rm at}~90\%~(95\%)$ confidence level. A significant signal is observed in the $\omega$ dimuon mass region for the first time.

baryon to pµ + µ − is simulated with a three-body phase-space model. The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [23] as described in Ref. [24]. The Λ + c baryons are produced in two ways at a hadron collider; as prompt Λ + c or in b-hadron decays. The simulation contains a mixture of these two production mechanisms, according to the known Λ + c and b-hadron production cross-sections [25,26].
The simulated samples are used to determine the selection criteria, in particular to train a multivariate classifier that is aimed at distinguishing signal signatures in the background-dominated data set. The simulated samples are also used to calculate the efficiencies of several selection steps.
Candidate events of Λ + c → pµ + µ − decay are reconstructed by combining a pair of charged tracks identified as muons with one identified as a proton. Candidates that pass the trigger selections are subject to further requirements consisting of kinematic and particle identification criteria and based on the response of a multivariate classifier. Each of the final-state tracks is required to be of good quality, to have p T > 300 MeV/c and to be incompatible with originating from any of the PVs in the event. The tracks are also required to form a good-quality secondary vertex with a corresponding flight distance of at least 0.1 mm from all of the PVs in the event. The invariant mass of the dimuon system is required to be smaller than 1400 MeV/c 2 . Three dimuon mass regions are defined: • a region around the known φ mass, [985, 1055] MeV/c 2 , used as a normalization channel; • a region around the known ω mass (the ω denotes hereafter the ω(782) meson), [759, 805] MeV/c 2 , used to isolate the Λ + c → pω decay; • a nonresonant region (Λ + c → pµ + µ − ), with excluded ranges ±40 MeV/c 2 around the known ω and φ masses.
After the preselection, the normalization channel is still dominated by combinatorial background, i.e. combinations of tracks that do not all originate from a genuine Λ + c baryon. A boosted decision tree (BDT) is trained to reduce the combinatorial background to manageable level. The BDT is trained using the kinematic and topological variables of the Λ + c candidate, related to its flight distance, decay vertex quality, p T and impact parameter with respect to the primary vertex. In the BDT training, Λ + c → pµ + µ − simulated events are used as a proxy for the signal and data outside the signal pµ + µ − invariant mass region extending up to ±300 MeV/c 2 around the known Λ + c mass is used as a proxy for the background.
A k-folding technique is used to ensure the training is unbiased [27], while keeping the full available data sets for further analysis. A loose BDT cut is applied to reduce the background to the same level as the normalization channel yield.
A fit to the pµ + µ − invariant-mass distribution of Λ + c → pφ(µ + µ − ) candidates after the loose BDT requirement is shown in Fig. 1. The shape of the Λ + c peak is parametrized by a Crystal Ball function [28] with parameters determined from the simulation, while the background is modeled with a first-order polynomial. The yield of the Λ + c → pφ(µ + µ − ) decay is determined to be 395±45 candidates. This sample is used for the final optimization of selection requirements. It is checked at this stage that the variables used in the signal selection are well described by simulation within the available sample size. For the final selection a second BDT is trained, which includes additional variables related to Λ + c -baryon decay properties and the isolation of the proton and muons in the detector. The final discrimination is performed in three dimensions: the BDT variable and two particle identification (PID) variables, the proton-identification discriminant and the muon-identification discriminant. The optimal set of BDT and PID requirements is determined by finding the best expected upper limit on the branching fraction of the signal relative to the normalization channel using the CL s method [29] by means of Monte Carlo methods.
Several sources of background have been considered. An irreducible background due to long-distance contributions originates from Λ + c → pV (µ + µ − ) decays, with intermediate resonances indicated by V . The ρ(770) 0 , ω and η resonances are studied, however, their contribution to the nonresonant region is expected to be negligible, because the V meson mass is well separated from the nonresonant region and/or the Λ + c → pV (µ + µ − ) branching fraction is small. Another background source considered is due to misidentification of final-state particles in hadronic D + , D + s and Λ + c decays. The expected contribution from this source has been estimated using large samples of simulated events. Given the tight PID requirements obtained from the optimization, only 2.0 ± 1.1 candidates are expected to fall into the Λ + c mass window in the nonresonant region. The ratio of branching fractions is measured using where N sig (N norm ) is the observed yield for the signal (normalization) decay mode. The factors sig and norm indicate the corresponding total efficiencies for signal and normalization channels, respectively. The efficiencies are determined from the simulation.
In the case of the observation of the decay Λ + c → pV , the ratio of branching fractions is determined by  where N V (N norm ) is the number of candidates observed for the Λ + c → pV (normalization) decay mode. The factors V and norm indicate the corresponding total efficiencies for Λ + c → pV and normalization channel, respectively. As the final states of the signal and normalization channels are identical, many sources of systematic uncertainty cancel in the ratio of the efficiencies. There are three significant sources of systematic uncertainty. The first is related to the finite size of the simulation samples, which limits the precision on the efficiency ratio. The second is linked to residual differences between data and simulation of the BDT distribution. The third is associated to the simulation of PID and is determined from the uncertainty on the PID calibration samples. The values of the contributions are given in Table 1.
Several other sources of systematic uncertainty were considered: the trigger efficiency, the shapes used in the invariant mass fit for signal and normalization channels, the shape of the combinatorial background, and the fraction of prompt Λ + c baryons and Λ + c baryons from b-hadron decays. All of these, however, are at negligible level when compared to three dominant sources of systematic uncertainty.
The simulated Λ + c → pµ + µ − decays have been generated according to a phase-space model for the decay products. As the exact physics model for the decay is not known, no systematic uncertainty is assigned. Instead, the weights needed to recast the result in terms of any physics model are provided in Fig. 2. The weights are described by a function of the dimuon invariant mass squared m 2 (µ + µ − ) and the invariant mass of the proton and the negatively charged muon squared m 2 (pµ − ). The weights are normalized to the average efficiency.
The distributions of the pµ + µ − invariant mass for the Λ + c → pµ + µ − candidates after final selections in the three dimuon mass ranges are presented in Fig. 3. The Λ + c peak is parametrized by a Crystal Ball [28] function with parameters determined from the simulation and the background is described by a first-order polynomial. The fits are used to determine the signal yields. No significant signal is observed in the nonresonant region (Fig. 3a). The yield for the normalization channel is determined to be 96 ± 11 candidates (Fig. 3b). An accumulation of 13.2 ± 4.3 candidates at the Λ + c mass is observed in the ω region (Fig. 3c). The statistical significance of the excess is determined to be 5.0σ using Wilks' theorem [30].
The distribution of the dimuon invariant mass of the Λ + c candidates is shown in Fig. 4. An excess is seen at the known ω and φ resonance masses. The data is well described by  [31] convolved with a Gaussian function to take into account the experimental resolution. The addition of a component for the ρ(770) 0 resonance (and its interference with the ω meson) does not improve the fit quality. It is therefore assumed that the observed candidates in the ω region are dominated by decays via the ω resonance.
As no evidence for nonresonant Λ + c → pµ + µ − decays is found, an upper limit on the branching fractions is determined using the CL s method. The systematic uncertainties are included in the construction of CL s . The following upper limits are obtained at different confidence levels (CL) The corresponding distribution of CL s is shown in Fig. 5. Using the values of the branching fractions for Λ + c → pφ and φ → µ + µ − decays from Ref. [31] and including their uncertainties in the CL s construction, an upper limit on the branching fraction is determined to be Under the above-mentioned assumption of the Λ + c → pω dominance in the ω region, the relative branching fraction with respect to the normalization channel is determined according to Eq. 2 = 0.23 ± 0.08 (stat) ± 0.03 (syst).
Using the relevant branching fractions from Ref. [31], the branching fraction of Λ + c → pω is determined to be B(Λ + c → pω) = (9.4 ± 3.2 (stat) ± 1.0 (syst) ± 2.0 (ext)) × 10 −4 , where the first uncertainty is statistical, the second corresponds to the above-mentioned systematic effects and the third is due to the limited knowledge of the relevant branching fractions. Assuming lepton universality, the branching fraction B(ω → e + e − ) is used instead of B(ω → µ + µ − ).
In summary, a search for the Λ + c → pµ + µ − decay is reported, using pp data collected with the LHCb experiment. The analysis is performed in three regions of dimuon mass: φ, ω and nonresonant. The upper limit on the nonresonant mode is improved by two orders of magnitude with respect to the previous measurement [5]. For the first time the signal is seen in the ω region with a statistical significance of 5 standard deviations.