Test of lepton-ﬂavor universality in B → K ∗ (cid:96) + (cid:96) − decays at Belle

We present a measurement of R K ∗ , the branching fraction ratio B ( B → K ∗ µ + µ − )/ B ( B → K ∗ e + e − ), for both charged and neutral B mesons. The ratio for the charged case, R K ∗ + , is the ﬁrst measurement ever performed. In addition, we report absolute branching fractions for the individual modes in bins of the squared dilepton invariant mass, q 2 . The analysis is based on a data sample of 711 fb − 1 , containing 772 × 10 6 B ¯ B events, recorded at the Υ(4 S ) resonance with the Belle detector at the KEKB asymmetric-energy e + e − collider. The obtained results are consistent with Standard Model expectations.

is the first measurement ever performed. In addition, we report absolute branching fractions for the individual modes in bins of the squared dilepton invariant mass, q 2 . The analysis is based on a data sample of 711 fb −1 , containing 772 × 10 6 BB events, recorded at the Υ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e + e − collider. The obtained results are consistent with Standard Model expectations.
In the Standard Model (SM), the coupling of gauge bosons to leptons is independent of lepton-flavor, a concept known as lepton-flavor universality (LFU). Therefore, experimental tests of LFU are excellent probes for New Physics (NP). In this Letter, we present a test of LFU in B → K * + − decays, where is either e or µ. These decays have been studied by several experiments, and some results suggest an intriguing possibility that the underlying b → s + − transition may be affected by physics beyond the SM in modes involving muons [1][2][3][4][5][6]. The ratio of branching fractions, is well suited to test LFU [7]. The theoretical predictions for R K * are robust [7][8][9], as uncertainties related to form factors cancel out in the ratio. This observable is expected to be close to unity in the SM. For this measurement, we reconstruct the decay channels B 0 → K * 0 µ + µ − , B + → K * + µ + µ − , B 0 → K * 0 e + e − , and B + → K * + e + e − . The K * meson is reconstructed in the K + π − , K + π 0 , and K 0 S π + decay modes. The inclusion of charge-conjugate states is implied throughout this paper. Compared to the previous analysis [6], the full Υ(4S) data sample containing 772 × 10 6 BB events, recorded with the Belle detector [10] at the KEKB asymmetric-energy e + e − collider [11], is used.
Belle is a large-solid-angle magnetic spectrometer that consists of a silicon vertex detector, a 50-layer central drift chamber (CDC), an array of aerogel threshold Cherenkov counters (ACC), a barrel-like arrangement of time-of-flight scintillation counters (TOF), and an electromagnetic calorimeter comprised of CsI(Tl) crystals (ECL). All these components are located inside a superconducting solenoid coil that provides a 1.5 T magnetic field. An iron flux return placed outside of the coil is instrumented with resistive plate chambers to detect K 0 L mesons and muons (KLM).
The analysis is validated and optimized with simulated Monte Carlo (MC) data samples, from which also the selection efficiencies are derived. The EvtGen [12] and PYTHIA [13] packages are used to generate decay chains, where the final-state-radiation effect is incorporated with PHOTOS [14]. The detector response is simulated with GEANT3 [15].
All tracks, except for those from K 0 S decays, need to satisfy requirements on their impact parameter with respect to the interaction point along the z axis (|dz| < 5.0 cm) and in the transverse x-y plane (|dr| < 1.0 cm).
The z axis is in the direction opposite to that of the e + beam. We calculate a particle identification (PID) likelihood for each track using energy loss in the CDC, information from the TOF, number of the photoelectrons from the ACC, the transverse shower shape and energy in the ECL, and hit information from the KLM. Electrons are identified using the likelihood ratio P e = L e /(L e + L π ), where L i is the PID likelihood for the particle type i. Charged tracks satisfying P e > 0.9 are accepted as electron candidates. Energy losses due to bremsstrahlung are recovered by adding the momenta of photons to that of the electron's momentum if they lie within 0.05 rad of the initial track direction. Tracks are selected as muon candidates if they satisfy P µ > 0.9, where P µ is the analogous likelihood ratio for muons. For electron (muon) candidates we require the momentum to be greater than 0.4 (0.7) GeV/c so that they can reach the ECL (KLM), which improves the PID. These requirements select electron (muon) candidates with an efficiency greater than 86% (92%) while rejecting more than 99% of pions. Charged kaons are distinguished from pions (and vice versa) by requiring the likelihood ratio P K = L K /(L K + L π ) to be greater than 0.1 (smaller than 0.9). This requirement retains more than 99% of kaons (pions) while reducing the misidentification rate of pions (kaons) by 94% (86%).
The K 0 S candidates are reconstructed with an efficiency of 74% from two oppositely charged tracks (treated as pions) by applying selection criteria on their invariant mass and vertex-fit quality [16]. We reconstruct π 0 candidates from photon pairs, where each photon is required to have an energy greater than 30 MeV. Furthermore, the invariant mass of the photon pair is required to be in the [115, 153] MeV/c 2 range, which corresponds to approximately ±4 times the π 0 reconstructed-mass resolution. We form K * candidates from K + π − , K + π 0 , and K 0 S π + combinations with an invariant mass lying in the range [0.6, 1.4] GeV/c 2 . We also apply a requirement on the K * vertex-fit quality to reduce background. The K * candidates are combined with two oppositely charged leptons to form B meson candidates.
The dominant background is due to incorrect combinations of tracks. This combinatorial background is suppressed by applying requirements on the beamenergy-constrained mass, M bc = E 2 beam /c 4 − | p B | 2 /c 2 , and the energy difference, ∆E = E B − E beam , where E beam is the beam energy, and E B and p B are the energy and momentum, respectively, of the reconstructed B-meson candidate. All of these quantities are calculated in the center-of-mass frame. Correctly recon-structed signal events peak near the B-meson mass [17] in M bc and at zero in ∆E. The ∆E distribution is wider for electron modes as some bremsstrahlung photons are not reconstructed. We retain B decay candidates that satisfy 5.22 GeV/c 2 < M bc < 5.30 GeV/c 2 and −0.10 (−0.05) GeV < ∆E < 0.05 GeV in the electron (muon) mode.
Large irreducible background contributions arise in the ∆E and M bc distributions from the decays B → J/ψK * and B → ψ(2S)K * , where the charmonium states further decay into two leptons. We veto this background by rejecting candidates with −0.25 (−0.15) GeV/c 2 < M −m J/ψ < 0.08 GeV/c 2 and −0.20 (−0.10) GeV/c 2 < M − m ψ(2S) < 0.08 GeV/c 2 for the electron (muon) channel. In the electron case, the veto is applied twice: before and after the bremsstrahlung-recovery treatment. This is done to prevent charmonium backgrounds from shifting out of the veto region when an incorrect photon is combined with the electron.
A multivariate analysis technique is developed to suppress combinatorial background. A dedicated neural network classifier is trained with MC samples to identify each particle type used in the decay chain, from which a signal probability is calculated for each candidate. The neural networks dedicated to identifying the particles e ± , µ ± , K ± , K 0 S , π 0 , and π ± are identical to those used in Ref. [18]. The networks for K * selection use input variables related to the K * daughter particles. Most of the discrimination of the K * selection comes from vertex-fit information, decay-product neural-network outputs, and momenta of the decay products. The final signal selection is performed with a dedicated neural network for each B decay channel. The inputs to these B-decay classifiers include event-shape variables (modified Fox-Wolfram moments [19]), vertex-fit information, and kinematic variables such as the reconstructed mass of the K * and the angle between its momentum vector and the initial direction extracted from the vertex fit. The most discriminating of these input variables are ∆E, the reconstructed K * mass, the product of the network outputs for all daughter particles, and the distance between the two leptons projected onto the z axis as derived from a fit to the Bdecay vertex. The final selection requirement on the Bdecay classifier output value is optimized by maximizing a figure of merit, n s / √ n s + n b , where n s (n b ) is the expected number of signal (background) events calculated from MC samples in the region M bc > 5.27 GeV/c 2 .
Less than 2% of events contain multiple B candidates. In such cases, we choose the one with the highest signal probability, estimated from the neural network output values. This procedure selects the correct B candidate with an efficiency between 82% and 92%, depending on the channel. Individual decay channels in these samples are normalized according to the branching fraction values reported in Ref. [17].
We extract signal yields in various regions of the squared dilepton invariant mass, q 2 , using an unbinned extended maximum-likelihood fit to the M bc distribution of B → K * + − candidates. We consider four different components in the likelihood fit. First, a signal component is parametrized by a Crystal Ball function [20], with the shape parameters determined from B → J/ψK * candidates that fail the J/ψ veto in data. Second, a combinatorial background component is described by an ARGUS function [21]. Third, there is a component from events in which charmonium decays pass the veto when they are misreconstructed; for example, when the bremsstrahlung recovery fails to detect photons. This background component is studied using an MC sample with 100 times higher statistics than that expected from the charmonium decays in the data sample. The shape of the charmonium background is determined via kernel density estimation (KDE) [22]. Lastly, a peaking background component from double misidentification of particle type, where two particles have been assigned the wrong hypothesis such as B → K * π + π − , is studied using MC samples, with the shape parametrized via KDE. As the expected yields of charmonium and doublemis-identification backgrounds are small, their yields are fixed in the fit to values obtained from MC simulation. The determination of signal efficiency is verified by measuring the well-known B → J/ψK * branching fractions, which are found to be compatible with world averages [17]. As a cross-check, the LFU ratio of B[B → J/ψ(→ µ + µ − )K * ] and B[B → J/ψ(→ e + e − )K * ] is measured to be 1.015 ± 0.025 ± 0.038, where the first error is statistical and the second due to uncertainty in data-MC corrections for lepton identification. This cross-check neglects contributions from the B → K * channel in the J/ψ control region.
The reconstruction procedure for this analysis is optimized for maximal statistical sensitivity to R K * , at the cost of systematic uncertainties due to the use of multivariate selections in particle identification. Systematic uncertainties arises from the determination of the signal yield and reconstruction efficiency. All considered systematic uncertainties for R K * are listed in Table I. The uncertainty due to the signal yield is evaluated by varying the Crystal Ball shape parameters within their uncertainties. The maximum yield deviation is taken as the systematic uncertainty. The normalizations of peaking and charmonium backgrounds are varied in the fit by ±50% and ±25%; these ranges are chosen according to the maximum uncertainties on the branching fractions used to generate the respective MC samples. The resulting signal-yield deviations are included as part of the systematic uncertainty. We correct for differences in the lepton-identification efficiency between data and MC by using the results obtained from a control sample of two-photon e + e − → e + e − e + e − /e + e − µ + µ − events. The input distributions used by the top-level classifiers are compared between data and simulation, and no sig-nificant differences are found. In order to estimate the resulting uncertainty, the ratio of B → J/ψK * branching fractions between data and MC is obtained in bins of the classifier output. The obtained ratio is propagated as classifier output-dependent weights to candidates in all fits to M bc distributions, and changes in the resulting signal yields are taken as systematic uncertainties. The statistical uncertainty of this reweighting procedure is evaluated in simulations on signal MC samples, and this adds 1-2% additional uncertainty. Further uncertainties arise from limited MC statistics. Effects due to migration of events between different q 2 bins are studied using MC events and found to be negligible. In the case of results for the full region of q 2 > 0.045 GeV 2 /c 4 , the different veto regions for the electron and muon channels need to be accounted for in the determination of reconstruction efficiency. This introduces model dependence to our signal simulation, which uses form factors from Ref. [23]. We estimate the systematic uncertainty due to this model dependence using different signal MC samples generated with form factors from QCD sum rules [24] and quark models [25]. The maximum difference in selection efficiency with respect to the nominal model, in each q 2 region, is taken as our estimate for the size of this effect. This results on average in a difference of 0.4 ± 2.4% with a maximum of 6.5%, depending on the mode and q 2 region. As discussed in the beginning, this uncertainty only applies to the branching fractions not to the LFU ratios. The systematic uncertainty for hadron identification and K * selection is covered in the uncertainty for the top-level classifiers due to the multivariate selection approach. For the branching fraction measurements additional uncertainties from tracking (0.35% per track) and the total number of BB events in data are taken into account. The dominant uncertainty originates from lepton identification, ranging between 5% and 10% depending on the mode and q 2 region, as also here a more conservative estimation of uncertainty is performed to account for residual correlations with the top-level classifiers.
In the range q 2 > 0.045 GeV 2 /c 4 we find 103.0 +13.4 −12.7 (139.9 +16.0 −15.4 ) events in the electron (muon) channels. Example fits are presented in Fig. 1. Using the fitted signal yields we construct the LFU ratio R K * for all signal channels combined, as well as separate ratios for the B 0 and B + decays, R K * 0 and R K * + . Our measurement of R K * + is the first ever performed. Results are shown in Table II and Fig. 2. The branching fractions are calculated assuming equal production of B + and B 0 mesons and the results are presented in Table III. In summary, all our results are consistent with the SM expectations [26,27]. Global analyses of measurements of b → s + − mediated decays prefer NP models that predict R K * values smaller than unity [27]. The largest deviation along this direction is observed in the lowest q 2 bin, in the same region where LHCb reports a measurement deviating from the SM [4]. Our separate results for the B-meson isospin partners, R K * + and R K * 0 , are statistically compatible, which would also be expected if contributions from NP arise from the b → s + − transition. The Belle II experiment [28,29] is expected to record a 50 times larger data sample than Belle, providing ideal conditions to precisely study lepton flavour universality in these modes. We thank the KEKB group for the excellent operation of the accelerator; the KEK cryogenics group for the efficient operation of the solenoid; and the KEK computer group, and the Pacific Northwest National Laboratory (PNNL) Environmental Molecular Sciences Laboratory (EMSL) computing group for strong computing support;     [10 −7 ] in the corresponding q 2 range in GeV 2 /c 4 . The first uncertainty is statistical and the second is systematic.