Search for $B^- \to \Lambda \bar p \nu \bar\nu$ with the BABAR experiment

We search for the rare flavor-changing neutral current process $B^- \to \Lambda {\overline p} \nu{\overline{\nu}}$ using data from the BABAR experiment. A total of 424 fb$^{-1}$ of $e^+e^-$ collision data collected at the center-of-mass energy of the $\Upsilon$(4S) resonance is used in this study, corresponding to a sample of ${(471 \pm 3) \times 10^{6}}$ $B\overline{B}$ pairs. Signal $B^- \to \Lambda {\overline p} \nu{\overline{\nu}}$ candidates are identified by first fully reconstructing a $B^+$ decay in one of many possible exclusive decays to hadronic final states, then examining detector activity that is not associated with this reconstructed $B^+$ decay for evidence of a signal $B^- \to \Lambda {\overline p} \nu{\overline{\nu}}$ decay. The data yield is found to be consistent with the expected background contribution under a null signal hypothesis, resulting in an upper limit of ${{\cal B} (B^- \to \Lambda {\overline p} \nu{\overline{\nu}})<3.0\times 10^{-5}}$ at the $90\%$ confidence level.

Flavor-changing neutral current (FCNC) processes are suppressed in the standard model (SM) of particle interactions, first appearing at one-loop level.Consequently, new physics contributions could result in potentially measurable deviations from SM predictions.The process B − → Λpνν (CP conjugate processes are implied throughout this paper) is the baryonic analog of B → K ( * ) νν, occurring in the SM via a FCNC b → sνν transition through Z-penguin or W -box processes (see Fig. 1).The branching fraction is predicted to be B(B − → Λpνν) = (7.9± 1.9) × 10 −7 [1].Although B → K ( * ) νν has previously been studied at B factory experiments [2,3], it is challenging due to the presence of two (unobserved) neutrinos in the final state and current measurements leave room for new physics [4].By comparison, the presence of two baryons in the final state of B − → Λpνν provides stronger background rejection.This paper presents the first search for the decay B − → Λpνν, using data recorded by the BABAR experiment at the PEP-II energy-asymmetric e + e − collider.These data were collected at the Υ (4S) resonance, representing an integrated luminosity of 424 fb −1 [5], corresponding to (471 ± 3) × 10 6 BB pairs [6].
The BABAR detector is described in detail in Refs.[7,8].The charged-particle tracking system comprises a fivelayer silicon vertex tracker and a 40-layer cylindrical drift chamber.A 1.5 T magnetic field produced by a superconducting solenoid enables momentum measurement of charged particles.Identification of (anti)protons and other charged particles is based on measurement of the specific ionization, dE/dx, in the tracking detectors, combined with information from the electromagnetic calorimeter and Cherenkov-photon angle information from an array of fused silica quartz bars.Energy and position measurements for photons are provided by an electromagnetic calorimeter comprising 6580 CsI(Tl) crystals arrayed as a cylindrical central barrel and a conical forward endcap.
Simulated Monte Carlo (MC) event samples are used to develop the signal selection and to estimate the selection efficiency.Studies of background channels are based on samples of simulated events representing BB production at Υ (4S), and continuum production of e + e − → qq and e + e − → τ + τ − .The qq simulation is separated into cc and light quark (uu, dd, ss) samples.The BB samples are produced using EvtGen [9], while JETSET [10] is used for generation and hadronization of continuum backgrounds, with EvtGen handling decays.KK [11] is used for τ + τ − generation, with Tauola [12] handling τ decays.The detector simulation uses GEANT4 [13].The B + B − , B 0 B 0 , and cc simulation samples correspond to an integrated luminosity ten times that of data, and the other samples are four times that of data.A dedicated B − → Λpνν, Λ → pπ − signal MC sample of 4.053 × 10 6 events is used for efficiency and optimization studies.These events are generated according to a invariance, the most general forms of the " B ! B " B 0 transition form factors are given by [23] hB " B 0 j " q 0 bj " with q¼ p B þ p " B 0 and p ¼ p " B À q, for the vector and axial-vector quark currents, respectively.For the momentum dependences, the form factors f i and g i (i ¼ 1; 2; . . .; 5) are taken to be [19] with t q 2 m 2 B " B 0 , where D f i and D g i are constants to be determined by the measured data in " B ! p " pM decays.Note that 1=t 3 arises from three hard gluons as the propagators to form a baryon pair in the approach of the perturbative quantum chromodynamics counting rules [18,[32][33][34], where two of them attach to valence quarks in B " B 0 , while the third one kicks and speeds up the spectator quark in " B. It is worth to note that, due to f i , g i / 1=t 3 , the dibaryon invariant mass spectrum peaks at the threshold area and flattens out at the large energy region.Hence, this so-called threshold effect measured as a common feature in " B ! p " pM decays should also appear in the B À !Ã " p ' " ' decay.To integrate over the phase space for the amplitude squared j " Aj 2 , which is obtained by assembling the required elements in Eqs. ( 2)-( 4) and summing over all fermion spins, the knowledge of the kinematics for the four-body decay is needed.For this reason, we use the with ða; b; t, s ðp þ phase space.between pB of flight of th while the an plane, which pair and the rest frame o given by The decay br the integratio the three neu We can also asymmetries

III. NUME
For the nu em , sin 2 W parameters. hB " B 0 j " q 0 bj " with q¼ p B þ p " B 0 and p ¼ p " B À q, for the vector and axial-vector quark currents, respectively.For the momentum dependences, the form factors f i and g i (i ¼ 1; 2; . . .; 5) are taken to be [19] with t q 2 m 2 B " B 0 , where D f i and D g i are constants to be determined by the measured data in " B ! p " pM decays.Note that 1=t 3 arises from three hard gluons as the propagators to form a baryon pair in the approach of the perturbative quantum chromodynamics counting rules [18,[32][33][34], where two of them attach to valence quarks in B " B 0 , while the third one kicks and speeds up the spectator quark in " B. It is worth to note that, due to f i , g i / 1=t 3 , the dibaryon invariant mass spectrum peaks at the threshold area and flattens out at the large energy region.Hence, this so-called threshold effect measured as a common feature in " B ! p " pM decays should also appear in the B À !Ã " p ' " ' decay.To integrate over the phase space for the amplitude squared j " Aj 2 , which is obtained by assembling the required elements in Eqs. ( 2)-(4) and summing over all fermion spins, the knowledge of the kinematics for the four-body decay is needed.For this reason, we use the partial decay width [35-37] with ða; b; t, s ðp þ phase space.between pB of flight of th while the an plane, which pair and the rest frame o given by The decay br the integratio the three neu We can also asymmetries

III. NUME
For the nu em , sin 2 W parameters. hB " B 0 j " q 0 bj " with q¼ p B þ p " B 0 and p ¼ p " B À q, for the vector and axial-vector quark currents, respectively.For the momentum dependences, the form factors f i and g i (i ¼ 1; 2; . . .; 5) are taken to be [19] with t q 2 m 2 B " B 0 , where D f i and D g i are constants to be determined by the measured data in " B ! p " pM decays.Note that 1=t 3 arises from three hard gluons as the propagators to form a baryon pair in the approach of the perturbative quantum chromodynamics counting rules [18,[32][33][34], where two of them attach to valence quarks in B " B 0 , while the third one kicks and speeds up the spectator quark in " B. It is worth to note that, due to f i , g i / 1=t 3 , the dibaryon invariant mass spectrum peaks at the threshold area and flattens out at the large energy region.Hence, this so-called threshold effect measured as a common feature in " B ! p " pM decays should also appear in the B À !Ã " p ' " ' decay.To integrate over the phase space for the amplitude squared j " Aj 2 , which is obtained by assembling the required elements in Eqs. ( 2)-(4) and summing over all fermion spins, the knowledge of the kinematics for the four-body decay is needed.For this reason, we use the partial decay width [35-37] with ða; b; c t, s ðp þ phase space.between pB ( of flight of th while the ang plane, which pair and the rest frame o given by The decay bra the integratio the three neu We can also asymmetries,

III. NUME
For the nu em , sin 2 W parameters.I with q¼ p B þ p " B 0 and p ¼ p " B À q, for the vector and axial-vector quark currents, respectively.For the momentum dependences, the form factors f i and g i (i ¼ 1; 2; . . .; 5) are taken to be [19] with t q 2 m 2 B " B 0 , where D f i and D g i are constants to be determined by the measured data in " B ! p " pM decays.Note that 1=t 3 arises from three hard gluons as the propagators to form a baryon pair in the approach of the perturbative quantum chromodynamics counting rules [18,[32][33][34], where two of them attach to valence quarks in B " B 0 , while the third one kicks and speeds up the spectator quark in " B. It is worth to note that, due to f i , g i / 1=t 3 , the dibaryon invariant mass spectrum peaks at the threshold area and flattens out at the large energy region.Hence, this so-called threshold effect measured as a common feature in " B ! p " pM decays should also appear in the B À !Ã " p ' " ' decay.To integrate over the phase space for the amplitude squared j " Aj 2 , which is obtained by assembling the required elements in Eqs. ( 2)-( 4) and summing over all fermion spins, the knowledge of the kinematics for the four-body decay is needed.For this reason, we use the partial decay width [35-37] , and are five variables in phase space.As seen from Fig. 2, the angle BðLÞ between pB ( p ) in the B " B 0 ( " ) rest frame and the l of flight of the B " B 0 ( " ) system in the rest frame of the while the angle is between the B " B 0 plane and the plane, which are defined by the momenta of the B pair and the momenta of the " pair, respectively, in rest frame of " B. The ranges of the five variables given by The decay branching ratio of BðB À !Ã " p " Þ depends the integration in Eqs. ( 5)-( 7), where we have to sum o the three neutrino flavors since they are indistinguishab We can also define the integrated angular distribut asymmetries, given by

III. NUMERICAL RESULTS AND DISCUSSION
For the numerical analysis, we take the values of G em , sin 2 W and V Ã ts V tb in the PDG [38] as the in parameters.In the large t limit, the approach of  phase-space model, but are adapted to the form factor model described in Ref. [1] by applying a re-weighting of the di-baryon invariant mass, m Λp , at the analysis level.
Because the decay B − → Λpνν has two undetected neutrinos, it cannot be fully reconstructed from its final state particles.Instead, by reconstructing the hadronic decay of one of the B mesons in Υ (4S) → BB events, referred to as the "tag B" (B tag ), all remaining particles in the event can then be inferred to be daughters of the other B, referred to as the "signal B" (B sig ).The 4-vector of the B sig can be calculated from the B tag momentum vector, p * Btag , and the known CM energy, E * CM : , where p * Bsig is the threemomentum vector of the B sig , E * CM is the CM energy, and m B is the B meson mass, with the direction of p * Bsig defined to be opposite that of p * Btag , where asterisks indicate quantities in the CM frame.The missing momentum four-vector, p * miss , is determined by subtracting the CM four-momentum of all identified particles that are not used in the reconstruction of the B tag from that of B sig .Since the B tag has been fully reconstructed, all missing momentum in the event is attributable to the B sig candidate.This method has been used in previous BABAR analyses, e.g.Refs.[2,16,17].
The reconstruction of B tag candidates considers B decays into a large number of possible hadronic decay modes, B → SX, where S is a "seed" meson, and X is an hadronic system comprising up to five kaons or pions with total charge 0 or ±1.Both neutral and charged B tag candidates are reconstructed, but only B ± candidates are retained for this study.The seed meson can be D ( * )0 , D ( * )± , D * ± s , or J/ψ .The D me-son seeds are reconstructed as: s → φπ + , and K 0 S K + .The J/ψ seed is reconstructed via e + e − and µ + µ − .π 0 → γγ, K 0 S → π + π − , and φ → K + K − are reconstructed.A kinematic fit is applied, which imposes vertex and particle mass constraints on the candidates.The resulting seed candidates are then combined with kaons or pions to create B tag candidates.Two kinematic variables are used to define these candidates: Btag , and , where E 0 and p 0 are the energy and momentum of the e + e − system in the lab frame, and √ s is the energy of the e + e − system in the CM frame.The B tag candidates are selected by requiring −0.12 GeV < ∆E < 0.12 GeV and 5.20 GeV/c 2 < m ES < 5.30 GeV/c 2 .If multiple candidates are present in an event, they are ranked based on the value of the reconstructed seed candidate mass with respect to the nominal mass of this particle, and the magnitude of ∆E.Only a single B tag candidate per event is retained.Individual B tag modes with a measured high level of combinatorial background are subsequently excluded.The overall tagging efficiency is sub-percent [15].Correctlyreconstructed B tag candidates contribute to a peak in the m ES distribution near the B meson mass.The interval 5.27 GeV/c 2 < m ES < 5.29 GeV/c 2 is defined as the signal region, and the interval 5.20 GeV/c 2 < m ES < 5.26 GeV/c 2 as the sideband region.Continuum processes, from non-resonant e + e − → q q, and incorrectly reconstructed BB decays result in a substantial combinatorial background in both the signal and sideband regions.The continuum background is suppressed using a multivariate likelihood comprising six inputs which distinguish between comparatively jet-like non-resonant processes and more isotropic decay topologies of Υ (4S) → BB.The inputs are: the ratio of the second and zeroth Fox-Wolfram moments [18], calculated using all reconstructed charged tracks and calorimeter clusters in the event; the event thrust vector, the sum of the magnitudes of the momenta of all tracks and clusters projected onto the thrust axis, where the thrust axis is the axis that maximises the projection, and where the thrust vector is normalised with respect to the sum of the magnitudes of the momenta; the magnitude of the projection of the thrust vector onto the z-axis; the cosine of the angle between the B tag direction and the z-axis; the cosine of the angle between the event's missing momentum vector and the z-axis; the cosine of the angle between the thrust axes of the decay daughters of the B tag and of the B sig .These quantities are computed in the CM frame.The selector output, L BB , is shown in   The expected distribution for simulated B − → Λpνν events is also shown overlaid for a branching fraction of 0.4 × 10 −5 (dashed line), with yields per 0.01 given by the y-axis on the right-hand side.Fig. 2. Events with L BB > 0.35 are retained.This requirement rejects 76% of continuum background events and 16% of BB background events while retaining 82% of signal events.The m ES distribution of events selected by this criterion is shown in Fig. 3.
The B − → Λpνν candidates are identified by considering all activity in the detector which is not associated with the reconstructed B tag .Since only the Λ → pπ − decay mode is considered in this analysis, B sig candidates are required to possess exactly three charged tracks, with total charge opposite that of the B tag .Signal events typically contain several low-energy clusters in the calorimeter from hadronic shower fragments, bremsstrahlung, or beam-related sources.Physics backgrounds, however, frequently also produce higher energy clusters from π 0 decays and similar processes.These backgrounds are suppressed by requiring E extra < 400 MeV, where E extra is the total CM-frame energy of B sig clusters which have lab-frame energy exceeding 50 MeV; see Fig. 4 (top).
The background MC does not accurately reproduce the event yield in data at this point in the selection.This deficiency has been observed in previous BABAR analyses [2,16,17] and is understood to be due to a combination of inaccurate branching fractions and modelling of B tag reconstruction efficiencies in the simulation.A two step procedure is applied to correct this.Events in the m ES signal region can be divided into correctly reconstructed ("peaking") and combinatorial ("non-peaking") components.The non-peaking component in the signal region is determined from data by extrapolation of the m ES sideband data into the signal region.The shape of this distribution is obtained from background MC, and is characterized by the quantity R side , the ratio of the MC non-peaking background yield in the signal region to the yield in the sideband-region.After the signal selection described above, R side is evaluated as 0.215 ± 0.001, where the uncertainty is due to MC statistics.Scaled sideband data are then substituted for combinatorial MC in the m ES signal region when studying distributions of selection variables.Once the combinatorial contribution in the signal region has been determined, it is combined with the subset of B + B − MC in which a B tag has been correctly reconstructed, resulting in the peaking contribution in the m ES distribution.This peaking MC contribution is scaled by a factor C peak = 0.819 ± 0.006 to match data.Following this procedure, excellent agreement is observed in all kinematic variables used in this analysis, e.g.Figs. 4 -5.As the quantity C peak represents a global correction to the B tag yield, it is also applied to the signal efficiency.The reconstruction efficiency for Υ (4S) events containing a B − → Λpνν decay is estimated to be approximately 0.07%, after requiring that events possess a B tag with m ES in the signal region and satisfy the signal selection described above.The remainder of the event selection optimization is performed "blind", i.e., without knowledge of the data yield in the signal region until the selection procedure has been finalized.
Decays of B sig candidates are expected to contain a proton-antiproton pair and a single charged pion, where the (anti)proton with the same charge as the B tag is presumed to be the daughter of the Λ.Tight (anti)proton particle identification criteria are applied to the baryon    candidate tracks; no pion identification requirement is imposed on the third track.The (anti)proton selectors have an efficiency of approximately 95% within the momentum range relevant to this analysis [8].A kinematic fit is imposed on the Λ daughter tracks, applying pion and proton mass hypotheses and fitting the Λ vertex, including a constraint that the Λ originates within a B meson flight length of the event vertex.The three tracks are required to have a DOCA ordering consistent with a B − → Λpνν signal event, where DOCA is defined as the extrapolated distance of closest approach of a reconstructed track to the nominal event vertex.The p that is the daughter of the B sig originates from near the interaction point and so usually has the smallest DOCA.The two Λ → pπ − decay daughters typically   A simultaneous optimization of the L BB and E extra selection criteria is performed, with the expected branching fraction limit in the absence of signal used as the figure of merit.This optimization yields the selection criteria values presented previously.The signal efficiency is estimated to be (0.034 ± 0.001 (stat.))%.The background yield is determined by combining the peaking background from B + B − MC with the combinatorial background estimated from the m ES sideband, yielding 2.3 ± 0.7 (stat.)events.The dominant contribution of 1.7 ± 0.6 (stat.)arises from combinatorial background sources.
Systematic uncertainties arise in the determination of the signal efficiency and background yield.The combinatorial background yield is determined from data by extrapolation of the sideband into the m ES signal region.However, the shape of the combinatorial background distribution impacts the peaking yield correction and hence C peak is anti-correlated with R side .Consequently, the relevant systematic uncertainty is due to the extrapolation of the yield of combinatoric events in the m ES sideband to the signal region.The ratio R side is obtained from non-peaking background MC (qq, cc, τ + τ − , B 0 B 0 , and non-peaking B + B − ) and its value depends on the relative mix of the continuum and BB due to the difference in shape in the predicted m ES distributions of these two components.An uncertainty of 17% on background yield and 16% on signal efficiency is obtained by varying the shape of the m ES distribution between that given by BB and continuum MC, and determining the impact on the resulting signal efficiency and background estimates.The signal MC is produced using a phase-space model, which is subsequently weighted into the model of Ref. [1], based on the m Λp distribution.The impact of this weighting on the signal efficiency is evaluated by modifying the weighting scheme to include the other kinematic quantities m νν and θ B,L defined in that paper.A systematic uncertainty of 9.6% is assigned.
MC modelling of variables used in the signal selection impact both the signal efficiency and the background determination.The impact of (anti)proton particle identification is evaluated using standard BABAR procedures [8] for the relevant particle selectors and kinematic region.An uncertainty of 1.3% is assigned to the background yield and 1.4% to the signal efficiency.To determine the impact of the Λ selection procedure, the Λ yield is evaluated in the m ES sideband region, using a 4-vector sum of p and π − candidates to identify a Λ control sample which is independent of the nominal kinematic fit procedure.The relative Λ yields are determined from data and background MC, before and after applying the nominal Λ selection to this sample, resulting in a 13% correlated uncertainty on both the signal efficiency and background estimate.
The E extra cut introduces a systematic uncertainty due to possible mis-modeling of low-energy clusters in simulation.To evaluate this, the cluster energies in the MC are scaled to match the E extra distribution in data.Parametrically, the level of data-MC agreement in the E extra distribution (see Fig. 4) is found to be equivalent to applying a shift of 5 MeV per cluster.This correction is applied to the MC and a systematic of 1.9% for the signal efficiency and 11% for the background estimate is assigned, corresponding to the full impact of this correction.Systematic uncertainties are summarized in Table I.
The B − → Λpνν branching fraction is evaluated according to B(B − → Λpνν) = (N data − N bg )/( sig × N B ± ) , where N data and N bg are the number of events observed in data and the total estimated background yield, respectively.The overall B − → Λpνν signal ef-

1 FIG. 2 :
FIG.2: Output of the BB likelihood selector, L BB , for data (points with error bars) and background MC (stacked, shaded histograms) normalized to the data luminosity, for events with a reconstructed Btag with 5.27 GeV/c 2 < mES < 5.29 GeV/c 2 .The expected distribution for simulated B − → Λpνν events is also shown overlaid for a branching fraction of 0.4 × 10 −5 (dashed line), with yields per 0.01 given by the y-axis on the right-hand side. fig3

FIG. 3 :
FIG.3:The mES distribution for data (points with error bars) and background MC (stacked, shaded histograms) normalized to the data luminosity, for events which satisfy the continuum suppression criterion L BB > 0.35.The expected distribution for simulated B − → Λpνν events is also shown overlaid for a branching fraction of 0.4 × 10 −5 (dashed line), with event yields per 2 MeV/c 2 given by the y-axis on the right-hand side.
Sideband scaled data + Corrected MC peak combinatorial background

1 FIG. 4 :
FIG.4: Distribution of Eextra, calculated in the CM frame, in data and MC before (top) and after (bottom) application of the MC correction procedure for events with a reconstructed Btag with mES within the region.In the upper plot, data are shown as points with error bars, background MC is shown as stacked, shaded histograms.The expected distribution for simulated B − → Λpνν events is shown overlaid for a branching fraction of 0.4 × 10 −5 (dashed line), with yields given by the y-axis on the right-hand side.In the lower plot the shaded region is the sideband data scaled by R side , the unshaded region is the mES peaking component of the B + B − MC scaled by C peak .

1 FIG. 5 :
FIG.5:The pπ − invariant mass in events with a reconstructed Btag with mES within the signal region, with three charged tracks satisfying the (anti)proton selection and DOCA requirements.Data are shown points with error bars, the shaded region is the sideband data scaled by R side , the unshaded region is the mES peaking component of the B + B − MC scaled by C peak .
q = u, d, s) cc signal data

TABLE I :
Summary of systematic uncertainties on the signal efficiency and backgrounds.