Test of lepton universality with B0 → K *0 ℓ + ℓ − decays

JHEP08(2017)055 Published for SISSA by Springer Received:May 17, 2017 Revised:July 21, 2017 Accepted:August 1, 2017 Published:August 16, 2017 Test of lepton universality with B0→K∗0`+`− decays The LHCb collaboration E-mail: [email protected] Abstract: A test of lepton universality, performed by measuring the ratio of the branching fractions of the B0→K∗0µ+µ−and B0→K∗0e+e−decays, RK∗0, is presented. The K∗0 meson is reconstructed in the final state K+π−, which is required to have an invariant mass within 100 MeV/c2of the known K∗(892)0mass. The analysis is performed using proton-proton collision data, corresponding to an integrated luminosity of about 3 fb−1, collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. The ratio is measured in two regions of the dilepton invariant mass squared, q2, to be RK∗0=(0.66 + 0.11 −0.07 (stat) ±0.03 (syst) for 0.045 < q2<1.1 GeV2 /c4, 0.69 + 0.11 −0.07 (stat) ±0.05 (syst) for 1.1< q2<6.0 GeV2 /c4. The corresponding 95.4% confidence level intervals are [0.52,0.89] and [0.53,0.94]. The results, which represent the most precise measurements of RK∗0to date, are compatible with the Standard Model expectations at the level of 2.1–2.3 and 2.4–2.5 standard deviations in the two q2regions, respectively. Keywords: B physics, Branching fraction, Hadron-Hadron scattering (experiments), Rare decay ArXiv ePrint: 1705.05802 Open Access, Copyright CERN, for the benefit of the LHCb Collaboration. Article funded by SCOAP3. https://doi.org/10.1007/JHEP08(2017)055 JHEP08(2017)055 Contents 1 Introduction 1 2 The LHCb detector and data set 3 3 Electron reconstruction effects 5 4 Corrections to the simulation 6 5 Selection of signal candidates 7 6 Exclusive backgrounds 10 7 Fits to the K+π−`+`−invariant mass distributions 11 8 Efficiencies 13 9 Cross-checks 14 10 Systematic uncertainties 16 11 Results 19 12 Conclusions 19 The LHCb collaboration 26 1 Introduction In the Standard Model (SM) of particle physics, the electroweak couplings of leptons to gauge bosons are independent of their flavour and the model is referred to as exhibiting lepton universality (LU). Flavour-changing neutral-current (FCNC) processes, where a quark changes its flavour without altering its electric charge, provide an ideal laboratory to test LU. The SM forbids FCNCs at tree level and only allows amplitudes involving electroweak loop (penguin and box) Feynman diagrams. The absence of a dominant treelevel SM contribution implies that such transitions are rare, and therefore sensitive to the existence of new particles. The presence of such particles could lead to a sizeable increase or decrease in the rate of particular decays, or change the angular distribution of the final-state particles. Particularly sensitive probes for such effects are ratios of the type [1] RH=RdΓ(B→Hµ+µ−) dq2dq2 RdΓ(B→He+e−) dq2dq2, – 1 – JHEP08(2017)055 where Hrepresents a hadron containing an squark, such as a Kor a K∗meson. The decay rate, Γ, is integrated over a range of the squared dilepton invariant mass, q2. The RH ratios allow very precise tests of LU, as hadronic uncertainties in the theoretical predictions cancel, and are expected to be close to unity in the SM [1–3]. At e+e−colliders operating at the Υ(4S) resonance, the ratios RK(∗)have been measured to be consistent with unity with a precision of 20 to 50% [4,5]. More recently, the most precise determination to date of RKin the q2range between 1.0 and 6.0 GeV2 /c4has been performed by the LHCb collaboration. The measurement has a relative precision of 12% [6] and is found to be 2.6 standard deviations lower than the SM expectation [1]. Hints of LU violation have been observed in B→D(∗)`ν`decays [7–9]. Tensions with the SM have also been found in several measurements of branching fractions [10–12] and angular observables [13,14] of rare b→sdecays. Models containing a new, neutral, heavy gauge boson [15–20] or leptoquarks [21,22] have been proposed to explain these measurements. A precise measurement of RK∗0can provide a deeper understanding of the nature of the present discrepancies [23]. Some of the leading-order Feynman diagrams for the B0→K∗0`+`−decays, where `represents either a muon or an electron, are shown in figure 1for both SM and possible New Physics (NP) scenarios. If the NP particles couple differently to electrons and muons, LU could be violated. The K∗0represents a K∗(892)0 meson, which is reconstructed in the K+π−final state by selecting candidates within 100 MeV/c2of the known mass [24]. No attempt is made to separate the K∗0meson from S-wave or other broad contributions present in the selected K+π−region. The Swave fraction contribution to the B0→K∗0µ+µ−mode has been measured by the LHCb collaboration and found to be small [25]. Inclusion of charge-conjugate processes is implied throughout the paper, unless stated otherwise. The analysis is performed in two regions of q2that are sensitive to different NP contributions: a low-q2bin, between 0.045 and 1.1 GeV2 /c4, and a central-q2bin, between 1.1 and 6.0 GeV2 /c4. The lower boundary of the low-q2region corresponds roughly to the dimuon kinematic threshold. The boundary at 1.1 GeV2 /c4is chosen such that φ(1020)→`+`−decays, which could potentially dilute NP effects, are included in the low-q2interval. The upper boundary of the central-q2bin at 6.0 GeV2 /c4is chosen to reduce contamination from the radiative tail of the J/ψ resonance. The measurement is performed as a double ratio of the branching fractions of the B0→K∗0`+`−and B0→K∗0J/ψ(→`+`−) decays RK∗0=B(B0→K∗0µ+µ−) B(B0→K∗0J/ψ(→µ+µ−))B(B0→K∗0e+e−) B(B0→K∗0J/ψ(→e+e−)) , where the two channels are also referred to as the “nonresonant” and the “resonant” modes, respectively. The experimental quantities relevant for the measurement are the yields and the reconstruction efficiencies of the four decays entering in the double ratio. Due to the similarity between the experimental efficiencies of the nonresonant and resonant decay modes, many sources of systematic uncertainty are substantially reduced. This helps to mitigate the significant differences in reconstruction between decays with muons or electrons in the final state, mostly due to bremsstrahlung emission and the trigger response. The decay J/ψ →`+`−is measured to be consistent with LU [24]. In order to – 2 – JHEP08(2017)055 Figure 1. Feynman diagrams in the SM of the B0→K∗0`+`−decay for the (top left) electroweak penguin and (top right) box diagram. Possible NP contributions violating LU: (bottom left) a treelevel diagram mediated by a new gauge boson Z0and (bottom right) a tree-level diagram involving a leptoquark LQ. avoid experimental biases, a blind analysis was performed. The measurement is corrected for final-state radiation (FSR). Recent SM predictions for RK∗0in the two q2regions are reported in table 1. Note that possible uncertainties related to QED corrections are only included in ref. [26], and these are found to be at the percent level. The RK∗0ratio is smaller than unity in the low-q2region due to phase-space effects. The remainder of this paper is organised as follows: section 2describes the LHCb detector, as well as the data and the simulation samples used; the experimental challenges in studying electrons as compared to muons are discussed in section 3; section 4details how the simulation is adjusted in order to improve the modelling of the data; the selection of the candidates, rejection of the background and extraction of the yields are outlined in sections 5,6and 7; section 8discusses the efficiency determination; the cross-checks performed and the systematic uncertainties associated with the measurement are summarised in sections 9and 10, respectively; the results are presented in section 11; and section 12 presents the conclusions of the paper. 2 The LHCb detector and data set The LHCb detector [37,38] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed to study particles containing bor cquarks. The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector surrounding the pp interaction region, a large-area silicon-strip detector located upstream of – 3 – JHEP08(2017)055 q2range [ GeV2 /c4]RSM K∗0References [0.045,1.1] 0.906 ±0.028 BIP[26] 0.922 ±0.022 CDHMV[27–29] 0.919 + − 0.004 0.003 EOS[30–32] 0.925 ±0.004 flav.io[33–35] 0.920 + − 0.007 0.006 JC[36] [1.1,6.0] 1.000 ±0.010 BIP[26] 1.000 ±0.006 CDHMV[27–29] 0.9968 + − 0.0005 0.0004 EOS[30–32] 0.9964 ±0.005 flav.io[33–35] 0.996 ±0.002 JC[36] Table 1. Recent SM predictions for RK∗0. a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes placed downstream of the magnet. The tracking system provides a measurement of momentum, p, with a relative uncertainty that varies from 0.5% at low values to 1.0% at 200 GeV/c. The minimum distance of a track to a primary vertex (PV), the impact parameter (IP), is measured with a resolution of (15 + 29/pT)µm, where pTis the component of the momentum transverse to the beam, in GeV/c. Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov detectors. Photons, electrons and hadrons are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic calorimeter (ECAL) and a hadronic calorimeter (HCAL). Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers. The trigger system consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, which applies a full event reconstruction. The hardware muon trigger selects events containing at least one muon with significant pT(from ∼1.5 to ∼1.8 GeV/c, depending on the data-taking period). The hardware electron trigger requires the presence of a cluster of calorimeter cells with significant transverse energy, ET, (from ∼2.5 to ∼3.0 GeV, depending on the data-taking period) in the ECAL. The hardware hadron trigger requires the presence of an energy deposit with ETabove ∼3.5 GeV in the calorimeters. The software trigger requires a two-, threeor four-track secondary vertex, with a significant displacement from the PV. At least one charged particle must have significant pTand be inconsistent with originating from any PV. A multivariate algorithm [39] is used for the identification of secondary vertices consistent with the decay of a bhadron. The analysis is based on pp collision data collected with the LHCb detector at centreof-mass energies of 7 and 8 TeVduring 2011 and 2012, and corresponding to an integrated luminosity of about 3 fb−1. Samples of simulated B0→K∗0µ+µ−,B0→K∗0e+e−, B0→K∗0J/ψ(→µ+µ−) and B0→K∗0J/ψ(→e+e−) events are used to determine the ef- – 4 – JHEP08(2017)055 ficiency to trigger, reconstruct and select signal events, as well as to model the shapes used in the fits for signal candidates. In addition, specific simulated samples are utilised to estimate the contributions from backgrounds and to model their mass distributions. The pp collisions are generated using Pythia [40,41] with a specific LHCb configuration [42]. Decays of hadronic particles are described by EvtGen [43], in which FSR is generated using Photos [44], which is observed to agree with a full QED calculation at the level of ∼1% [26]. The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [45,46] as described in ref. [47]. 3 Electron reconstruction effects The experimental environment in which the LHCb detector operates leads to significant differences in the treatment of decays involving muons or electrons in the final state. The two types of leptons behave differently when travelling through the detector material. Electrons emit a much larger amount of bremsstrahlung which, if not accounted for, would result in a significant degradation of the momentum resolution and consequently in a degradation of the Bmass resolution. If the radiation occurs downstream of the dipole magnet, the photon energy is deposited in the same calorimeter cell as that of the lepton, and the momentum of the electron is correctly measured. If the photons are emitted upstream of the magnet, the electron and photon deposit their energy in different calorimeter cells, and the electron momentum is evaluated after bremsstrahlung emission. However, for both types of emissions, the ratio of the energy detected in the ECAL to the momentum measured by the tracking system, an important variable to identify electrons, remains unbiased. A dedicated bremsstrahlung recovery procedure is used to improve the electron momentum reconstruction. Searches are made within a region of the ECAL defined by the extrapolation of the electron track upstream of the magnet for energy deposits with ET>75 MeV that are not associated with charged tracks. Such “bremsstrahlung clusters” are added to the measured electron momentum. If the same cluster can be associated with both the e+and the e−, its energy is added to one of the two electrons at random. In B0→K∗0J/ψ(→e+e−) decays, one bremsstrahlung cluster is added to either electron of the pair in about half of the cases; the remaining half is equally split between cases when no bremsstrahlung cluster is found, or two or more clusters are added. These fractions are reproduced well by the simulation and depend only weakly on q2. The bremsstrahlung recovery procedure is limited in three ways: the energy threshold of the clusters that are added; the calorimeter acceptance and resolution; and the presence of energy deposits wrongly interpreted as bremsstrahlung clusters. These limitations degrade the resolution of the reconstructed invariant masses of both the dielectron pair and the Bcandidate. Since the occupancy of the calorimeters is significantly higher than that of the muon stations, the constraints on the trigger rate require that higher thresholds are imposed on the electron ETthan on the muon pT. In the central-q2region the higher threshold causes a loss of about half of the electron signal. The efficiency decreases slightly at lower q2 values. To partially mitigate this effect, decays with electrons in the final state can also be selected through the hadron hardware trigger, using clusters associated with the K∗0decay – 5 – JHEP08(2017)055 products, or by any hardware trigger from particles in the event that are not associated with the signal candidate. In decays with electrons, since the mass resolution of the reconstructed Bcandidate is worse than in final states with muons, the background contamination in the signal region is larger. The level of combinatorial background, arising from the accidental association of particles produced by different band c-hadron decays, is also higher in such channels, due to a larger number of electron candidates. As a result, the discriminating power of the fits to extract the signal yields is reduced (see section 7). Differences due to bremsstrahlung and the trigger response lead to a reconstruction efficiency for the B0→K∗0J/ψ(→e+e−) decays that is about five times smaller than for the B0→K∗0J/ψ(→µ+µ−) decays. 4 Corrections to the simulation In order to optimise the selection criteria and accurately evaluate the efficiencies, a set of corrections is determined from unbiased control samples selected from the data. The procedure is applied to the simulated samples of the nonresonant and resonant modes. The first correction accounts for differences between simulation and data in the particle identification (PID) performance [48]. The PID efficiencies are directly measured using a tag-and-probe method on high-purity data samples of pions and kaons from D∗+→D0(→K−π+)π+decays. Similarly, the electron and muon identification efficiencies are obtained from B+→K+J/ψ (→`+`−) decays. Corrections are determined as a function of the track momentum and pseudorapidity. The second step of the procedure adjusts the simulation for the charged-track multiplicity in the event, which is not described well in simulation. A small correction for the B0kinematics is also applied. Resonant B0→K∗0J/ψ(→µ+µ−) decays are used since the muon triggers are observed to be well modelled in simulation. The third step corrects the simulation of the trigger response for both the hardware and software levels using a tag-and-probe technique. Whenever possible, B0→K∗0J/ψ (→µ+µ−) decays are used as a control sample in place of B0→K∗0J/ψ (→e+e−) decays in order to take advantage of the larger sample size. In such cases, the two decays are compared and found to give consistent results. The tag sample is defined by events where the hardware trigger is fired by activity in the event not associated with any of the signal decay particles. Alternatively, when probing the leptonic (hadronic) hardware triggers, the tag is required to have triggered the hadronic (leptonic) hardware trigger. The corrections for the leptonic hardware triggers are parameterised as a function of the cluster ETor track pT. The hadron hardware trigger efficiency is known to be sensitive to tracks overlapping in the HCAL, however, a good description can be obtained when the efficiency is measured as a function of the pTof the K+π−pair instead of the kaon or the pion independently. Corrections are determined separately in the different calorimeter regions [37], in order to take into account potential differences due to different occupancies. When the hardware trigger is fired by activity in the event not associated with any of the signal decay particles, the correction is determined as a function of the B0 pTand the charged-track multiplicity in the event in order to take into account correlations – 6 – JHEP08(2017)055 in the production between the two bhadrons in the event. For the software trigger, the corrections are determined as a function of the minimum pTof the B0decay products. Finally, residual differences between data and simulation in the reconstruction performance are accounted for using B0→K∗0J/ψ (→`+`−) candidates to which the full selection is applied, as well as additional requirements to further reduce the background contamination. The corrections are determined by matching the distribution of the B0kinematics and vertex fit quality in simulation to the data, separately for muon and electron samples. The correction factors are determined sequentially as histograms, with the previous corrections applied before deriving the subsequent one. To avoid biases in the procedure due to common candidates being used for both the determination of the corrections and the measurement, a k-folding [49] approach with k= 10 is adopted. To dilute the dependence on the choice of the binning schemes, all corrections are linearly interpolated between adjacent bins. After all the corrections are applied to the simulation, a very good agreement with the data is obtained. 5 Selection of signal candidates AB0candidate is formed from a pair of well-reconstructed oppositely charged particles identified as either muons or electrons, combined with two well-reconstructed oppositely charged particles, one identified as a kaon and the other as a pion. The K+π−invariant mass is required to be within 100 MeV/c2of the known K∗0mass. The kaon and pion must have pTexceeding 250 MeV/c, while for the muons (electrons) pT>800 (500) MeV/c is required. Only dilepton pairs with a good-quality vertex are used to form signal candidates. The K∗0meson and `+`−pair are required to originate from a common vertex in order to form a B0candidate. When more than one PV is reconstructed, the one with the smallest χ2 IP is selected, where χ2 IP is the difference in χ2of a given PV reconstructed with and without the considered B0candidate. With respect to this selected PV, the impact parameter of the B0candidate is required to be small, its decay vertex significantly displaced, and the momentum direction of the B0is required to be consistent with its direction of flight. This direction is given by the vector between the PV and decay vertex. The distribution of q2as a function of the four-body invariant mass for the B0candidates is shown in figure 2for both muon and electron final states. The requirements on the neuralnetwork classifier and mcorr (see section 5) are not applied. In each plot, the contributions due to the charmonium resonances are clearly visible at the J/ψ and ψ(2S) masses. For electrons, these distributions visibly extend above the nominal mass values due to the calorimeter resolution affecting the bremsstrahlung recovery procedure (see section 3). The empty region in the top left corresponds to the kinematic limit of the B0→K∗0`+`−decay, while the empty region in the top right corresponds to the requirement that rejects the B+→K+`+`−background (see section 6). The B0mass resolution and the contributions of signal and backgrounds depend on the way in which the event was triggered. The data sample of decay modes involving an e+e−pair is therefore divided into three mutually exclusive categories, which in order of precedence are: candidates for which one of the electrons from the B0decay satisfies the – 7 – JHEP08(2017)055 ] 2 c) [MeV/ − µ + µ − π + K(m 4500 5000 5500 6000 ] 4 c/ 2 [GeV 2 q 0 2 4 6 8 10 12 14 16 18 20 1 10 2 10 3 10 4 10 LHCb ] 2 c) [MeV/ − e + e − π + K(m 4500 5000 5500 6000 ] 4 c/ 2 [GeV 2 q 0 2 4 6 8 10 12 14 16 18 20 1 10 2 10 LHCb Figure 2. Number of candidates for B0→K∗0`+`−final states with (left) muons and (right) electrons as a function of the dilepton invariant mass squared, q2, and the four-body invariant mass of the B0. hardware electron trigger (L0E), candidates for which one of the hadrons from the K∗0 decay meets the hardware hadron trigger (L0H) requirements, and candidates triggered by activity in the event not associated with any of the signal decay particles (L0I). For B0→K∗0µ+µ−candidates, at least one of the two leptons must satisfy the requirements of the hardware muon trigger. For the B0→K∗0J/ψ (→µ+µ−) decay mode, a dimuon mass interval within 100 MeV/c2of the known J/ψ mass is selected to identify candidates. It is not possible to apply a tight q2requirement to identify the B0→K∗0J/ψ (→e+e−) mode as, despite the bremsstrahlung recovery, the e+e−invariant mass distribution has a long radiative tail towards low values. This tail can be seen in figure 2. The q2interval used to select B0→K∗0J/ψ (→e+e−) candidates is between 6.0 and 11.0 GeV2 /c4, with the lower limit corresponding to the upper boundary of the central-q2bin. The separation of the signal from the combinatorial background is based on neuralnetwork classifiers [50]. The same classifier is used for the resonant and nonresonant modes, but muon and electron channels are treated separately. The classifiers are trained using simulated B0→K∗0`+`−decays, which have been corrected for known differences between data and simulation (see section 4), to represent the signal. Data candidates with K+π−`+`−invariant masses larger than 5400 MeV/c2and 5600 MeV/c2are used to represent background samples for the muon and electron channel, respectively. To best exploit the size of the available data sample for the training procedure, a k-folding technique [49] is adopted with k= 10. The variables used as input to the classifiers are: the transverse momentum, the quality of the vertex fit, the χ2 IP, the χ2 VD (the χ2on the measured distance between the PV and the decay vertex), and the angle between the direction of flight and the momentum of the B0candidate, the K+π−and the dilepton pairs; the minimum and maximum of the kaon and pion pT, and of their χ2 IP; the minimum and maximum of the lepton pTvalues, and of their χ2 IP; and finally, the most discriminating variable, the quality of the kinematic fit to the decay chain (this fit is performed with a constraint on the vertex that requires the B0candidate to originate from the PV). In each fold, only variables that significantly improve the discriminating power of the classifier are kept. – 8 – JHEP08(2017)055 ε`+`−/εJ/ψ (`+`−) low-q2central-q2 µ+µ−0.679 ±0.009 0.584 ±0.006 e+e−(L0E) 0.539 ±0.013 0.522 ±0.010 e+e−(L0H) 2.252 ±0.098 1.627 ±0.066 e+e−(L0I) 0.789 ±0.029 0.595 ±0.020 Table 3. Efficiency ratios between the nonresonant and resonant modes, ε`+`−/εJ/ψ (`+`−), for the muon and electron (in the three trigger categories) channels. The uncertainties are statistical only. which is expected to be equal to unity. This quantity represents an extremely stringent test, as it does not benefit from the large cancellation of the experimental systematic effects provided by the double ratio. The rJ/ψ ratio is measured to be 1.043±0.006±0.045, where the first uncertainty is statistical and the second systematic. The same sources of systematic uncertainties as in the RK∗0measurement are considered (see section 10). The result, which is in good agreement with unity, is observed to be compatible with being independent of the decay kinematics, such as pTand ηof the B0candidate and final-state particles, and the charged-track multiplicity in the event. The extent of the cancellation of residual systematics in RK∗0is verified by measuring a double ratio, Rψ(2S), where B0→K∗0ψ(2S)(→`+`−) decays are used in place of B0→K∗0`+`−. The Rψ(2S)ratio, measured with a statistical precision of about 2%, is found to be compatible with unity within one standard deviation. The branching fraction of the decay B0→K∗0µ+µ−is measured and found to be in good agreement with ref. [25]. Furthermore, the branching fraction of the B0→K∗0γ decay, where decays with a photon conversion are used, is determined with a statistical precision of about 7% and is observed to be in agreement with the expectation within two standard deviations. The B0→K∗0γ(→e+e−) selection and determination of the signal yield closely follows that of the B0→K∗0e+e−decay. If no correction is made to the simulation, the ratio of the efficiencies changes by less than 5%. The relative population of the three bremsstrahlung categories is compared between data and simulation using both B0→K∗0J/ψ (→e+e−) and B0→K∗0γ(→e+e−) candidates to test possible q2dependence of the modelling. Good agreement is observed, as shown in figure 5. The sPlot technique [57], where m(K+π−`+`−) is used as the discriminating variable, is adopted to subtract statistically the background from the B0→K∗0`+`−selected data, and test the agreement between muons and electrons, data and simulation, using several control quantities (see figure 8): the q2distributions show good agreement in both q2 regions; a clear K∗0peak is visible in the K+π−invariant mass distributions, and the muon and electron channels show good agreement; while the distribution of the opening angle between the two leptons in the central-q2region are very similar between the muon – 15 – JHEP08(2017)055 ∆RK∗0/RK∗0[%] low-q2central-q2 Trigger category L0E L0H L0I L0E L0H L0I Corrections to simulation 2.5 4.8 3.9 2.2 4.2 3.4 Trigger 0.1 1.2 0.1 0.2 0.8 0.2 PID 0.2 0.4 0.3 0.2 1.0 0.5 Kinematic selection 2.1 2.1 2.1 2.1 2.1 2.1 Residual background — — — 5.0 5.0 5.0 Mass fits 1.4 2.1 2.5 2.0 0.9 1.0 Bin migration 1.0 1.0 1.0 1.6 1.6 1.6 rJ/ψ ratio 1.6 1.4 1.7 0.7 2.1 0.7 Total 4.0 6.1 5.5 6.4 7.5 6.7 Table 4. Systematic uncertainties on the RK∗0ratio for the three trigger categories separately (in percent). The total uncertainty is the sum in quadrature of all the contributions. and electron channels, this is not the case at low-q2due to the difference in lepton masses; the distribution of the distance between the K+π−and `+`−vertices shows that the pairs of hadrons and leptons consistently originate from the same decay vertex. 10 Systematic uncertainties Since RK∗0is measured as a double ratio, many potential sources of systematic uncertainty cancel. The remaining systematics and their effects on RK∗0are summarised in table 4 and are described below. Corrections to simulation: the uncertainty induced by the limited size of the simulated sample used to compute the efficiencies is considered; an additional systematic uncertainty is determined using binned corrections instead of interpolated ones; finally, since the data samples used to determine the corrections have a limited size, particularly for the electron hardware trigger, a systematic uncertainty is assessed with a bootstrapping technique [58]. Trigger efficiency: for the hardware triggers, the corrections to the simulation are determined using different control samples and the change in the result is assigned as a systematic uncertainty; for the software trigger, the corrections to the simulation do not show dependences on the kinematic of the decays, and therefore only the statistical uncertainty on the overall correction is considered as a systematic uncertainty. – 16 – JHEP08(2017)055 ] 4 c/ 2 [GeV 2 q 0.5 1 Fraction of candidates [%] 0 0.1 0.2 0.3 0.4 0.5 LHCb − µ + µ 0* K→ 0 BData Simulation − e + e 0* K→ 0 BData Simulation ] 4 c/ 2 <1.1 [GeV 2 q0.045< ] 4 c/ 2 [GeV 2 q 2 3 4 5 6 Fraction of candidates [%] 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 LHCb − µ + µ 0* K→ 0 BData Simulation − e + e 0* K→ 0 BData Simulation ] 4 c/ 2 <6.0 [GeV 2 q1.1< ] 2 c) [MeV/ − π + K(m 800 850 900 950 Fraction of candidates [%] 0 0.1 0.2 0.3 0.4 0.5 LHCb − µ + µ 0* K→ 0 BData Simulation − e + e 0* K→ 0 BData Simulation ] 4 c/ 2 <1.1 [GeV 2 q0.045< ] 2 c) [MeV/ − π + K(m 800 850 900 950 Fraction of candidates [%] 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 LHCb − µ + µ 0* K→ 0 BData Simulation − e + e 0* K→ 0 BData Simulation ] 4 c/ 2 <6.0 [GeV 2 q1.1< [mrad] lepton θ 0 0.02 0.04 0.06 0.08 0.1 Fraction of candidates [%] 0 0.1 0.2 0.3 0.4 0.5 0.6 LHCb − µ + µ 0* K→ 0 BData Simulation − e + e 0* K→ 0 BData Simulation ] 4 c/ 2 <1.1 [GeV 2 q0.045< [mrad] lepton θ 0 0.05 0.1 0.15 0.2 Fraction of candidates [%] 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 LHCb − µ + µ 0* K→ 0 BData Simulation − e + e 0* K→ 0 BData Simulation ] 4 c/ 2 <6.0 [GeV 2 q1.1< [mm] vertex z ∆ 10−5−0 5 10 Fraction of candidates [%] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 LHCb − µ + µ 0* K→ 0 BData Simulation − e + e 0* K→ 0 BData Simulation ] 4 c/ 2 <1.1 [GeV 2 q0.045< [mm] vertex z ∆ 10−5−0 5 10 Fraction of candidates [%] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 LHCb − µ + µ 0* K→ 0 BData Simulation − e + e 0* K→ 0 BData Simulation ] 4 c/ 2 <6.0 [GeV 2 q1.1< Figure 8. (hatched) Background-subtracted distributions for (darker colour) B0→K∗0µ+µ−and (lighter colour) B0→K∗0e+e−candidates, compared to (full line) simulation. From top to bottom: q2,K+π−invariant mass, m(K+π−), opening angle between the two leptons, θlepton, and projection along the beam axis of the distance between the K+π−and `+`−vertices, ∆zvertex. The distributions are normalised to unity. The hatched areas correspond to the statistical uncertainties only. The data are not efficiency corrected. – 17 – JHEP08(2017)055 Particle identification: the particle identification response is calibrated using data; a systematic uncertainty due to the procedure and kinematic differences between these control samples and the signal modes is included; the effects due to the identification of leptons and hadrons are considered; however, discrepancies in the description of the latter are small and further cancel in the double ratio. Kinematic selection: a systematic uncertainty due to the choice of the mass fit range and to the two-dimensional requirement on χ2 VD and mcorr is determined by comparing the efficiencies in simulation and background-subtracted samples of B0→K∗0J/ψ (→µ+µ−) or B0→K∗0J/ψ (→e+e−) decays. Residual background: background due to B0→K∗0J/ψ (→e+e−) decays where one of the hadrons is misidentified as an electron and vice versa is studied; using simulation that is tuned to data (see section 4) this contribution is estimated to be small; however, a few candidates with one electron of the dilepton pair having a low probability to be genuine are observed in background subtracted data; a systematic uncertainty is assigned based on the distribution of the PID information of these candidates. Mass fit: the systematic uncertainty due to the parameterisation of the signal invariant mass distributions is found to be negligible for the muon channel; for the electron channel, the signal PDF is changed from the sum of a CB and a Gaussian function to the sum of two CB functions, where the mean parameter is shared and, additionally, the mass shift and the width scale factors are constrained using the B0→K∗0γ(→e+e−) decay mode instead of B0→K∗0J/ψ(→e+e−); the relative fractions of the three bremsstrahlung categories are measured in data using B0→K∗0J/ψ (→e+e−) and the observed differences with respect to simulation are used in the mass fit (see figure 5); for the backgrounds, a component that describes candidates where the hadron identities are swapped is added both to the muon and electron B0→K∗0J/ψ (→`+`−) modes, and constrained to the expected values observed in simulation; the kernel of the nonparametric models is also varied, as well as the mixture of the K+ 1(1270) and K∗+ 2(1430) components that is constrained using data [59]; the contributions to the systematic uncertainty from these sources are evaluated using pseudoexperiments that are generated with modified parameters and fitted with the PDFs used to fit the data. Bin migration: for the electron channel, the degraded q2resolution due to bremsstrahlung emission causes a nonnegligible fraction of signal candidates to migrate in and out of the given q2bin; the effect is included in the efficiency determination, but introduces a small dependence on the shape of the differential branching fraction that no longer perfectly cancels in the ratio to the muon channel; pseudoexperiments are generated, where the parameters modelling the dΓ(B0→K∗0e+e−)/dq2distribution are varied within their uncertainties [35]; the maximum spread of the variation in RK∗0is taken as a systematic uncertainty; furthermore, the q2resolution is smeared for differences between data and simulation that are observed in the resonant mode. – 18 – JHEP08(2017)055 rJ/ψ ratio: the ratio of the efficiency-corrected yield of the resonant modes (see section 9) is expected to be unity to a very high precision; deviations from unity are therefore considered to be a sign of residual imperfections in the evaluation of the efficiencies; the rJ/ψ ratio is studied as a function of various event and kinematic properties of the decay products, and the observed residual deviations from unity are used to assign a systematic uncertainty on RK∗0. For the RK∗0measurement, all the uncertainties are treated as uncorrelated among the trigger categories, except for those related to particle identification, to the kinematic selection criteria, to the residual background, to the fit to the invariant mass and to bin migration. 11 Results The determination of RK∗0exploits the log-likelihoods resulting from the fits to the invariant mass distributions of the nonresonant and resonant channels in each trigger category and q2region. Each log-likelihood is used to construct the PDF of the true number of decays, which is used as a prior to obtain the PDF of RK∗0. The true number of decays is assumed to have a uniform prior. The three electron trigger categories are combined by summing the corresponding log-likelihoods. Uncorrelated systematic uncertainties are accounted for by convolving the yield PDFs with a Gaussian distribution of appropriate width. Correlated systematic uncertainties are treated by convolving the RK∗0PDF with a Gaussian distribution. The one, two and three standard deviation intervals are determined as the ranges that include 68.3%, 95.4% and 99.7% of the PDF. In each q2region, the measured values of RK∗0are found to be in good agreement among the three electron trigger categories (see figure 9). The results are given in table 5and presented in figure 10, where they are compared both to the SM predictions (see table 1) and to previous measurements from the Bfactories [4,5]. The combined RK∗0PDF is used to determine the compatibility with the SM expectations. The p-value, calculated by integrating the PDF above the expected value, is translated into a number of standard deviations. The compatibility with the SM expectations [26–36] is determined to be 2.1–2.3 and 2.4–2.5 standard deviations, for the low-q2 and the central-q2regions, respectively, depending on the theory prediction used. 12 Conclusions This paper reports a test of lepton universality performed by measuring the ratio of the branching fractions of the decays B0→K∗0µ+µ−and B0→K∗0e+e−. The K∗0meson is reconstructed in the final state K+π−, which is required to have an invariant mass within 100 MeV/c2of the known K∗(892)0mass. Data corresponding to an integrated luminosity of 3 fb−1of pp collisions, recorded by the LHCb experiment during 2011 and 2012, are used. – 19 – JHEP08(2017)055 *0 K R 0 0.5 1 1.5 2 ) best L ln − L (ln − 0 1 2 3 4 5 6 7 8 LHCb L0E L0H L0I Combined Comb. (stat) ] 4 c/ 2 <1.1 [GeV 2 q0.045< *0 K R 0 0.5 1 1.5 2 ) best L ln − L (ln − 0 1 2 3 4 5 6 7 8 LHCb L0E L0H L0I Combined Comb. (stat) ] 4 c/ 2 <6.0 [GeV 2 q1.1< Figure 9. Distributions of the RK∗0delta log-likelihood for the three trigger categories separately and combined. low-q2central-q2 RK∗00.66 + 0.11 −0.07 ±0.03 0.69 + 0.11 −0.07 ±0.05 95.4% CL [0.52,0.89] [0.53,0.94] 99.7% CL [0.45,1.04] [0.46,1.10] Table 5. Measured RK∗0ratios in the two q2regions. The first uncertainties are statistical and the second are systematic. About 50% of the systematic uncertainty is correlated between the two q2bins. The 95.4% and 99.7% confidence level (CL) intervals include both the statistical and systematic uncertainties. Figure 10. (Left) Comparison of the LHCb RK∗0measurements with the SM theoretical predictions: BIP [26] CDHMV [27–29], EOS [30–32], flav.io [33–35] and JC [36]. The predictions are displaced horizontally for presentation. (right) Comparison of the LHCb RK∗0measurements with previous experimental results from the Bfactories [4,5]. In the case of the Bfactories the specific vetoes for charmonium resonances are not represented. – 20 – JHEP08(2017)055 The RK∗0ratio is measured in two regions of the dilepton invariant mass squared to be RK∗0=   0.66 + 0.11 −0.07 (stat) ±0.03 (syst) for 0.045 < q2<1.1 GeV2 /c4, 0.69 + 0.11 −0.07 (stat) ±0.05 (syst) for 1.1< q2<6.0 GeV2 /c4. The corresponding 95.4% confidence level intervals are [0.52,0.89] and [0.53,0.94]. The results, which represent the most precise measurements of RK∗0to date, are compatible with the SM expectations [26–36] at 2.1–2.3 standard deviations for the low-q2region and 2.4–2.5 standard deviations for the central-q2region, depending on the theoretical prediction used. Model-independent fits to the ensemble of FCNC data that allow for NP contributions [27–36] lead to predictions for RK∗0in the central-q2region that are similar to the value observed; smaller deviations are expected at low-q2. The larger data set currently being accumulated by the LHCb collaboration will allow for more precise tests of these predictions. Acknowledgments We would like to thank F. Le Diberder for many interesting and helpful discussions on statistics. We express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at the LHCb institutes. We acknowledge support from CERN and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy); NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES and FASO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (U.S.A.). We acknowledge the computing resources that are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN (Italy), SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID (Poland) and OSC (U.S.A.). We are indebted to the communities behind the multiple open source software packages on which we depend. Individual groups or members have received support from AvH Foundation (Germany), EPLANET, Marie Sk lodowska-Curie Actions and ERC (European Union), Conseil G´en´eral de Haute-Savoie, Labex ENIGMASS and OCEVU, R´egion Auvergne (France), RFBR and Yandex LLC (Russia), GVA, XuntaGal and GENCAT (Spain), Herchel Smith Fund, The Royal Society, Royal Commission for the Exhibition of 1851 and the Leverhulme Trust (United Kingdom). Open Access. 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