Angular analysis of the decay B0 ---> K*0 (mű)+(mű)- from pp collisions at (square root)s = 8 TeV

Physics Letters B 753 (2016) 424–448 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Angular analysis of the decay B0→K∗0μ+μ−from pp collisions at √s=8TeV .CMS Collaboration CERN, Switzerland a r t i c l e i n f o a b s t r a c t Article history: Received 29 July 2015 Received in revised form 30 November 2015 Accepted 7 December 2015 Available online 11 December 2015 Editor: M. Doser Keywords: CMS Physics B0 decays The angular distributions and the differential branching fraction of the decay B0→K∗(892)0μ+μ− are studied using data corresponding to an integrated luminosity of 20.5 fb−1collected with the CMS detector at the LHC in pp collisions at √s=8TeV. From 1430 signal decays, the forward–backward asymmetry of the muons, the K∗(892)0longitudinal polarization fraction, and the differential branching fraction are determined as a function of the dimuon invariant mass squared. The measurements are among the most precise to date and are in good agreement with standard model predictions. ©2015 CERN for the benefit of the CMS Collaboration. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 1. Introduction Phenomena beyond the standard model (SM) of particle physics can manifest themselves directly, via the production of new particles, or indirectly, by affecting the production and decay of SM particles. Analyses of flavor-changing neutral current (FCNC) decays are particularly sensitive to the effect of new physics, since such decays are highly suppressed in the SM. The FCNC decay, B0→K∗0μ+μ−(K∗0indicates the K∗(892)0, and charge-conjugate states are implied for all particles unless stated otherwise), provides many opportunities to search for new phenomena. In addition to the branching fraction, other properties of the decay can be measured, including the forward–backward asymmetry of the muons, AFB, and the longitudinal polarization fraction of the K∗0, FL. To better understand this decay, these quantities can be measured as a function of the dimuon invariant mass squared (q2). New physics may modify any of these quantities [1–17] relative to their SM values [1,18–24]. While previous measurements by BaBar, Belle, CDF, LHCb, and CMS are consistent with the SM [25–29], they are still statistically limited, and more precise measurements offer the possibility to uncover physics beyond the SM. In this Letter, we present measurements of AFB, FL, and the differential branching fraction dB/dq2from B0→K∗0μ+μ−decays, using data collected from pp collisions at the CERN LHC by the CMS experiment at a center-of-mass energy of 8TeV. The data correspond to an integrated luminosity of 20.5 ±0.5fb −1[30]. The E-mail address: cms-publication-committee-c[email protected]. K∗0is reconstructed through its decay to K+π−, and the B0is reconstructed by fitting the two identified muon tracks and the two hadron tracks to a common vertex. The values of AFB and FLare measured by fitting the distribution of events as a function of two angular variables: the angle between the positively charged muon and the B0in the dimuon rest frame, and the angle between the K+and the B0in the K∗0rest frame. All measurements are performed in q2bins from 1 to 19 GeV2. The q2bins 8.68 <q2<10.09 GeV2and 12.90 <q2<14.18 GeV2, corresponding to the B0→J/ψK∗0and B0→ψK∗0decays (ψrefers to the ψ(2S)), respectively, are used to validate the analysis. The former is also used to normalize the differential branching fraction. 2. CMS detector A detailed description of the CMS detector, together with a definition of the coordinate system used and the standard kinematic variables, can be found in Ref. [31]. The main detector components used in this analysis are the silicon tracker and the muon detection systems. The silicon tracker, located in the 3.8 T field of a superconducting solenoid, consists of three pixel layers and ten strip layers (four of which have a stereo view) in the barrel region accompanied by similar endcap pixel and strip detectors on each side that extend coverage out to |η| <2.5. For tracks with transverse momenta 1 <pT<10 GeV and |η| <1.4, the resolutions are typically 1.5% in pTand 25–90 (45–150) μm in the transverse (longitudinal) impact parameter [32]. Muons are measured in the range |η| <2.4, with detection planes made using three technologies: drift tubes, cathode strip chambers, and resistive plate http://dx.doi.org/10.1016/j.physletb.2015.12.020 0370-2693/©2015 CERN for the benefit of the CMS Collaboration. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. CMS Collaboration / Physics Letters B 753 (2016) 424–448 425 chambers [33]. In addition to the tracker and muon detectors, CMS is equipped with electromagnetic and hadronic calorimeters that cover |η| <5. Events are selected using a two-level trigger system. The first level has specialized hardware processors that use information from the calorimeters and muon systems to select the most interesting events. A high-level trigger processor farm further decreases the event rate from around 90 kHz to around 400 Hz, before data storage. 3. Reconstruction, event selection, and efficiency The criteria used to select the candidate events during data taking (trigger) and after full event reconstruction take advantage of the fact that B0mesons have relatively long lifetimes and therefore decay on average about 1mm from their production point. The trigger only uses muons to select events, while the offline selection includes the full reconstruction of all decay products. All events used in this analysis were recorded with the same trigger, requiring two identified muons of opposite charge to form a vertex that is displaced from the pp collision region (beamspot). The beamspot position (most probable collision point) and size (the extent of the luminous region covering 68% of the collisions in each dimension) were continuously measured through Gaussian fits to reconstructed vertices as part of the online data quality monitoring. The trigger required each muon to have pT>3.5GeV, |η| <2.2, and to pass within 2cm of the beam axis. The dimuon system was required to have pT>6.9GeV, a vertex fit χ2probability larger than 10%, and a separation of the vertex relative to the beamspot in the transverse plane of at least 3σ, where σincludes the calculated uncertainty in the vertex position and the measured size of the beamspot. In addition, the cosine of the angle, in the transverse plane, between the dimuon momentum vector and the vector from the beamspot to the dimuon vertex was required to be greater than 0.9. The offline reconstruction requires two muons of opposite charge and two oppositely charged hadrons. The muons are required to match those that triggered the event readout, and also to pass general muon identification requirements. These include a track matched to at least one muon segment (collection of hits in a muon chamber consistent with the passage of a charged particle), a track fit χ2per degree of freedom less than 1.8, hits in at least six tracker layers with at least two from the pixel detector, and a transverse (longitudinal) impact parameter with respect to the beamspot less than 3cm (30 cm). The reconstructed dimuon system must also satisfy the same requirements that were applied in the trigger. The hadron tracks are required to fail the muon identification criteria, have pT>0.8GeV, and have an extrapolated distance of closest approach to the beamspot in the transverse plane greater than twice the sum in quadrature of the distance uncertainty and the beamspot transverse size. The two hadrons must have an invariant mass within 90 MeV of the accepted K∗0mass [34] for either the K+π−or K−π+hypothesis. To remove contamination from φ(1020) →K+K−decays, the invariant mass of the hadron pair must be greater than 1.035 GeV when the charged kaon mass is assigned to both hadrons. The B0candidates are obtained by fitting the four charged tracks to a common vertex, and applying a vertex constraint to improve the resolution of the track parameters. The B0candidates must have pT>8GeV, |η| <2.2, vertex fit χ2probability larger than 10%, vertex transverse separation from the beamspot greater than 12 times the sum in quadrature of the separation uncertainty and the beamspot transverse size, and cosαxy >0.9994, where αxy is the angle, in the transverse plane, between the B0momentum vector and the line-of-flight between the beamspot and the B0vertex. The invariant mass mof the B0 candidate must also be within 280 MeV of the accepted B0mass mB0[34] for either the K−π+μ+μ−or K+π−μ+μ−hypothesis. The selection criteria are optimized using simulated signal samples (described below) and background from data using sidebands of the B0mass. After applying the selection criteria, events in which at least one candidate is found contain on average 1.05 candidates. A single candidate is chosen from each event based on the best B0 vertex fit χ2. From the selected events, the dimuon invariant mass qand its calculated uncertainty σqare used to distinguish the signal from the control samples. The control samples B0→J/ψK∗0and B0→ψK∗0are defined by |q −mJ/ψ | <3σqand |q −mψ| <3σq, respectively, where mJ/ψ and mψare the accepted masses [34]. The average value for σqis about 26 MeV. The signal sample is composed of the events that are not assigned to the J/ψ and ψ samples. The signal sample still contains contributions from the control samples, mainly due to unreconstructed soft photons in the charmonium decay. These events will have a low qvalue and fall outside the selection described above. These events will also have a low mvalue and therefore they can be selectively removed using a combined selection on qand m. For q <mJ/ψ (q >mJ/ψ ), we require |(m −mB0) −(q −mJ/ψ )| >160 (60)MeV. For q <mψ (q >mψ), we require |(m −mB0) −(q −mψ)| >60 (30)MeV. The requirements are set such that less than 10% of the background events originate from the control channels. The four-track vertex candidate is identified as a B0or B0depending on whether the K+π−or K−π+invariant mass is closest to the accepted K∗0mass. The fraction of candidates assigned to the incorrect state is estimated from simulations to be 12–14%, depending on q2. The global efficiency, , is the product of the acceptance and the combined trigger, reconstruction, and selection efficiency, both of which are obtained from Monte Carlo (MC) simulations. The pp collisions are simulated using pythia [35] version 6.424, the unstable particles are decayed by evtgen [36] version 9.1 (using the default matrix element for the signal), and the particles are propagated through a detailed model of the detector with Geant4[37]. The reconstruction and selection of the generated events proceed as for data. Three simulated samples were created in which the B0 was forced to decay to K∗0(K+π−)μ+μ−, J/ψ(μ+μ−)K∗0(K+π−), or ψ(μ+μ−)K∗0(K+π−). The samples were constructed to ensure that the number and spatial distribution of pp collision vertices in each event match the distributions found in data. The acceptance is obtained from generated events, before the particle propagation with Geant4, and is calculated as the fraction of events passing the single-muon requirement of pT(μ) >3.3 GeV and |η(μ)| <2.3 relative to all events with pT(B0) >8 GeV and |η(B0)| <2.2. As the acceptance requirements are placed on the generated quantities, they are less restrictive than the final selection requirements, which are based on the reconstructed quantities, to allow for the effect of finite resolution. Only events passing the acceptance criteria are processed through the geant simulation, the trigger simulation, and the reconstruction software. The combined trigger, reconstruction, and selection efficiency is the ratio of the number of events that pass the trigger and selection requirements and have a reconstructed B0compatible with the generated B0in the event, relative to the number of events that pass the acceptance criteria. The compatibility of generated and reconstructed particles is enforced by requiring the reconstructed K+, π−, μ+, and μ−to have (η)2+(ϕ)2less than 0.3 (0.004) for hadrons (muons), where ηand ϕare the differences in ηand ϕbetween the reconstructed and generated particles. Requiring all four particles in the B0decay to be matched results in an efficiency of 99.6% 426 CMS Collaboration / Physics Letters B 753 (2016) 424–448 Fig. 1. Sketch showing the definition of the angular observables θl(left), θK(middle), and φ(right) for the decay B0→K∗0(K+π−)μ+μ−. (0.4% of the events have a correctly reconstructed B0that is not matched to a generated B0) and a purity of 99.5% (0.5% of the matched candidates are not a correctly reconstructed B0). Efficiencies are determined for both correctly tagged (the K and πhave the correct charge) and mistagged (the K and πcharges are reversed) candidates. 4. Analysis method This analysis measures AFB, FL, and dB/dq2of the decay B0→ K∗0μ+μ−as a function of q2. Fig. 1 shows the angular observables needed to define the decay: θKis the angle between the kaon momentum and the direction opposite to the B0B0in the K∗0 K∗0rest frame, θlis the angle between the positive (negative) muon momentum and the direction opposite to the B0B0in the dimuon rest frame, and φis the angle between the plane containing the two muons and the plane containing the kaon and pion. As the extracted angular parameters AFB and FLdo not depend on φand the product of the acceptance and efficiency is nearly constant as a function of φ, the angle φis integrated out. Although the K+π−invariant mass must be consistent with that of a K∗0, there can be a contribution from spinless (S-wave) K+π−combinations [24,38–40]. This is parametrized with two terms: FS, which is related to the S-wave fraction, and AS, which is the interference amplitude between the S-wave and P-wave decays. Including this component, the angular distribution of B0→K∗0μ+μ−can be written as [24]: 1  d3 dcosθKdcosθldq2 =9 16 2 3FS+AScosθK1−cos2θl +(1−FS)2FLcos2θK1−cos2θl +1 2(1−FL)1−cos2θK1+cos2θl +4 3AFB 1−cos2θKcosθl.(1) For each q2bin, the observables of interest are extracted from an unbinned extended maximum-likelihood fit to three variables: the K+π−μ+μ−invariant mass mand the two angular variables θKand θl. For each q2bin, the unnormalized probability density function (PDF) has the following expression: PDF(m,θ K,θ l)=YC SSC(m)Sa(θK,θ l)C(θK,θ l) +fM 1−fMSM(m)Sa(−θK,−θl)M(θK,θ l) +YBBm(m)BθK(θK)Bθl(θl), (2) where the contributions correspond to correctly tagged signal events, mistagged signal events, and background events. The parameters YC Sand YBare the yields of correctly tagged signal events and background events, respectively, and are free parameters in the fit. The parameter fMis the fraction of signal events that are mistagged and is determined from MC simulation. The signal mass probability functions SC(m)and SM(m)are each the sum of two Gaussian functions and describe the mass distribution for correctly tagged and mistagged signal events, respectively. In the fit, there is one free parameter for the mass value in both signal functions, while the other parameters (four Gaussian σparameters and two fractions relating the contribution of each Gaussian) are obtained from MC simulation, which has been found to accurately reproduce the data. The function Sa(θK, θl)describes the signal in the two-dimensional (2D) space of the angular observables and corresponds to Eq. (1). The combination Bm(m) BθK(θK) Bθl(θl)is obtained from B0sideband data and describes the background in the space of (m, θK, θl), where the mass distribution is an exponential function and the angular distributions are polynomials ranging from second to fourth degree, depending on the q2bin and the angular variable. The functions C(θK, θl)and M(θK, θl)are the efficiencies in the 2D space of −1 ≤cos θK≤1, −1 ≤cos θl≤1for correctly tagged and mistagged signal events, respectively. The efficiency function for correctly tagged events is obtained from a fit to the 2D-binned efficiency from simulation and is constrained to be positive. There are 30 bins (5 in cosθKand 6 in cosθl), and the efficiency fit function is a polynomial of third degree in cosθKand fifth degree in cosθl(and all cross terms), for a total of 24 free parameters. This procedure does not work for the mistagged events because of the much smaller number of events (resulting in empty bins) and a more complicated efficiency. For mistagged events, the 2D efficiency is calculated in 5×5bins of cos θKand cos θl, and an interpolation is performed. This interpolation function is used to generate a new binned efficiency (in 120 ×120 bins), with all bin contents constrained to be nonnegative. The efficiency function uses this finely binned efficiency, with linear interpolation between bins. The efficiencies for both correctly tagged and mistagged events peak at cosθlnear 0 for q2<10 GeV2, becoming flat for larger values of q2. The efficiency for correctly tagged events tends to decrease with increasing cosθK, and for q2>14 GeV2a small decrease is seen for cosθKnear −1. The efficiency for mistagged events is maximal near cosθK=0, with an increase as cosθKapproaches +1 that becomes more pronounced as q2increases. The fit is performed in two steps. The initial fit uses the data from the sidebands of the B0mass to obtain the BθK(θK)and Bθl(θl)distributions (the signal component is absent from this fit). The sideband regions are 3σm<|m −mB0| <5.5σm, where σmis the average mass resolution (≈45 MeV), obtained from fitting the MC simulation signal to a sum of two Gaussians with a common mean. The distributions obtained in this step are then fixed for the second step, which is a fit to the data over the full mass range. The free parameters in this fit are AFB, FL, FS, AS, the parameters in CMS Collaboration / Physics Letters B 753 (2016) 424–448 427 Bm(m), the mass parameter in SC(m)and SM(m), and the yields YC Sand YB. In addition, the remaining parameters in SC(m)and SM(m)are free parameters with Gaussian constraints from previous fits to simulated signal events. The PDF in Eq. (2) is only guaranteed to be nonnegative for particular ranges of AFB, FL, AS, and FS. While the definition of the precise physical region is a more complicated expression, the approximate ranges of validity are: 0 <FL<1, |AFB| <3 4(1−FL), 0 <FS<min3(1−FL) 1+3FL,1, and |AS| <FS+3FL(1−FS). In addition, the interference term ASmust vanish if either of the two interfering components vanish. From Ref. [24], this constraint is implemented as |AS| <√12FS(1−FS)FLR, where Ris a ratio related to the S-wave and P-wave line shapes, estimated to be 0.89 near the K∗0mass. During the minuit [41] minimization, penalty terms are introduced to ensure that parameters remain in the physical region. When assessing the statistical uncertainties with Minos [41], the penalty terms are removed. However, a negative value for Eq. (2) results in the minimizing algorithm generating a large positive jump in the negative log-likelihood, tending to remove the unphysical region. The results of the fit in each signal q2 bin are AFB, FL, AS, FS, and the correctly tagged signal yield YC S. The differential branching fraction, dB/dq2, is measured relative to the normalization channel B0→J/ψK∗0using: dBB0→K∗0μ+μ− dq2 =YC S C+YC SfM (1−fM)MYC N C N+YC NfM N (1−fM N)M N−1 × BB0→J/ψK∗0 q2,(3) where YC Sand YC Nare the yields of the correctly tagged signal and normalization channels, respectively; C Sand C Nare the efficiencies for the correctly tagged signal and normalization channels, respectively; fMand fM Nare the mistag rates for the signal and normalization channels, respectively; M Sand M Nare the efficiencies for the mistagged signal and normalization channels, respectively; and BB0→J/ψ(μ+μ−)K∗0=0.132% ×5.96% is the accepted branching fraction for the normalization channel [34], corresponding to the q2bin q2=8.68–10.09 GeV2. The efficiencies are obtained by integrating the efficiency functions over the angular variables, weighted by the decay rate in Eq. (1), using the values obtained from the fit of Eq. (2) to the data. The fit formalism and results are validated through fits to pseudo-experimental samples, MC simulation samples, and control channels. Additional details, including the sizes of the systematic uncertainties assigned from these fits, are described in Section 5. 5. Systematic uncertainties Since the efficiency is computed with simulated events, it is essential that the MC simulation program correctly reproduces the data, and extensive checks have been performed to verify the accuracy of the simulation. The systematic uncertainties associated with the efficiencies, and other sources of systematic uncertainty are described below and summarized in Table 1. The correctness of the fit function and the procedure for measuring the variables of interest are verified in three ways. First, a high-statistics MC sample (approximately 400 times that of the data) is used to verify that the fitting procedure produces results consistent with the input values to the simulation. This MC sample includes the full simulation of signal and control channel events Table 1 Systematic uncertainty contributions for the measurements of FL, AFB, and the branching fraction for the decay B0→K∗0μ+μ−. The values for FLand AFB are absolute, while the values for the branching fraction are relative. The total uncertainty in each q2bin is obtained by adding each contribution in quadrature. For each item, the range indicates the variation of the uncertainty in the signal q2bins. Systematic uncertainty FL(10−3)AFB(10−3)dB/dq2(%) Simulation mismodeling 1–17 0–37 1.0–5.5 Fit bias 0–34 2–42 – MC statistical uncertainty 3–10 5–18 0.5–2.0 Efficiency 34 5 – Kπmistagging 1–4 0–7 0.1–4.1 Background distribution 20–36 12–31 0.0–1.2 Mass distribution 3 1 3.2 Feed-through background 0–27 0–5 0.0–4.0 Angular resolution 6–24 0–5 0.2–2.1 Normalization to B0→J/ψK∗0–– 4.6 Total systematic uncertainty 41–65 18–74 6.4–8.6 plus background events obtained from the PDF in Eq. (2). The discrepancy between the input and output values in this check is assigned as a simulation mismodeling systematic uncertainty. It was also verified that fitting a sample with only mistagged events gives the correct results. Second, 1000 pseudo-experiments, each with the same number of events as the data sample, are generated in each q2bin using the PDF in Eq. (2), with parameters obtained from the fit to the data. These are used to estimate the fit bias. Much of the observed bias is a consequence of the fitted parameters lying close to the boundaries of the physical region. In addition, the distributions of results are used to check the returned statistical uncertainty from the fit and are found to be consistent. Third, the high-statistics MC signal sample is divided into 400 subsamples and combined with background events to mimic 400 independent data sets of similar size to the data. Fits to these 400 samples do not reveal any additional systematic uncertainty. Because the efficiency functions are estimated from a finite number of simulated events, there is a corresponding statistical uncertainty in the efficiency. The efficiency functions are obtained from fits to simulated data. Alternatives to the default efficiency function are generated by randomly varying the fitted parameters within their uncertainties (including all correlations). The effect of these different efficiency functions on the final result is used to estimate the systematic uncertainty. The main check of the correctness of the efficiency is obtained by comparing the efficiency-corrected results for the control channels with the corresponding world-average values. The efficiency as a function of the angular variables is checked by comparing the FLand AFB measurements from the B0→J/ψK∗0sample, composed of 165 000 signal events. The value of FLobtained in this analysis is 0.537 ±0.002 (stat), compared with the world-average value of 0.571 ±0.007 (stat +syst)[34], indicating a discrepancy of 0.034, which is taken as the systematic uncertainty for the signal measurements of FL. For AFB, the measured value is 0.008 ± 0.003 (stat), compared to a SM expectation of ≈0. Adding an Swave contribution in the fit changes the measured value of AFB by less than 0.001. From this, we conclude that the S-wave effects are minimal, and assign a systematic uncertainty of 0.005 for AFB. To validate that the simulation accurately reproduces the efficiency as a function of q2, we measure the branching ratio between two different q2bins, namely the two control channels. The branching ratio result, BB0→ψK∗0/BB0→J/ψK∗0=0.479 ±0.005, is in excellent agreement with the most precise reported measurement: 0.476 ±0.014 (stat) ±0.010 (syst)[42]. The PDF used in the analysis accommodates cases in which the kaon and pion charges are correctly and incorrectly assigned. Both of these contributions are treated as signal. The mistag frac- 428 CMS Collaboration / Physics Letters B 753 (2016) 424–448 tion is fixed to the value obtained from MC simulation. In the high-statistics control channel B0→J/ψK∗0, the mistag fraction is allowed to float in the fit and a value of fM=(14.5 ±0.5)%is found, to be compared to the simulated value of (13.7 ±0.1)%. The effect of this 5.8% difference in the mistag fraction on the measured values is taken as a systematic uncertainty. The systematic uncertainty associated with the functions used to model the angular distribution of the background is obtained from the sum in quadrature of two uncertainties. The first uncertainty is evaluated by fitting the background with polynomials of one degree greater than used in the default analysis and taking the difference in the observables of interest between these two fits as the systematic uncertainty. The second uncertainty is owing to the statistical uncertainty in the background shape, as these shapes are fixed in the final fit. This uncertainty is obtained by taking the difference in quadrature between the returned statistical uncertainties on the parameters of interest when the background shapes are fixed and allowed to vary. In q2bins where the unconstrained fit does not converge, the associated uncertainty is obtained from extrapolation of nearby bins. The mass distributions for the correctly tagged and mistagged events are each described by the sum of two Gaussian functions, with a common mean for all four Gaussian functions. The mean value is obtained from the fit to the data, while the other parameters (four σand two ratios) are obtained from fits to MC-simulated events, with the uncertainty from those fits used as Gaussian constraints in the fits to the data. For the high-statistics control channels, it is possible to fit the data, while allowing some of the parameters to vary. The maximum changes in the measured values in the two control channel q2bins when the parameters are varied are taken as the systematic uncertainty for all q2bins. The q2bins just below and above the J/ψ region may be contaminated with B0→J/ψK∗0feed-through events that are not removed by the selection criteria. A special fit in these two bins is made, in which an additional background term is added to the PDF. This background distribution is obtained from the MC simulation and the background yield is a free parameter. The resulting changes in the fit parameters are used as estimates of the systematic uncertainty associated with this contribution. The effects from angular resolution in the reconstructed values for the angular variables θKand θlare estimated by performing two fits on the same MC-simulated events. One fit uses the true values of the angular variables and the other fit their reconstructed values. The difference in the fitted parameters between the two fits is taken as an estimate of the systematic uncertainty. The differential branching fraction has an additional systematic uncertainty of 4.6% coming from the uncertainty in the branching fraction of the normalization mode B0→J/ψK∗0. The systematic uncertainties are measured and applied in each q2bin, with the total systematic uncertainty obtained by adding the individual contributions in quadrature. 6. Results The signal data, corresponding to 1430 signal events, are fit in seven disjoint q2bins from 1 to 19 GeV2. Results are also obtained for a wide, low-q2bin (1 <q2<6GeV 2), where the theoretical uncertainties are best understood. The K+π−μ+μ−invariant mass distributions for all of the q2signal bins, as well as the fit projections, are shown in Fig. 2. Fig. 3 plots the projections of the fit and the data on the cosθK(top) and cosθl(bottom) axes for the combined low-q2bin (left, 1 <q2<6GeV 2) and the highest q2 bin (right, 16 <q2<19 GeV2). The fitted values of signal yield, FL, AFB, and dB/dq2, along with their associated uncertainties, are given for each of the disjoint q2regions in Table 2. These results are also shown in Fig. 4, along with two SM predictions. The fitted values for FSare all less than 0.03, while the values for ASvary from −0.3to +0.3. The SM predictions, derived from Refs. [18,20], combine two calculational techniques. In the low-q2region, a quantum chromodynamic factorization approach [43] is used, which is applicable for q2<4m2 c, where mcis the charm quark mass. In the high-q2 region, an operator product expansion in the inverse bquark mass and 1/ q2[44,45] is combined with heavy-quark form-factor relations [46]. This is valid above the open-charm threshold (q2 13.9GeV 2). The two SM predictions shown in Fig. 4 differ in the calculation of the form factors. The light-cone sum rules (LCSR) calculation is made at low q2[47] and is extrapolated to high q2[48]. The lattice gauge (Lattice) calculation of the form factors is from Ref. [49]. Controlled theoretical predictions are not available near the J/ψ and ψresonances. The SM predictions are in good agreement with the CMS experimental results, indicating no strong contribution from physics beyond the standard model. The results described are combined with previous CMS measurements, obtained from an independent data sample collected at √s=7TeV[29]. The systematic uncertainties associated with the efficiency, Kπmistagging, mass distribution, angular resolution, and the B0→J/ψK∗0branching fraction are assumed to be fully correlated between the two samples, with the remaining uncertainties assumed to be uncorrelated. To combine the results from the 7TeV and 8TeV data, the uncorrelated systematic uncertainties are combined in quadrature with the statistical uncertainties. To account for the asymmetric uncertainties, the linear variance method from Ref. [50] is used to average the 7TeV and 8TeV measurements, as well as to average the two q2bins covering 4.30 to 8.68 GeV2, which was a single bin in the 7TeV analysis. After the combination, the correlated systematic uncertainties are added in quadrature. The combined CMS measurements of AFB, FL, and the differential branching fraction versus q2are compared to previous measurements [26–29,51,52] in Fig. 5. The CMS measurements are consistent with the other results, with comparable or higher precision. Table 3 provides a comparison of the measured quantities in the low dimuon invariant mass region: 1 <q2<6GeV 2, as well as the corresponding theoretical calculations. 7. Summary Using pp collision data recorded at √s=8TeVwith the CMS detector at the LHC, corresponding to an integrated luminosity of 20.5 fb−1, an angular analysis has been carried out on the decay B0→K∗0μ+μ−. The data used for this analysis include 1430 signal decays. For each bin of the dimuon invariant mass squared (q2), unbinned maximum-likelihood fits were performed to the distributions of the K+π−μ+μ−invariant mass and two decay angles, to obtain values of the forward–backward asymmetry of the muons, AFB, the fraction of longitudinal polarization of the K∗0, FL, and the differential branching fraction, dB/dq2. The results are among the most precise to date and are consistent with standard model predictions and previous measurements. Acknowledgements We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. CMS Collaboration / Physics Letters B 753 (2016) 424–448 429 Fig. 2. The K+π−μ+μ−invariant mass distributions for the seven signal q2bins and the combined 1 <q2<6GeV 2bin. Overlaid on each is the projection of the results for the total fit, as well as the three components: correctly tagged signal, mistagged signal, and background. The vertical bars give the statistical uncertainties, the horizontal bars the bin widths. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: BMWFW and FWF (Austria); Fonds De La Recherche Scientifique - FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MoST, and NSFC (China); COLCIENCIAS (Colombia); MSES and CSF (Croatia); RPF (Cyprus); MoER, ERC IUT and ERDF (Estonia); Academy of Finland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NIH (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); 430 CMS Collaboration / Physics Letters B 753 (2016) 424–448 Fig. 3. Data and fit results for 1 <q2<6GeV 2(left) and 16 <q2<19 GeV2(right), projected onto the cosθKaxis (top), and cosθlaxis (bottom). The fit results show the total fit, as well as the three components: correctly tagged signal, mistagged signal, and background. The vertical bars give the statistical uncertainties, the horizontal bars the bin widths. Table 2 The measured values of signal yield (including both correctly tagged and mistagged events), FL, AFB, and differential branching fraction for the decay B0→K∗0μ+μ−in bins of q2. The first uncertainty is statistical and the second (when present) is systematic. The bin ranges are selected to allow comparisons to previous measurements. q2 (GeV2) Signal yield FLAFB dB/dq2 (10−8GeV−2) 1.00–2.00 84 ±11 0.64 +0.10 −0.09 ±0.07 −0.27 +0.17 −0.40 ±0.07 4.6±0.7±0.3 2.00–4.30 145 ±16 0.80 ±0.08 ±0.06 −0.12 +0.15 −0.17 ±0.05 3.3±0.5±0.2 4.30–6.00 117 ±15 0.62 +0.10 −0.09 ±0.07 0.01 ±0.15 ±0.03 3.4±0.5±0.3 6.00–8.68 254 ±21 0.50 ±0.06 ±0.06 0.03 ±0.10 ±0.02 4.7±0.4±0.3 10.09–12.86 362 ±25 0.39 ±0.05 ±0.04 0.16 ±0.06 ±0.01 6.2±0.4±0.5 14.18–16.00 225 ±18 0.48 +0.05 −0.06 ±0.04 0.39 +0.04 −0.06 ±0.01 6.7±0.6±0.5 16.00–19.00 239 ±18 0.38 +0.05 −0.06 ±0.04 0.35 ±0.07 ±0.01 4.2±0.3±0.3 Table 3 Measurements from CMS (the 7TeV results [29], this work for 8TeV, and the combination), LHCb [28], BaBar [52], CDF [27, 51], and Belle [26] of FL, AFB, and dB/dq2in the region 1 <q2<6GeV 2for the decay B0→K∗0μ+μ−. The CMS and LHCb results are from B0→K∗0μ+μ−decays. The remaining experiments add the corresponding B+decay, and the BaBar and Belle experiments also include the dielectron mode. The first uncertainty is statistical and the second is systematic. For the combined CMS results, only the total uncertainty is reported. The two SM predictions are also given. Experiment FLAFB dB/dq2(10−8GeV−2) CMS (7 TeV) 0.68 ±0.10 ±0.02 −0.07 ±0.12 ±0.01 4.4±0.6±0.4 CMS (8 TeV, this analysis) 0.73 ±0.05 ±0.04 −0.16 +0.10 −0.09 ±0.05 3.6±0.3±0.2 CMS (7 TeV +8TeV) 0.72 ±0.06 −0.12 ±0.08 3.8±0.4 LHCb 0.65 +0.08 −0.07 ±0.03 −0.17 ±0.06 ±0.01 3.4±0.3+0.4 −0.5 BaBar – – 4.1+1.1 −1.0±0.1 CDF 0.69 +0.19 −0.21 ±0.08 0.29 +0.20 −0.23 ±0.07 3.2±1.1±0.3 Belle 0.67 ±0.23 ±0.05 0.26 +0.27 −0.32 ±0.07 3.0+0.9 −0.8±0.2 SM (LCSR) 0.79 +0.09 −0.12 −0.02 +0.03 −0.02 4.6+2.3 −1.7 SM (Lattice) 0.73 +0.08 −0.10 −0.03 +0.04 −0.03 3.8+1.2 −1.0 CMS Collaboration / Physics Letters B 753 (2016) 424–448 431 Fig. 4. Measured values of FL, AFB, and dB/dq2versus q2for B0→K∗0μ+μ−. The statistical uncertainty is shown by the inner vertical bars, while the outer vertical bars give the total uncertainty. The horizontal bars show the bin widths. The vertical shaded regions correspond to the J/ψ and ψresonances. The other shaded regions show the two SM predictions after rate averaging across the q2bins to provide a direct comparison to the data. Controlled theoretical predictions are not available near the J/ψ and ψresonances. INFN (Italy); MSIP and NRF (Republic of Korea); LAS (Lithuania); MOE and UM (Malaysia); CINVESTAV, CONACYT, SEP, and UASLPFAI (Mexico); MBIE (New Zealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR (Dubna); MON, RosAtom, RAS and RFBR (Russia); MESTD (Serbia); SEIDI and CPAN (Spain); Swiss Funding Agencies (Switzerland); MST (Taipei); ThEPCenter, IPST, STAR and NSTDA (Thailand); TUBITAK and TAEK (Turkey); NASU and SFFR (Ukraine); STFC (United Kingdom); DOE and NSF (USA). Individuals have received support from the Marie-Curie program and the European Research Council and EPLANET (European Union); the Leventis Foundation; the A.P. Sloan Foundation; the Alexander von Humboldt Foundation; the Belgian Federal Science Policy Office; the Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Council of Science and Industrial Research, India; the Fig. 5. Measured values of FL, AFB, and dB/dq2versus q2for B0→K∗0μ+μ−from CMS (combination of the 7TeV[29] results and this analysis), Belle [26], CDF [27, 51], BaBar [52], and LHCb [28]. The CMS and LHCb results are from B0→K∗0μ+μ− decays. The remaining experiments add the corresponding B+decay, and the BaBar and Belle experiments also include the dielectron mode. The vertical bars give the total uncertainty. 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Wallny Institute for Particle Physics, ETH Zurich, Zurich, Switzerland T.K. Aarrestad, C. Amsler 45, L. Caminada, M.F. Canelli, V. Chiochia, A. De Cosa, C. Galloni, A. Hinzmann, T. Hreus, B. Kilminster, C. Lange, J. Ngadiuba, D. Pinna, P. Robmann, F.J. Ronga, D. Salerno, Y. Yang Universität Zürich, Zurich, Switzerland 442 CMS Collaboration / Physics Letters B 753 (2016) 424–448 M. Cardaci, K.H. Chen, T.H. Doan, Sh. Jain, R. Khurana, M. Konyushikhin, C.M. Kuo, W. Lin, Y.J. Lu, R. Volpe, S.S. Yu National Central University, Chung-Li, Taiwan Arun Kumar, R. Bartek, P. Chang, Y.H. Chang, Y.W. Chang, Y. Chao, K.F. Chen, P.H. Chen, C. Dietz, F. Fiori, U. Grundler, W.-S. Hou, Y. Hsiung, Y.F. Liu, R.-S. Lu, M. Miñano Moya, E. Petrakou, J.F. Tsai, Y.M. Tzeng National Taiwan University (NTU), Taipei, Taiwan B. Asavapibhop, K. Kovitanggoon, G. Singh, N. Srimanobhas, N. Suwonjandee Chulalongkorn University, Faculty of Science, Department of Physics, Bangkok, Thailand A. Adiguzel, M.N. 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Yang Fermi National Accelerator Laboratory, Batavia, USA D. Acosta, P. Avery, P. Bortignon, D. Bourilkov, A. Carnes, M. Carver, D. Curry, S. Das, G.P. Di Giovanni, R.D. Field, I.K. Furic, J. Hugon, J. Konigsberg, A. Korytov, J.F. Low, P. Ma, K. Matchev, H. Mei, P. Milenovic 62, G. Mitselmakher, D. Rank, R. Rossin, L. Shchutska, M. Snowball, D. Sperka, J. Wang, S. Wang, J. Yelton University of Florida, Gainesville, USA S. Hewamanage, S. Linn, P. Markowitz, G. Martinez, J.L. Rodriguez Florida International University, Miami, USA A. Ackert, J.R. Adams, T. Adams, A. Askew, J. Bochenek, B. Diamond, J. Haas, S. Hagopian, V. Hagopian, K.F. Johnson, A. Khatiwada, H. Prosper, V. Veeraraghavan, M. Weinberg Florida State University, Tallahassee, USA V. Bhopatkar, M. Hohlmann, H. Kalakhety, D. Noonan, T. Roy, F. Yumiceva Florida Institute of Technology, Melbourne, USA M.R. Adams, L. Apanasevich, D. Berry, R.R. Betts, I. Bucinskaite, R. Cavanaugh, O. Evdokimov, L. Gauthier, C.E. Gerber, D.J. 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Velasco Northwestern University, Evanston, USA A. Brinkerhoff, N. Dev, M. Hildreth, C. Jessop, D.J. Karmgard, N. Kellams, K. Lannon, S. Lynch, N. Marinelli, F. Meng, C. Mueller, Y. Musienko 34, T. Pearson, M. Planer, A. Reinsvold, R. Ruchti, G. Smith, S. Taroni, N. Valls, M. Wayne, M. Wolf, A. Woodard University of Notre Dame, Notre Dame, USA L. Antonelli, J. Brinson, B. Bylsma, L.S. Durkin, S. Flowers, A. Hart, C. Hill, R. Hughes, K. Kotov, T.Y. Ling, B. Liu, W. Luo, D. Puigh, M. Rodenburg, B.L. Winer, H.W. Wulsin The Ohio State University, Columbus, USA O. Driga, P. Elmer, J. Hardenbrook, P. Hebda, S.A. Koay, P. Lujan, D. Marlow, T. Medvedeva, M. Mooney, J. Olsen, C. Palmer, P. Piroué, X. Quan, H. Saka, D. Stickland, C. Tully, J.S. Werner, A. Zuranski Princeton University, Princeton, USA S. Malik University of Puerto Rico, Mayaguez, USA 446 CMS Collaboration / Physics Letters B 753 (2016) 424–448 V.E. Barnes, D. Benedetti, D. Bortoletto, L. Gutay, M.K. Jha, M. Jones, K. Jung, M. 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Ledovskoy, H. Li, C. Lin, C. Neu, E. Wolfe, J. Wood, F. Xia University of Virginia, Charlottesville, USA C. Clarke, R. Harr, P.E. Karchin, C. Kottachchi Kankanamge Don, P. Lamichhane, J. Sturdy Wayne State University, Detroit, USA D.A. Belknap, D. Carlsmith, M. Cepeda, A. Christian, S. Dasu, L. Dodd, S. Duric, E. Friis, B. Gomber, R. Hall-Wilton, M. Herndon, A. Hervé, P. Klabbers, A. Lanaro, A. Levine, K. Long, R. Loveless, CMS Collaboration / Physics Letters B 753 (2016) 424–448 447 A. Mohapatra, I. Ojalvo, T. Perry, G.A. Pierro, G. Polese, I. Ross, T. Ruggles, T. Sarangi, A. Savin, A. Sharma, N. Smith, W.H. Smith, D. Taylor, N. Woods University of Wisconsin, Madison, USA †Deceased. 1Also at Vienna University of Technology, Vienna, Austria. 2Also at CERN, European Organization for Nuclear Research, Geneva, Switzerland. 3Also at State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, China. 4Also at Institut Pluridisciplinaire Hubert Curien, Université de Strasbourg, Université de Haute Alsace Mulhouse, CNRS/IN2P3, Strasbourg, France. 5Also at National Institute of Chemical Physics and Biophysics, Tallinn, Estonia. 6Also at Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia. 7Also at Universidade Estadual de Campinas, Campinas, Brazil. 8Also at Centre National de la Recherche Scientifique (CNRS) – IN2P3, Paris, France. 9Also at Laboratoire Leprince-Ringuet, Ecole Polytechnique, IN2P3-CNRS, Palaiseau, France. 10 Also at Joint Institute for Nuclear Research, Dubna, Russia. 11 Also at British University in Egypt, Cairo, Egypt. 12 Now at Beni-Suef University, Bani Sweif, Egypt. 13 Now at Ain Shams University, Cairo, Egypt. 14 Also at Zewail City of Science and Technology, Zewail, Egypt. 15 Also at Université de Haute Alsace, Mulhouse, France. 16 Also at Tbilisi State University, Tbilisi, Georgia. 17 Also at University of Hamburg, Hamburg, Germany. 18 Also at Brandenburg University of Technology, Cottbus, Germany. 19 Also at Institute of Nuclear Research ATOMKI, Debrecen, Hungary. 20 Also at Eötvös Loránd University, Budapest, Hungary. 21 Also at University of Debrecen, Debrecen, Hungary. 22 Also at Wigner Research Centre for Physics, Budapest, Hungary. 23 Also at University of Visva-Bharati, Santiniketan, India. 24 Now at King Abdulaziz University, Jeddah, Saudi Arabia. 25 Also at University of Ruhuna, Matara, Sri Lanka. 26 Also at Isfahan University of Technology, Isfahan, Iran. 27 Also at University of Tehran, Department of Engineering Science, Tehran, Iran. 28 Also at Plasma Physics Research Center, Science and Research Branch, Islamic Azad University, Tehran, Iran. 29 Also at Università degli Studi di Siena, Siena, Italy. 30 Also at Purdue University, West Lafayette, USA. 31 Also at International Islamic University of Malaysia, Kuala Lumpur, Malaysia. 32 Also at Malaysian Nuclear Agency, MOSTI, Kajang, Malaysia. 33 Also at Consejo Nacional de Ciencia yTecnología, Mexico city, Mexico. 34 Also at Institute for Nuclear Research, Moscow, Russia. 35 Also at St. Petersburg State Polytechnical University, St. Petersburg, Russia. 36 Also at National Research Nuclear University ‘Moscow Engineering Physics Institute’ (MEPhI), Moscow, Russia. 37 Also at California Institute of Technology, Pasadena, USA. 38 Also at Faculty of Physics, University of Belgrade, Belgrade, Serbia. 39 Also at Facoltà Ingegneria, Università di Roma, Roma, Italy. 40 Also at National Technical University of Athens, Athens, Greece. 41 Also at Scuola Normale e Sezione dell’INFN, Pisa, Italy. 42 Also at University of Athens, Athens, Greece. 43 Also at Warsaw University of Technology, Institute of Electronic Systems, Warsaw, Poland. 44 Also at Institute for Theoretical and Experimental Physics, Moscow, Russia. 45 Also at Albert Einstein Center for Fundamental Physics, Bern, Switzerland. 46 Also at Gaziosmanpasa University, Tokat, Turkey. 47 Also at Mersin University, Mersin, Turkey. 48 Also at Cag University, Mersin, Turkey. 49 Also at Piri Reis University, Istanbul, Turkey. 50 Also at Adiyaman University, Adiyaman, Turkey. 51 Also at Ozyegin University, Istanbul, Turkey. 52 Also at Izmir Institute of Technology, Izmir, Turkey. 53 Also at Mimar Sinan University, Istanbul, Istanbul, Turkey. 54 Also at Marmara University, Istanbul, Turkey. 55 Also at Kafkas University, Kars, Turkey. 56 Also at Yildiz Technical University, Istanbul, Turkey. 57 Also at Hacettepe University, Ankara, Turkey. 58 Also at Rutherford Appleton Laboratory, Didcot, United Kingdom. 59 Also at School of Physics and Astronomy, University of Southampton, Southampton, United Kingdom. 60 Also at Instituto de Astrofísica de Canarias, La Laguna, Spain. 61 Also at Utah Valley University, Orem, USA. 62 Also at University of Belgrade, Faculty of Physics and Vinca Institute of Nuclear Sciences, Belgrade, Serbia. 63 Also at Argonne National Laboratory, Argonne, USA. 448 CMS Collaboration / Physics Letters B 753 (2016) 424–448 64 Also at Erzincan University, Erzincan, Turkey. 65 Also at Texas A&M University at Qatar, Doha, Qatar. 66 Also at Kyungpook National University, Daegu, Republic of Korea.