Search for $B$ Mesogenesis at BABAR

A new mechanism has been proposed to simultaneously explain the presence of dark matter and the matter-antimatter asymmetry in the universe. This scenario predicts exotic $B$ meson decays into a baryon and a dark sector anti-baryon ($\psi_D$) with branching fractions accessible at $B$ factories. We present a search for $B \rightarrow \Lambda \psi_D$ decays using data collected by the $BABAR$ experiment at SLAC. This reaction is identified by fully reconstructing the accompanying $B$ meson and requiring the presence of a single $\Lambda$ baryon in the remaining particles. No significant signal is observed, and bounds on the $B \rightarrow \Lambda \psi_D$ branching fraction are derived in the range $0.13 - 5.2\times 10^{-5}$ for $1.0<m_{\psi_D}<4.2$ GeV/$c^{2}$. These results set strong constraints on the parameter space allowed by the theory.

The nature of dark matter (DM) and the baryon asymmetry of the Universe (BAU) are perhaps two of the deepest mysteries of modern particle physics.The latest cosmological observations reveal that visible matter only accounts for about 15% of the matter in the universe, while the remaining 85% is constituted by DM [1,2].Beyond its coupling to gravity, the particle properties of DM remain to be elucidated, and many models have been proposed to explain the observed abundance.The visible matter density is equally mysterious, as cosmology predicts a universe born with equal amount of matter and antimatter.A dynamical mechanism, baryogenesis, is required to produce an initial excess of baryons over antibaryons consistent with cosmic microwave background and big-bang-nucleosynthesis measurements [3,4].
The B-Mesogenesis scenario has been recently pro-posed [5,6] to simultaneously explain the DM abundance and the BAU.This model introduces several new fields, including a light dark-sector anti-baryon and a new TeVscale color-triplet bosonic mediator.The baryogenesis mechanism relies on the out-of-thermal-equilibrium production of b and b quarks in the early universe through the decay of a massive, long-lived scalar field Φ, as illustrated in Fig. 1.A fraction of these quarks hadronizes into B 0 and B0 mesons, which undergo CP -violating oscillations before decaying into a baryon B, a darksector anti-baryon ψ D , and any number of additional light mesons M. As a result, matter-antimatter asymmetries are generated in the visible and dark sectors with equal but opposite magnitudes, keeping the total baryon number conserved.We note that our search is strongly related in its experimental signature to a recently proposed [7] search for supersymmetry in B meson decay to a baryon and undetected light neutralino.
The baryon asymmetry is determined by the charge asymmetry in semi-leptonic B decays, which specifies the level of CP violation in mixing in the B 0 − B0 system, and the branching fraction of the inclusive B → ψ D BM decays.The B-Mesogenesis mechanism would imply a robust lower bound on the total branching fraction BR(B → ψ D BM) > 10 −4 [6].Constraints on exclusive B 0 → ψ D B decays are calculated using phase-space considerations for different baryons [6].The results depend on the effective operators O i,j = ψ D bij mediating the decay, where i = u, c and j = d, s specify the quark content.The ratio of exclusive to inclusive branching fractions ranges from about 1 to 100%, depending on the ψ D mass.Furthermore, bounds on inclusive b decays with missing energy [8], searches for TeV-scale color-triplet scalars at the LHC [9,10], and dark matter stability require 0.94 < m ψ D < 3.5 GeV/c 2 [6].At present, the best constraints on this scenario arise from a measurement of the exclusive B → ψ D Λ decay by the Belle Collaboration [11] excluding branching fractions larger than ∼ (2 − 3) × 10 −5 for m ψ D > 1.0 GeV/c 2 .We report herein a search for the decay B 0 → ψ D Λ in the mass range 1.0 < m ψ D < 4.2 GeV/c 2 .The analysis is based on 398.5 fb −1 of data collected at the Υ (4S) resonance with the BABAR detector at the PEP-II e + e − storage ring at SLAC, corresponding to 4.35 × 10 8 B B pairs [12].The BABAR detector is described in detail elsewhere [13,14].An additional 32.5 fb −1 of data are used to optimize the analysis strategy and are subsequently discarded.The remaining data are not examined until the analysis procedure is finalized.
Simulated signal events are created using the EVT-GEN [15] Monte Carlo (MC) event generator.Eight different samples, each with a different ψ D mass, are generated.The mass values range from 1 to 4.2 GeV/c 2 .The background is studied with samples of inclusive e + e − → B B decays (EVTGEN) and continuum e + e − → q q events with q = u, d, s, c (JETSET [16]).The detector response is simulated with Geant4 [17,18].
Since dark-sector particles escape undetected, we identify the signal by fully reconstructing the second B meson (B tag ) from hadronic decay modes, and require the presence of a single Λ baryon among the remaining particles.The ψ D is identified as the system recoiling against the B tag and Λ candidates.Hadronic B meson decays proceed mostly through charmed mesons, and the B tag candidate is reconstructed via the decays B → SX by a hierarchical algorithm that combines a "seed" meson S, such as D ( * )0 , D ( * )± , D * ± s , or J/ψ, with a hadronic system X containing up to five kaons and/or pions with total charge 0 or ±1 [19].The selection of B tag candidates is based on two kinematic variables: the energy difference ∆E = E beam − E tag and the beam-energy-substituted , where E tag and p Btag are the energy and momentum of the B tag candidate in the e + e − center-of-mass frame, and E beam is the beam energy in the same frame.
The remaining particles are associated with the signal B → Λψ D candidate (B sig ).The Λ candidates are reconstructed as pair of oppositely charged tracks identified as a proton and a pion.A kinematic fit is performed on the Λ candidate, constraining the two tracks to originate from the same point in space and requiring the momentum vector to point back to the beam interaction region.The Λ flight length is calculated as the distance between the primary interaction point and the secondary decay vertex.The flight length significance, defined as the flight length divided by its uncertainty, must be greater than 1.0.If more than one combination of B tag and Λ candidates is found, the one with the smallest χ 2 is selected.After reconstructing the B tag and Λ candidates, no additional track must be present in the event.The distributions of m ES and the reconstructed Λ mass (m Λ ) are shown in Fig. 2. We require events to satisfy 5.27 < m ES < 5.29 GeV/c 2 and 1.110 < m Λ < 1.121 GeV/c 2 .
A multivariate selection using boosted decision trees (BDT) [20] is used to further increase the signal purity.The BDT includes the following variables: m ES and ∆E of the B tag candidate; information about the B tag hadronic decay channel and its purity, defined as the fraction of correctly reconstructed B tag candidates for a given decay mode [21]; the magnitude of the B tag thrust vector, defined as the sum of the magnitudes of the momenta of all tracks and calorimeter clusters projected onto the thrust axis [21]; the B sig momentum vector in the laboratory frame, inferred from the initial beam electrons and the recoiling B tag ; the number of calorimeter clusters associated with B sig ; the total neutral energy associated with B sig ; the number of π 0 candidates associated with B sig ; the Λ flight length significance; the χ 2 of the kinematic fit performed on the Λ candidate; and the energy and momentum of the Λ candidate in the laboratory frame.The ψ D mass is specifically excluded from the BDT in order to limit potential bias in the classifier, and the BDT is trained on a signal sample spanning a wide range of ψ D masses.The distribution of the BDT score, ν BDT , is shown in Fig. 3.We select events with a BDT score greater than 0.75, selecting 41 events in the data.The resulting ψ D mass distribution is shown in Fig. 4. Approximately half of the expected background consists of e + e − → q q events, and the remainder arises from B B events.The signal efficiency varies between 5.9 × 10 −4 at m ψ D = 1.0 GeV/c 2 and 2.1 × 10 −4 around m ψ D = 4.2 GeV/c 2 , taking into account the B tag reconstruction efficiency, the selection criteria, and the Λ → pπ − branching fraction.As shown in Fig. 3, the inclusive background MC samples do not accurately reproduce the data.This discrepancy arises from a mis-modeling of sev-eral branching fractions used in the simulation, resulting in differences in B tag reconstruction efficiencies [22], as well as differences in charged and neutral particle reconstruction efficiencies, PID efficiencies, and the modeling of variables used in the BDT.We correct the simulation in a two-step procedure, using sideband data selected with the criteria, described above, applied before the BDT selection, except with the looser requirement 5.20 < m ES < 5.29 GeV/c 2 .The region −0.5 < ν BDT < 0.75, largely dominated by e + e − → q q (q = u, d, s, c) events, is used to extract a correction factor for continuum production, f udsc , by rescaling the corresponding MC predictions to the number of observed events.The correction factor for B B production, f B 0 B0 , is determined from data in the complementary region ν BDT < −0.5, assuming equal contributions from B 0 B0 and B + B − .We obtain f udsc = 1.34 ± 0.10 and f B 0 B0 = 1.06 ± 0.08.Under the assumption that the B B correction factor is independent of the signal B decay mode, we rescale the signal efficiency by f B 0 B0 , and propagate the corresponding uncertainty as a systematic uncertainty.
We extract the signal yield by scanning the ψ D mass spectrum in steps of the signal mass resolution, σ m , probing a total of 193 mass hypotheses.The resolution is estimated by performing fits of a Bukin function [23] to the ψ D mass distribution for each signal MC sample, and interpolating the results to the full mass range.The results vary between 90 MeV/c 2 at m ψ D = 1.0 GeV/c 2 and 6 MeV/c 2 at m ψ D = 4.2 GeV/c 2 .The signal yield is determined by counting the number of events in a window of ±3σ m centered around the ψ D mass hypothesis.The background is evaluated in two sideband regions of ±3σ m surrounding the signal window, except near m ψ D = 4.2 GeV/c 2 , where a single region is used.The largest local significance is found to 2.3σ, observed near m ψ D = 3.7 GeV/c 2 , corresponding to a global significance of 0.4σ after including trial factors [24], consistent with the null hypothesis.
In the absence of a signal, upper limits on the branching fraction B 0 → ψ D Λ are derived at 90% confidence level (CL) by applying a profile likelihood method [25] for each ψ D mass hypothesis.The number of signal and background events is assumed to follow Poisson distributions, while the efficiency is modeled with a Gaussian having a variance equal to the total systematic uncertainty.Systematic uncertainties arising from track and neutral reconstruction efficiencies, B tag reconstruction efficiencies, selection criteria, and modeling of the BDT variables are included in the B B correction factor described above.Other sources of uncertainty include the Λ → pπ − branching fraction (0.8%), the integrated luminosity (0.6%) [12], and the limited statistical precision of the signal MC samples (0.7-4.6%).The total systematic uncertainty, obtained by summing in quadrature the different contributions, varies between 7.8 and 9.1%.
The results are displayed in Fig. 5 In summary, we report a search for baryogenesis and dark matter in the process B 0 → Λψ D with a fully reconstructed B tag meson.No significant signal is observed, and upper limits on the branching fraction at the level of 10 −6 − 10 −5 are set.These results exclude a large fraction of the parameter space allowed by B Mesogenesis.Future measurements at Belle-II should be able to fully explore the remaining region.
We thank G. Elor and M. Escudero for useful discussions on the B-Mesogenesis mechanism.We are grateful for the extraordinary contributions of our PEP-II colleagues in achieving the excellent luminosity and machine conditions that have made this work possible.The success of this project also relies critically on the expertise and dedication of the computing organizations that support BABAR.The collaborating institutions wish to thank SLAC for its support and the kind hospitality extended to them.

FIG. 2 .
FIG.2.Distribution of (top) the energy-substituted mass, mES, and (bottom) the reconstructed Λ mass, mΛ, for data (points), signal MC for m ψ D = 2.0 GeV/c 2 (red histogram) and inclusive background MC predictions (stacked histograms).The normalization of the signal events is arbitrary.

FIG. 3 .FIG. 4 .
FIG.3.The distribution of the BDT score after applying all other selection criteria for data (points), signal MC for m ψ D = 2.0 GeV/c 2 (red histogram) and inclusive background MC predictions (stacked histograms).The normalization of the signal events is arbitrary.