Search for the lepton number violating decays $B^{+}\to \pi^- \mu^+ \mu^+$ and $B^{+}\to K^- \mu^+ \mu^+$

A search is performed for the lepton number violating decay $B^{+}\to h^- \mu^+ \mu^+$, where $h^-$ represents a $K^-$ or a $\pi^-$, using data from the LHCb detector corresponding to an integrated luminosity of $36pb^{-1}$. The decay is forbidden in the Standard Model but allowed in models with a Majorana neutrino. No signal is observed in either channel and limits of $B(B^{+} \to K^- \mu^+ \mu^+)<5.4\times 10^{-8}$ and $B(B^{+} \to \pi^- \mu^+ \mu^+)<5.8\times 10^{-8}$ are set at the 95% confidence level. These improve the previous best limits by factors of 40 and 30, respectively.

A search is performed for the lepton number violating decay B + → h − µ + µ + , where h − represents a K − or a π − , using data from the LHCb detector corresponding to an integrated luminosity of 36 pb −1 .The decay is forbidden in the Standard Model but allowed in models with a Majorana neutrino.No signal is observed in either channel and limits of B(B + → K − µ + µ + ) < 5.4 × 10 −8 and B(B + → π − µ + µ + ) < 5.8 × 10 −8 are set at the 95% confidence level.These improve the previous best limits by factors of 40 and 30, respectively.
PACS numbers: 11.30.Fs, 13.20.He, 13.35.Hb Lepton number is conserved in the Standard Model but can be violated in a range of new physics models such as those with Majorana neutrinos [1] or left-right symmetric models with a doubly charged Higgs boson [2].In this letter a search for lepton number violating decays of the type B + → h − µ + µ + , where h − represents a K − or a π − , is presented.The inclusion of charge conjugated modes is implied throughout.A search for any lepton number violating process that mediates the B + → h − µ + µ + decay is made.A specific search for B + → h − µ + µ + decays mediated by an on-shell Majorana neutrino (Fig. 1) is also performed.Such decays would give rise to a narrow peak in the invariant mass spectrum of the hadron and one of the muons [3], m ν = m hµ , if the mass of the neutrino is between m K(π) +m µ and m B −m µ .The previous best experimental limit on the 2) × 10 −6 at 90% confidence level (CL) [4].
The search for B + → h − µ + µ + is carried out with data from the LHCb experiment at the Large Hadron Collider at CERN.The data corresponds to 36 pb −1 of integrated luminosity of proton-proton collisions at √ s = 7 TeV collected in 2010.The LHCb detector is a single-arm spectrometer designed to study b-hadron decays with an acceptance for charged tracks with pseudorapidity between 2 and 5.Primary proton-proton vertices (PVs), and secondary B vertices are identified in a silicon strip vertex detector.Tracks from charged particles are reconstructed by the vertex detector and a set of tracking stations.The curvature of the tracks in a dipole magnetic field allows momenta to be determined with a precision of δp/p = 0.35-0.5%.Two Ring Imaging CHerenkov (RICH) detectors allow kaons to be separated from pions/muons over a momentum range 2 < p < 100 GeV/c.Muons with momentum above 3 GeV/c are identified on the basis of the number of hits left in detectors interleaved with an iron muon filter.Further details about the LHCb detector can be found in Ref. [5].
The search for B + → h − µ + µ + decays is based on the selection of B + → h ± µ + µ ∓ candidates.The B + → J/ψ K + decay with J/ψ → µ + µ − is included in the same selection.It is subsequently used as a normalisation mode when setting a limit on the branching fraction of the B + → h − µ + µ + decays.The selection is designed to minimise and control the difference between decays with same-and opposite-sign muons and thus cancel most of where the decay is mediated by an on-shell Majorana neutrino.
the systematic uncertainty from the normalisation.The only differences in efficiency between the signal and normalisation channels are due to the decay kinematics and the presence of a same-sign muon pair, rather than an opposite-sign pair, in the final state.
In the trigger, the B + → h ± µ + µ ∓ candidates are required to pass the initial hardware trigger based on the p T of one of the muons.In the subsequent software trigger, one of the muons is required to have a large impact parameter (IP) with respect to all the PVs in the event and to pass requirements on the quality of the track fit and the compatibility of the candidate with the muon hypothesis.Finally, the muon candidate combined with another track is required to form a vertex displaced from the PVs.
Further event selection is applied offline on fully reconstructed B decay candidates.The selection is designed to reduce combinatorial backgrounds, where not all the selected tracks come from the same decay vertex; and peaking backgrounds, where a single decay is selected but with some of the particle types misidentified.The combinatorial background is smoothly distributed in the reconstructed B-candidate mass and the level of background is assessed from the sidebands around the signal window.Peaking backgrounds from B decays to hadronic final states, final states with a J/ψ and semileptonic final states are also considered.
Proxies are used in the optimisation of the selection for both the signal and the background to avoid a selection bias.The B + → J/ψ K + decay is used as a proxy for the signal.The background proxy comprises opposite-sign B + → h + µ + µ − candidates with an invariant mass in the upper mass sideband and with muon pairs incompatible with a J/ψ or a ψ(2S) hypothesis.The bias introduced by using B + → J/ψ K + for both optimisation and as a normalisation mode is insignificant due to the large number of candidates.
The combinatorial background is reduced by requiring that the decay products of the B have p T > 800 MeV/c.Tracks are selected which are incompatible with originating from a PV based on the χ 2 of the tracks' impact parameters (χ 2 IP > 45).The direction of the candidate B + momentum is required to be within 8 mrad of the reconstructed B + line of flight.The B + vertex is also required to be of good quality (χ 2 < 12 for three degrees of freedom) and significantly displaced from the PV (χ 2 of vertex separation larger than 144).
The selection uses a range of particle identification (PID) criteria, based on information from the RICH and muon detectors, to ensure the hadron and the muons are correctly identified.For example, DLL Kπ is the difference in log-likelihoods between the K and π hypotheses.For the B + → K − µ + µ + final state, DLL Kπ > 1 is required to select kaon candidates.For the To reject background events where two tracks that are close together in the tracking system share hits in the muon detector, a requirement is made on the maximum number of muon system hits that two candidate muons may have in common.This requirement can introduce a bias in the relative efficiency between signal and normalisation channels, as both tracks from the same-sign muon pair for B + → h − µ + µ + will curve in the same direction in the dipole field.Simulated events give an estimate of 0.3% for the effect on the relative efficiency between the signal and normalisation channel.In order to avoid selecting a muon as the pion or kaon, the candidate hadron is also required to be within the acceptance of the muon system but not have a track segment there.
After the application of the above criteria the combinatorial background is completely dominated by candidates with two real muons, rather than by hadrons misidentified as muons.
The invariant mass distribution and the relevant misidentification rates are required in order to evaluate the peaking background.These are evaluated, respectively, from a full simulation using Pythia [6] followed by Geant4 [7], and from control channels which provide an unambiguous and pure source of particles of known type.The control channel events are selected to have the same kinematics as the signal decay, without the application of any PID criteria.D * → D 0 π, D 0 → Kπ decays give pure sources of pions and kaons.A pure source of muons is selected by using a tag-and-probe approach with J/ψ → µ + µ − decays [8].
Under the B + → K − µ + µ + hypothesis, any crossfeed from B + → J/ψ K + decays would peak strongly in the signal mass region.The K → µ mis-id rate is evaluated from the above D * sample and the µ → K mis-id rate from the J/ψ sample.The later mis-id rate is consistent with zero.The number of B + → J/ψ K + events expected in the signal region is therefore also zero but with a large uncertainty which dominates the error on the total exclusive background expected in the signal region.The B + → π − π + K + decay contributes the most to the peaking background with an expected (1.7 ± 0.1) × 10 −3 candidates, followed by the B + → K − π + K + decay with (6.1 ± 0.8) × 10 −4 candidates.The total peaking background expected in the B + → K − µ + µ + signal region is (3.4 +14.0 −0.2 )×10 −3 events with the asymmetric error caused by the zero expectation from the B + → J/ψ K + decay.
In Fig. 2(a), the m K + µ + µ − invariant mass distribution for B + → K + µ + µ − events with |m µ + µ − − m J/ψ | < 50 MeV/c 2 is shown, after the application of the selection.In the B + → J/ψ K + sample, there are no events containing more than one candidate.An unbinned maximum likelihood fit to the B + → J/ψ K + mass peak is made with a Crystal Ball [9] function which accounts for the radiative tail.The combinatorial background is assumed to be flat, and the partially reconstructed events in the lower mass sideband are fitted with a Gaussian distribution.The signal peak has a Gaussian component of width 20 MeV/c 2 , and a signal mass window of 5280 ± 40 MeV/c 2 is chosen.The B + → J/ψ K + peak contains 3407 ± 59 signal events within the signal window.B + → J/ψ π + candidates were also examined and, accounting for a shoulder in the mass distribution from B + → J/ψ K + , the yield observed agrees with the expectation.
The m K + µ + µ − invariant mass distribution for events with |m µ + µ − − m J/ψ ,ψ(2S) | > 70 MeV/c 2 is shown in Fig. 2(b).Using the same fit model, with all shape parameters fixed to those from the above fit, the signal peak was determined to contain 27 ± 5 events from the B + → K + µ + µ − decay.The ratio of branching fractions between B + → J/ψ K + and B + → K + µ + µ − decays [10] and the trigger efficiency ratio predicted by the simu- FIG. 2. Invariant mass distribution of K + µ + µ − events after the application of the selection criteria.In (a) requiring the muon pair to be compatible with coming from a J/ψ decay and in (b) excluding invariant mass windows around the J/ψ and ψ(2S) for the muon pair.The curve is the fit to data as described in the text.lation, give an expectation of 29 ± 4 B + → K + µ + µ − decays.The observed yield is consistent with the expectation showing that the selection does not favour candidates with a dimuon mass close to the J/ψ mass.
The difference in efficiency between the signal and normalisation channels was evaluated using Monte Carlo simulation samples.The relative selection efficiency across the phase space is shown for B + → K − µ + µ + in Fig. 3.The efficiency of the signal selection in a given phase space bin is divided by the average efficiency of B + → J/ψ K + , to yield the relative efficiency for that bin.The D * control channel is used to determine the PID efficiencies required to normalise Assuming a signal that is uniformly distributed in phase space, the relative efficiency of B + → K − µ + µ + and B + → J/ψ K + was calculated to be 89.1±0.4 (stat)± 0.3 (syst)%.The relative efficiency of B + → π − µ + µ + and B + → J/ψ K + was calculated to be 82.7 ± 0.6 (stat) ± 0.8 (syst)%.The systematic uncertainties associated with these estimates are detailed below.These relative efficiencies together with the number of events observed in the normalisation channel, give single event sensitivities of 2.0 In order to compute the efficiency under a given Majorana neutrino mass hypothesis, a model for the variation of efficiency with m hµ is required.For a given value of m hµ this is obtained by varying the polarisation of the Majorana neutrino in the decay and taking the lowest (most conservative) value of the efficiency.
The dominant systematic uncertainty (under the assumption of a flat phase-space distribution) for the single event sensitivity is the 3.4% uncertainty on the B + → J/ψ K + branching fraction.The statistical uncertainty  on the B + → J/ψ K + yield gives an additional systematic uncertainty of 1.7% and the uncertainty from the model used to fit the data is 1.6%.The latter is evaluated by changing the Crystal Ball signal function used in the fit to a Gaussian and the polynomial background function to an exponential.There are several sources of uncertainty associated with the calculation of the relative efficiency between the signal and normalisation channels.In addition to the statistical uncertainty of the simulation samples, there are systematic uncertainties from: the differences in the effect of the IP selection criteria between the simulation and data; the statistical uncertainty on the measured PID efficiencies; the uncertainties associated with the simulation of the trigger; and the uncertainty in the tracking efficiency.In each case the systematic uncertainty is estimated by varying the relevant criteria at the level of the expected effect and re-evaluating the relative efficiency.For the B + → π − µ + µ + decay, there is an additional uncertainty from the correction for the relative kaon-and pion-identification efficiencies.The systematic uncertainties averaged over the three-body phase space are given in Table I.
A limit on the branching fraction of each of the B + → h − µ + µ + decays is set by counting the number of observed events in the mass windows, and using the single event sensitivity.The probability is modelled with a Poisson distribution where the mean has contributions from a potential signal, the combinatorial and peaking backgrounds.The combinatorial background is unconstrained by measurements from the simulation or the opposite-sign data.The number of events in the upper mass sideband is therefore used to constrain the contribution of the combinatorial background to the Poisson mean.The upper mass sideband is restricted to masses above m hµµ > 5.4 GeV/c 2 such that any peaking background component can be ignored.In both the B + → K − µ + µ + and B + → π − µ + µ + cases no events are found in either the upper or lower mass sidebands.This is consistent with the observation of three opposite-sign candidates seen in the B + → K + µ + µ − upper mass side-band (Fig. 2) and two candidates in the B + → π + µ + µ − upper mass sideband.The peaking background estimates are explicitly split into two components, the contribution from B + → h − h + h + decays and that from B + → J/ψ K + decays.The latter has a large uncertainty.The central values for both peaking background components are taken from the estimates described above.
Systematic uncertainties on the peaking background, single event sensitivity and signal-to-sideband scale factor are included in the limit-setting procedure using a Bayesian approach.The unknown parameter is integrated over and included in the probability to observe a given number of events in the signal and upper mass window.
In the signal mass windows of B + → K − µ + µ + and B + → π − µ + µ + no events are observed.This corresponds to limits on the B + → h − µ + µ + branching fractions of B(B + → K − µ + µ + ) < 5.4 (4.1) × 10 −8 at 95% (90%) CL, B(B + → π − µ + µ + ) < 5.8 (4.4) × 10 −8 at 95% (90%) CL.The observation of no candidates in the sidebands as well as the signal region is compatible with a backgroundonly hypothesis.The m hµ dependence of the limit in models where the Majorana neutrino can be produced on mass shell is shown in Fig. 4. The shapes of the limits arise from the changing efficiency as a function of mass.
In summary, a search for the B + → K − µ + µ + and B + → π − µ + µ + decays modes has been performed with 36 pb −1 of integrated luminosity collected with the LHCb detector in 2010.No signal is observed in either de-cay and, using B + → J/ψ K + as a normalisation channel, the present best limits on B(B + → K − µ + µ + ) and B(B + → π − µ + µ + ) are improved by factors of 40 and 30, respectively [4].