Angular analysis of charged and neutral B → Kμ + μ − decays

JHEP05(2014)082 Published for SISSA by Springer Received:April 1, 2014 Accepted:April 15, 2014 Published:May 19, 2014 Angular analysis of charged and neutral B→Kµ+µ− decays The LHCb collaboration E-mail: [email protected] Abstract: The angular distributions of the rare decays B+→K+µ+µ−and B0→ K0 Sµ+µ−are studied with data corresponding to 3 fb−1of integrated luminosity, collected in proton-proton collisions at 7 and 8 TeV centre-of-mass energies with the LHCb detector. The angular distribution is described by two parameters, FHand the forward-backward asymmetry of the dimuon system AFB, which are determined in bins of the dimuon mass squared. The parameter FHis a measure of the contribution from (pseudo)scalar and tensor amplitudes to the decay width. The measurements of AFB and FHreported here are the most precise to date and are compatible with predictions from the Standard Model. Keywords: Rare decay, B physics, Flavour Changing Neutral Currents, Flavor physics, Hadron-Hadron Scattering ArXiv ePrint: 1403.8045 Open Access, Copyright CERN, for the benefit of the LHCb Collaboration. Article funded by SCOAP3. doi:10.1007/JHEP05(2014)082 JHEP05(2014)082 Contents 1 Introduction 1 2 Data and detector description 2 3 Selection of signal candidates 3 4 Angular acceptance 5 5 Angular analysis 6 6 Results 7 7 Conclusion 12 A Two-dimensional confidence intervals 13 The LHCb collaboration 20 1 Introduction The B+→K+µ+µ−and B0→K0 Sµ+µ−decays are rare, flavour-changing neutral-current processes that are mediated by electroweak box and penguin amplitudes in the Standard Model (SM).1In well motivated extensions of the SM [1,2], new particles can introduce additional amplitudes that modify the angular distribution of the final-state particles predicted by the SM. In this paper, the angular distributions of the final-state particles are probed by determining the differential rate of the Bmeson decays as a function of the angle between the direction of one of the muons and the direction of the K+or K0 Smeson in the rest frame of the dimuon system. The analysis is performed in bins of q2, the dimuon invariant mass squared. The angular distribution of B+→K+µ+µ−decays has previously been studied by the BaBar [3], Belle [4], CDF [5] and LHCb [6] experiments with less data. For the decay B+→K+µ+µ−, the differential decay rate can be written as [2,7] 1 Γ dΓ d cos θl =3 4(1 −FH)(1 −cos2θl) + 1 2FH+AFB cos θl,(1.1) where θlis the angle between the direction of the µ−(µ+) lepton and the K+(K−) meson for the B+(B−) decay. The differential decay rate depends on two parameters, the forward-backward asymmetry of the dimuon system, AFB, and a second parameter FH, 1The inclusion of charge conjugated processes is implied throughout. – 1 – JHEP05(2014)082 which corresponds to the fractional contribution of (pseudo)scalar and tensor amplitudes to the decay width in the approximation that muons are massless. The decay width, AFB and FHall depend on q2. The structure of eq. (1.1) follows from angular momentum conservation in the decay of a pseudo-scalar Bmeson into a pseudo-scalar Kmeson and a pair of muons. In contrast to the decay B0→K∗0µ+µ−,AFB is zero up to tiny corrections in the SM. A sizable value of AFB is possible in models that introduce large (pseudo)scalaror tensor-like couplings [1,2]. The parameter FHis non-zero, but small, in the SM due to the finite muon mass. For eq. (1.1) to remain positive at all lepton angles, AFB and FHhave to satisfy the constraints 0≤FH≤3 and |AFB| ≤ FH/2. Since the B0and B0meson can decay to the same K0 Sµ+µ−final state, it is not possible to determine the flavour of the Bmeson from the decay products. Without tagging the flavour of the neutral Bmeson at production, it is therefore not possible to unambiguously chose the correct muon to determine θl. For this reason, θlis always defined with respect to the µ+for decays to the K0 Sµ+µ−final-state. In this situation any visible AFB would indicate that there is either a difference in the number of B0and B0mesons produced, CP violation in the decay or that the AFB of the B0and B0decay differ. Any residual asymmetry can be canceled by performing the analysis in terms of |cos θl|, 1 Γ dΓ d|cos θl|=3 2(1 −FH)(1 −|cos θl|2) + FH,(1.2) where the constraint 0 ≤FH<3 is needed for this expression to remain positive at all values of |cos θl|. This simplification of the angular distribution is used for the B0→K0 Sµ+µ− decay in this paper. 2 Data and detector description The data used for the analysis correspond to 1 fb−1of integrated luminosity collected by the LHCb experiment in pp collisions at √s= 7 TeV in 2011 and 2 fb−1of integrated luminosity collected at √s= 8 TeV in 2012. The average number of pp interactions, yielding a charged particle in the detector acceptance, per bunch crossing was 1.4 in 2011 and 1.7 in 2012. The LHCb detector [8] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of particles containing bor c quarks. 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 a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes [9] placed downstream of the magnet. The combined tracking system provides a momentum measurement with relative uncertainty that varies from 0.4% at 5 GeV/c to 0.6% at 100 GeV/c, and impact parameter resolution of 20 µm for tracks with large transverse momentum. Different types of charged hadrons are distinguished by information from two ring-imaging Cherenkov detectors [10]. Photon, electron and hadron candidates are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic calorimeter and a hadronic – 2 – JHEP05(2014)082 calorimeter. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers [11]. Samples of simulated B+→K+µ+µ−and B0→K0 Sµ+µ−decays are used to understand how the detector geometry, the reconstruction and subsequent event selection bias the angular distribution of the decays. In the simulation, pp collisions are generated using Pythia [12] with a specific LHCb configuration [13]. Decays of hadronic particles are described by EvtGen [14], in which final state radiation is generated using Photos [15]. The interaction of the generated particles with the detector and its response are implemented using the Geant4 toolkit [16,17] as described in ref. [18]. 3 Selection of signal candidates The LHCb trigger system [19] 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. In the hardware stage of the trigger, candidates are selected with at least one muon candidate with transverse momentum, pT>1.48 (1.76) GeV/c in 2011 (2012). In the second stage of the trigger, at least one of the final-state particles from the B0or B+ meson decay is required to have pT>1.0 GeV/c and impact parameter larger than 100 µm with respect to any primary vertex (PV) from the pp interactions in the event. Tracks from two or more of the final-state particles are required to form a secondary vertex that is displaced from all of the PVs. The K0 Smesons from the decay B0→K0 Sµ+µ−are reconstructed through their decay K0 S→π+π−in two different categories: the first category contains K0 Smesons that decay early enough that the final-state pions are reconstructed in the vertex detector; and the second contains K0 Smesons that decay later, such that the first track segment that can be reconstructed is in the large-area silicon-strip detector. These categories are referred to as long and downstream, respectively. Candidates in the long category have better mass, momentum and vertex resolution. Reconstructed tracks that leave hits in the LHCb muon system are positively identified as muons. Two muons of opposite charge are then combined with either a track (K+) or a reconstructed K0 Sto form a B+or B0candidate. The π+π−pair from the reconstructed K0 Sis constrained to the known K0 Smass when determining the mass of the B0candidate. Neural networks, using information from the RICH detectors, calorimeters and muon system, are used to reject backgrounds where either a pion is misidentified as the kaon in the B+decay or a pion or kaon are incorrectly identified as one of the muons. An initial selection is applied to B+and B0candidates to reduce the level of the background. The selection criteria are common to those described in ref. [20]: the µ±and the K+candidates are required to have χ2 IP >9, where χ2 IP is defined as the minimum change in χ2of the vertex fit to any of the PVs in the event when the particle is added to that PV; the dimuon pair vertex fit has χ2<9; the Bcandidate is required to have a vertex fit χ2<8 per degree of freedom; the Bmomentum vector is aligned with respect to one of the PVs in the event within 14 mrad, the Bcandidate has χ2 IP <9 with respect to that PV and the vertex fit χ2of that PV increases by more than 121 when including the Bdecay products. In addition, the K0 Scandidate is required to have a decay time larger than 2 ps. – 3 – JHEP05(2014)082 The initial selections are followed by tighter multivariate selections, based on boosted decision trees (BDTs) [21] with the AdaBoost algorithm [22]. The working points for the BDTs are chosen to maximise NS/√NS+NB, where NSand NBare the expected numbers of signal and background candidates within ±50 MeV/c2of the known B0or B+meson masses, respectively. For the B+→K+µ+µ−decay, the variables used in the BDT are identical to those of ref. [20]. In contrast to that analysis, however, the multivariate selection is trained using a sample of simulated events to model the signal and candidates from the data with K+µ+µ−invariant masses in the range 5700 < m(K+µ+µ−)<6000 MeV/c2for the background. This background sample is not used in the subsequent analysis, where the invariant mass of the candidates is restricted to the range 5170 < m(K+µ+µ−)<5700 MeV/c2. The multivariate selection has an efficiency of 89% for signal and removes 94% of the background that remains after the initial selection. For the B0→K0 Sµ+µ−decay, two independent BDTs are trained for the long and downstream categories. Samples of simulated events are used in the signal training and candidates from the data with masses 5700 < m(K0 Sµ+µ−)<6000 MeV/c2for the background training. The following information is used in the classifiers: the B0candidate momentum and pT, its vertex quality (χ2) and decay time, the K0 Scandidate pT, and the angle between the B0candidate momentum and the direction between the PV and the B0 decay vertex. For the long category, the K0 Scandidate χ2 IP is also included. The multivariate selection removes 99% of the combinatorial background and is 66% and 48% efficient for the long and downstream signal categories. Combinatorial backgrounds for the B+→K+µ+µ−decay, where the K+ ,µ+and µ−candidates do not all come from the same b-hadron decay, are reduced to a small level by the multivariate selection. After applying the multivariate selection, the signalto-background ratio in a ±50 MeV/c2range around the known B+mass is better than six-to-one. Remaining backgrounds mainly come from b-hadron decays that are fully or partially reconstructed in the detector. The B+→J/ψK+and B+→ψ(2S)K+decays2 are rejected by removing the regions of dimuon mass around the charmonium resonances (8.0< q2<11.0 GeV2/c4and 12.5< q2<15.0 GeV2/c4). These decays can also form a background to the B+→K+µ+µ−decay if the kaon is incorrectly identified as a muon and the muon with the same charge is incorrectly identified as a kaon. This background is removed by rejecting candidates with a K+µ−pair whose invariant mass (under the µ+µ− mass hypothesis) is consistent with that of the J/ψ or ψ(2S) meson, if the reconstructed kaon can also be matched to hits in the muon system. A narrow range in q2from 0.98 < q2<1.10 GeV2/c4is also removed to reject B+→φK+decays, followed by the φ→µ+µ− decay. The region m(K+µ+µ−)<5170 MeV/c2is contaminated by partially reconstructed b-hadron decays such as B0→K∗0µ+µ−where the pion from the K∗0→K+π−decay is not reconstructed. This region is not used in the subsequent analysis and dictates the lower bound of the 5170 < m(K+µ+µ−)<5700 MeV/c2mass range. Backgrounds from fully hadronic b-hadron decays, such as the decay B+→K+π+π−, are reduced to a 2Throughout this paper the decays B+→J/ψ K+and B0→J/ψ K0 Srefer to decays of B+and B0 mesons to K+µ+µ−and K0 Sµ+µ−final-states, respectively, through the decay J/ψ →µ+µ−. – 4 – JHEP05(2014)082 negligible level using stringent muon-identification selection criteria. A further requirement is applied on the K+µ−pair to remove a small contribution from B+→D0π+decays with D0→K+π−, where the pions survive the muon-identification requirements. Candidates are rejected if the mass of the K+µ−pair, computed under the K+π−hypothesis, is in the range 1850 < m(K+π−)<1880 MeV/c2. After the application of all selection criteria, the background from other b-hadron decays is reduced to O(0.1%) of the level of the signal. The total efficiency for reconstructing and selecting the B+→K+µ+µ−decay is around 2%. Due to the long lifetime of the K0 Smeson, there are very few b-hadron decays that can be mistakenly identified as B0→K0 Sµ+µ−decays. The largest source of fully reconstructed background is the decay Λ0 b→Λµ+µ−, where the proton from the Λ→pπ−decay is incorrectly identified as a π+. This background is removed by rejecting K0 Smeson candidates if the mass of the π+π−pair, under the pπ−mass hypothesis, is consistent with that of a Λ baryon within ±10 MeV/c2(±15 MeV/c2) for long (downstream) candidates. This veto is 95% efficient on genuine K0 Smeson decays and removes more than 99% of Λbaryons. The total efficiency for reconstructing the B0→K0 Sµ+µ−decay is about 0.2%, which is a factor of ten lower than for the charged decay. This is due to a combination of three effects: the long flight distance of K0 Smesons in the detector, the K0 S→π+π−branching fraction, and the requirement of having four, rather than three, tracks within the detector acceptance. After applying the selection procedure, the signal-to-background ratio in a ±50 MeV/c2 range around the known B0mass is better than three-to-one for the B0→K0 Sµ+µ−decay. After applying the full selection criteria, more than 99% of the selected events contain only one B+or B0candidate. Events containing more than one candidate have all but one candidate removed at random in the subsequent analysis. 4 Angular acceptance The geometrical acceptance of the LHCb detector, the trigger and the event selection can all bias the cos θldistribution of the selected candidates. The angular acceptance is determined using a sample of simulated signal events. The acceptance as a function of cos θlis parameterised using a fourth-order polynomial function, fixing the odd-order terms to zero so that the acceptance is symmetric around zero. Any small asymmetry in the acceptance for Band Bmesons, due to charge asymmetries in the reconstruction, cancels when combining Band Bmeson decays. At small values of q2, there is a large reduction of the signal efficiency at values of cos θlclose to ±1, as seen in figure 1. This results from the requirement for muons to have p> ∼3 GeV/c to reach the muon system. Smaller reductions of the signal efficiency also arise from the pTrequirement of the hardware trigger and the impact parameter requirements on the µ±in the selection. For the decay B+→K+µ+µ−, the D0veto described in section 3introduces an additional bias to the angular acceptance: at a fixed value of q2, there is a one-to-one correspondence between cos θland the reconstructed D0mass, and the D0veto therefore removes a narrow region of cos θlin each q2bin. The D0veto results in the dip in the – 5 – JHEP05(2014)082 l θ cos -1 -0.5 0 0.5 1 Relative efficiency 0.2 0.4 0.6 0.8 (long) − µ + µ s 0 K → 0 B (downstream) − µ + µ s 0 K → 0 B − µ + µ + K → + B (a) LHCb simulation 4 c/ 2 < 6.0 GeV 2 q1.1 < l θ cos -1 -0.5 0 0.5 1 Relative efficiency 0.2 0.4 0.6 0.8 (long) − µ + µ s 0 K → 0 B (downstream) − µ + µ s 0 K → 0 B − µ + µ + K → + B (b) LHCb simulation 4 c/ 2 < 22.0 GeV 2 q15.0 < Figure 1. Angular acceptance as derived from simulation in the dimuon mass squared ranges (a) 1.1< q2<6.0 GeV2 /c4and (b) 15.0< q2<22.0 GeV2 /c4. The dip in the acceptance for B+→K+µ+µ−decays results from the veto used to reject B+→D0π+decays (see text). The acceptance is normalised to unit area to allow a comparison of the shape of the distributions. acceptance seen in figure 1. The impact of the veto is approximated as a step function in the acceptance model and determined using a SM-like sample of simulated events. 5 Angular analysis The m(K+µ+µ−) and m(K0 Sµ+µ−) invariant mass distributions of candidates that pass the full selection procedure are shown in figure 2, for two q2intervals. The long and downstream categories are combined for the decay B0→K0 Sµ+µ−. The angular distribution of the candidates is shown in figure 3. For the B+→K+µ+µ−decay, AFB and FHare determined by performing an unbinned maximum likelihood fit to the m(K+µ+µ−) and cos θldistributions of the candidates in bins of q2. The signal angular distribution is described by eq. (1.1), multiplied by the acceptance distribution described in section 4. The signal mass distribution is parameterised by the sum of two Gaussian functions with power-law tails, with common most probable values and common tail parameters, but different widths. The parameters of the these signal functions are obtained fitting the m(K+µ+µ−) distribution of B+→J/ψ K+candidates in data. The peak position and width parameters are then corrected, using simulated events, to account for kinematic differences between the decays B+→K+µ+µ−and B+→J/ψK+. The m(K+µ+µ−) distribution of the combinatorial background is parameterised by a falling exponential function. Its angular distribution is parameterised by a third-order polynomial function multiplied by the same angular acceptance function used for the signal. Decays of B0and B0mesons to the K0 Sµ+µ−final state cannot be separated based on the final-state particles. The angular distribution of |cos θl|is described by eq. (1.2), which depends only on FH. Simultaneous unbinned maximum likelihood fits are then performed to the |cos θl|and m(K0 Sµ+µ−) distributions of the two categories of K0 Smeson (long and downstream). The only parameter that is common between the two simultaneous fits is FH. The m(K0 Sµ+µ−) shape parameters of the two categories are determined in the same way as that of the decay B+→K+µ+µ−, using B0→J/ψK0 Sdecays. Information on the angular – 6 – JHEP05(2014)082 ] 2 c) [MeV/ − µ + µ + K(m 5200 5400 5600 ) 2 c Candidates / ( 10 MeV/ 0 100 200 300 400 500 LHCb 4 c/ 2 < 6.0 GeV 2 q(a) 1.1 < ] 2 c) [MeV/ − µ + µ + K(m 5200 5400 5600 ) 2 c Candidates / ( 10 MeV/ 0 100 200 300 400 500 LHCb 4 c/ 2 < 22.0 GeV 2 q(b) 15.0 < ] 2 c) [MeV/ − µ + µ S 0 K(m 5200 5400 5600 ) 2 c Candidates / ( 10 MeV/ 0 5 10 15 20 25 LHCb 4 c/ 2 < 6.0 GeV 2 q(c) 1.1 < ] 2 c) [MeV/ − µ + µ S 0 K(m 5200 5400 5600 ) 2 c Candidates / ( 10 MeV/ 0 5 10 15 20 25 LHCb 4 c/ 2 < 22.0 GeV 2 q(d) 15.0 < Figure 2. Top, reconstructed mass of B+→K+µ+µ−candidates in the ranges (a) 1.1< q2< 6.0 GeV2 /c4and (b) 15.0< q2<22.0 GeV2 /c4. Bottom, reconstructed mass of B0→K0 Sµ+µ− candidates in the ranges (c) 1.1< q2<6.0 GeV2 /c4and (d) 15.0< q2<22.0 GeV2 /c4. The data are overlaid with the result of the fit described in the text. The long and downstream K0 Scategories are combined for presentation purposes. The shaded region indicates the background contribution in the fit. shape of the background in the likelihood fit is obtained from the upper mass sideband, 5350 < m(K0 Sµ+µ−)<5700 MeV/c2. For candidates in the long K0 Scategory, the number of candidates in the sideband is so small that the shape is assumed to be uniform. For the downstream category, the shape is parameterised by a second-order polynomial. The signal and background angular distributions are then both multiplied by the signal angular acceptance distribution. The m(K0 Sµ+µ−) distribution of the background candidates is parameterised by a falling exponential function. The likelihood fits for the B+→K+µ+µ−decay and the two categories of K0 Smeson in the B0→K0 Sµ+µ−decay are performed in two dimensions, treating m(K+µ+µ−) and cos θlas independent variables. In total, there are 4746±81 reconstructed signal candidates for the B+→K+µ+µ−decay and 176 ±17 for the B0→K0 Sµ+µ−decay, summing the yields of the individual q2bins. 6 Results For the decay B+→K+µ+µ−, the results are presented as two-dimensional confidence regions for AFB and FHand as one-dimensional 68% confidence intervals for AFB and FH. The two-dimensional confidence regions demonstrate the correlation between AFB and FH – 7 – JHEP05(2014)082 l θ cos -1 -0.5 0 0.5 1 Candidates / 0.1 0 50 100 150 200 LHCb 4 c/ 2 < 6.0 GeV 2 q(a) 1.1 < l θ cos -1 -0.5 0 0.5 1 Candidates / 0.1 0 50 100 150 200 LHCb 4 c/ 2 < 22.0 GeV 2 q(b) 15.0 < | l θ |cos 0 0.2 0.4 0.6 0.8 1 Candidates / 0.1 0 10 20 30 LHCb 4 c/ 2 < 6.0 GeV 2 q(c) 1.1 < | l θ |cos 0 0.2 0.4 0.6 0.8 1 Candidates / 0.1 0 10 20 30 LHCb 4 c/ 2 < 22.0 GeV 2 q(d) 15.0 < Figure 3. Top, angular distribution of B+→K+µ+µ−candidates with (a) 1.1< q2<6.0 GeV2 /c4 and (b) 15.0< q2<22.0 GeV2 /c4. Bottom, angular distribution of B0→K0 Sµ+µ−candidates with (c) 1.1< q2<6.0 GeV2 /c4and (d) 15.0< q2<22.0 GeV2 /c4. Only candidates with a reconstructed mass within ±50 MeV/c2of the known B+or B0mass are shown. The data are overlaid with the result of the fit described in the text. The long and downstream K0 Scategories are combined for presentation purposes. The shaded region indicates the background contribution in the fit. arising from eq. (1.1). The one-dimensional intervals are intended for illustration purposes only. Two-dimensional confidence regions, for the q2ranges 1.1< q2<6.0 GeV2 /c4and 15.0< q2<22.0 GeV2 /c4are shown in figure 4; the other q2bins are provided in the appendix, with the numerical values available in the attachment.3The one-dimensional confidence intervals for B+→K+µ+µ−decays are shown in figure 5and given in table 1. The result of the fits to |cos θl|for the decay B0→K0 Sµ+µ−are shown in figure 6and given in table 2. Results are presented in 17 (5) bins of q2for the B+→K+µ+µ− (B0→K0 Sµ+µ−) decay. They are also presented in two wide bins of q2: one at low hadronic recoil above the open charm threshold and one at large recoil, below the J/ψ meson mass. The confidence intervals on FHand AFB are estimated using the Feldman-Cousins technique [23]. Nuisance parameters are incorporated using the so-called plug-in method [24]. At each value of FHand AFB considered, the maximum likelihood estimate of the nuisance parameters in data is used when generating the pseudoexperiments. For the B+→ K+µ+µ−decay, AFB (FH) is treated as if it were a nuisance parameter when determining the one-dimensional confidence interval on FH(AFB). The physical boundaries, described in 3Data files are provided as supplementary material and are available at this article’s web page. – 8 – JHEP05(2014)082 FB A -0.1 0 0.1 H F 0 0.1 0.2 0.3 0.4 LHCb 68% 90% 95% best fit (a) 11.00 < q2<11.75.00 GeV2/c4 FB A -0.1 0 0.1 H F 0 0.1 0.2 0.3 0.4 LHCb 68% 90% 95% best fit (b) 11.75 < q2<12.50 GeV2/c4 FB A -0.1 0 0.1 H F 0 0.1 0.2 0.3 0.4 LHCb 68% 90% 95% best fit (c) 15.00 < q2<16.00 GeV2/c4 Figure 9. Two-dimensional confidence regions for AFB and FHfor the decay B+→K+µ+µ−in the q2ranges (a) 11.00 < q2<11.75 GeV2 /c4, (b) 11.75 < q2<12.50 GeV2 /c4and (c) 15.00 < q2<16.00 GeV2 /c4. The confidence intervals are determined using the Feldman-Cousins technique and are purely statistical. The shaded (triangular) region illustrates the range of AFB and FHover which the signal angular distribution remains positive in all regions of phase-space. – 15 – JHEP05(2014)082 FB A -0.1 0 0.1 H F 0 0.1 0.2 0.3 0.4 LHCb 68% 90% 95% best fit (a) 16.00 < q2<17.00 GeV2/c4 FB A -0.1 0 0.1 H F 0 0.1 0.2 0.3 0.4 LHCb 68% 90% 95% best fit (b) 17.00 < q2<18.00 GeV2/c4 FB A -0.1 0 0.1 H F 0 0.1 0.2 0.3 0.4 LHCb 68% 90% 95% best fit (c) 18.00 < q2<19.00 GeV2/c4 Figure 10. Two-dimensional confidence regions for AFB and FHfor the decay B+→K+µ+µ− in the q2ranges (a) 16.00 < q2<17.00 GeV2 /c4, (b) 17.00 < q2<18.00 GeV2 /c4and (c) 18.00 < q2<19.00 GeV2 /c4. The confidence intervals are determined using the Feldman-Cousins technique and are purely statistical. The shaded (triangular) region illustrates the range of AFB and FHover which the signal angular distribution remains positive in all regions of phase-space. – 16 – JHEP05(2014)082 FB A -0.1 0 0.1 H F 0 0.1 0.2 0.3 0.4 LHCb 68% 90% 95% best fit (a) 19.00 < q2<20.00 GeV2/c4 FB A -0.1 0 0.1 H F 0 0.1 0.2 0.3 0.4 LHCb 68% 90% 95% best fit (b) 20.00 < q2<21.00 GeV2/c4 FB A -0.1 0 0.1 H F 0 0.1 0.2 0.3 0.4 LHCb 68% 90% 95% best fit (c) 21.00 < q2<22.00 GeV2/c4 Figure 11. Two-dimensional confidence regions for AFB and FHfor the decay B+→K+µ+µ− in the q2ranges (a) 19.00 < q2<20.00 GeV2 /c4, (b) 20.00 < q2<21.00 GeV2 /c4and (c) 21.00 < q2<22.00 GeV2 /c4. The confidence intervals are determined using the Feldman-Cousins technique and are purely statistical. 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Zvyagin38 1Centro Brasileiro de Pesquisas F´ısicas (CBPF), Rio de Janeiro, Brazil 2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil 3Center for High Energy Physics, Tsinghua University, Beijing, China 4LAPP, Universit´e de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France 5Clermont Universit´e, Universit´e Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France 6CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, Marseille, France 7LAL, Universit´e Paris-Sud, CNRS/IN2P3, Orsay, France 8LPNHE, Universit´e Pierre et Marie Curie, Universit´e Paris Diderot, CNRS/IN2P3, Paris, France 9Fakult¨at Physik, Technische Universit¨at Dortmund, Dortmund, Germany 10 Max-Planck-Institut f¨ur Kernphysik (MPIK), Heidelberg, Germany 11 Physikalisches Institut, Ruprecht-Karls-Universit¨at Heidelberg, Heidelberg, Germany 12 School of Physics, University College Dublin, Dublin, Ireland 13 Sezione INFN di Bari, Bari, Italy 14 Sezione INFN di Bologna, Bologna, Italy 15 Sezione INFN di Cagliari, Cagliari, Italy 16 Sezione INFN di Ferrara, Ferrara, Italy 17 Sezione INFN di Firenze, Firenze, Italy 18 Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy 19 Sezione INFN di Genova, Genova, Italy 20 Sezione INFN di Milano Bicocca, Milano, Italy 21 Sezione INFN di Milano, Milano, Italy 22 Sezione INFN di Padova, Padova, Italy 23 Sezione INFN di Pisa, Pisa, Italy 24 Sezione INFN di Roma Tor Vergata, Roma, Italy 25 Sezione INFN di Roma La Sapienza, Roma, Italy 26 Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Krak´ow, Poland 27 AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science, Krak´ow, Poland 28 National Center for Nuclear Research (NCBJ), Warsaw, Poland 29 Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania – 22 – JHEP05(2014)082 30 Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia 31 Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia 32 Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia 33 Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia 34 Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State University, Novosibirsk, Russia 35 Institute for High Energy Physics (IHEP), Protvino, Russia 36 Universitat de Barcelona, Barcelona, Spain 37 Universidad de Santiago de Compostela, Santiago de Compostela, Spain 38 European Organization for Nuclear Research (CERN), Geneva, Switzerland 39 Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne, Switzerland 40 Physik-Institut, Universit¨at Z¨urich, Z¨urich, Switzerland 41 Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands 42 Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, The Netherlands 43 NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine 44 Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine 45 University of Birmingham, Birmingham, United Kingdom 46 H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom 47 Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom 48 Department of Physics, University of Warwick, Coventry, United Kingdom 49 STFC Rutherford Appleton Laboratory, Didcot, United Kingdom 50 School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom 51 School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom 52 Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom 53 Imperial College London, London, United Kingdom 54 School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom 55 Department of Physics, University of Oxford, Oxford, United Kingdom 56 Massachusetts Institute of Technology, Cambridge, MA, United States 57 University of Cincinnati, Cincinnati, OH, United States 58 University of Maryland, College Park, MD, United States 59 Syracuse University, Syracuse, NY, United States 60 Pontif´ıcia Universidade Cat´olica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to 2 61 Institute of Particle Physics, Central China Normal University, Wuhan, Hubei, China, associated to 3 62 Institut f¨ur Physik, Universit¨at Rostock, Rostock, Germany, associated to 11 63 National Research Centre Kurchatov Institute, Moscow, Russia, associated to 31 64 Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC, Valencia, Spain, associated to 36 65 KVI - University of Groningen, Groningen, The Netherlands, associated to 41 66 Celal Bayar University, Manisa, Turkey, associated to 38 aUniversidade Federal do Triˆangulo Mineiro (UFTM), Uberaba-MG, Brazil bP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia cUniversit`a di Bari, Bari, Italy dUniversit`a di Bologna, Bologna, Italy eUniversit`a di Cagliari, Cagliari, Italy fUniversit`a di Ferrara, Ferrara, Italy gUniversit`a di Firenze, Firenze, Italy hUniversit`a di Urbino, Urbino, Italy iUniversit`a di Modena e Reggio Emilia, Modena, Italy – 23 – JHEP05(2014)082 jUniversit`a di Genova, Genova, Italy kUniversit`a di Milano Bicocca, Milano, Italy lUniversit`a di Roma Tor Vergata, Roma, Italy mUniversit`a di Roma La Sapienza, Roma, Italy nUniversit`a della Basilicata, Potenza, Italy oLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain pHanoi University of Science, Hanoi, Viet Nam qUniversit`a di Padova, Padova, Italy rUniversit`a di Pisa, Pisa, Italy sScuola Normale Superiore, Pisa, Italy tUniversit`a degli Studi di Milano, Milano, Italy – 24 –