Measurements of the S-wave fraction in B0 → K + π − μ + μ − decays and the B0 → K ∗(892)0 μ + μ − differential branching fraction

JHEP11(2016)047 Published for SISSA by Springer Received:June 16, 2016 Revised:August 25, 2016 Accepted:October 28, 2016 Published:November 8, 2016 Measurements of the S-wave fraction in B0→K+π−µ+µ−decays and the B0→K∗(892)0µ+µ−differential branching fraction The LHCb collaboration E-mail: [email protected] Abstract: A measurement of the differential branching fraction of the decay B0→K∗(892)0µ+µ−is presented together with a determination of the S-wave fraction of the K+π−system in the decay B0→K+π−µ+µ−. The analysis is based on ppcollision data corresponding to an integrated luminosity of 3 fb−1collected with the LHCb experiment. The measurements are made in bins of the invariant mass squared of the dimuon system, q2. Precise theoretical predictions for the differential branching fraction of B0→K∗(892)0µ+µ−decays are available for the q2region 1.1< q2<6.0 GeV2/c4. In this q2region, for the K+π−invariant mass range 796 < mKπ <996 MeV/c2, the S-wave fraction of the K+π−system in B0→K+π−µ+µ−decays is found to be FS= 0.101 ±0.017(stat) ±0.009(syst), and the differential branching fraction of B0→K∗(892)0µ+µ−decays is determined to be dB/dq2= (0.392+0.020 −0.019(stat) ±0.010(syst) ±0.027(norm)) ×10−7c4/GeV2. The differential branching fraction measurements presented are the most precise to date and are found to be in agreement with Standard Model predictions. Keywords: B physics, Hadron-Hadron scattering (experiments), Rare decay ArXiv ePrint: 1606.04731 Open Access, Copyright CERN, for the benefit of the LHCb Collaboration. Article funded by SCOAP3. doi:10.1007/JHEP11(2016)047 JHEP11(2016)047 Contents 1 Introduction 1 2 The angular distribution and FS3 3 Detector and simulation 5 4 Selection of signal candidates 5 5 The K+π−µ+µ−and K+π−mass distributions 6 6 Determination of the S-wave fraction 8 6.1 Efficiency correction 8 6.2 Fit to the mass and angular distributions 8 6.3 Result for FS10 7 Differential branching fraction of the decay B0→K∗(892)0µ+µ−10 8 Systematic uncertainties 12 8.1 Systematic uncertainties on the S-wave fraction 13 8.2 Systematic uncertainties on the differential branching fraction 15 9 Conclusions 15 A The mKπ distribution of the signal 16 B Likelihood fit projections 17 The LHCb collaboration 25 1 Introduction The decay B0→K∗0µ+µ−proceeds via a b→s `+`−flavour-changing neutral-current transition. In the Standard Model (SM), this transition is forbidden at tree level and must therefore occur via a loop-level process. Extensions to the SM predict new particles that can contribute to the b→s `+`−process and affect the rate and angular distribution of the decay. Recently, global analyses of measurements involving b→s `+`−processes have reported significant deviations from SM predictions [1–15]. These deviations could be explained either by new particles [3,4,10,11,14–16] or by unexpectedly large hadronic effects [9,13,17]. – 1 – JHEP11(2016)047 In this paper, the symbol K∗0denotes any neutral strange meson in an excited state that decays to a K+and a π−.1For invariant masses of the K+π−system in the range considered in this analysis, the K∗0decay products are predominantly found in a P- or S- wave state. The fractional size of the scalar (S-wave) component of the K+π−system (FS) depends on the squared invariant mass of the dimuon system (q2). This dependence is expected to be similar to that of the longitudinal polarisation fraction (FL) of the K∗(892)0 meson [18–20]. The S-wave fraction is predicted to be maximal in the q2range 1.0< q2<6.0 GeV2 /c4[18–20]. A previous analysis by the LHCb collaboration set an upper limit of FS<0.07 at 68% confidence level for invariant masses of the K+π−system in the range 792 < mKπ <992 MeV/c2[21]. The measurement was performed by exploiting the phase shift of the K∗(892)0Breit-Wigner function around the corresponding pole mass. In all previous determinations of the differential branching fraction of B0→K∗(892)0µ+µ−decays [21–25], the K∗(892)0was selected by requiring a window of size 80–380 MeV/c2around the known K∗(892)0mass, but no correction was made for the scalar fraction. This fraction was assumed to be small and was treated as a systematic uncertainty. The measurements of the differential branching fraction of B0→K∗(892)0µ+µ−decays are included in global analyses of b→s `+`−processes. As these analyses make use of theory predictions which are made purely for the resonant P-wave part of the K+π−system, an accurate assessment of the S-wave component in B0→K∗0µ+µ−decays is critical. In this paper, the first measurement of FSin B0→K∗0µ+µ−decays is presented. The measurement is performed through a fit to the kaon helicity angle [21,26], θK, and the mKπ spectrum, in the range 644 < mKπ <1200 MeV/c2. Motivated by previous estimates of the S-wave fraction [18–21], FSis also determined in a narrower window of 796 < mKπ <996 MeV/c2. The values of FSare reported in eight bins of q2 of approximately 2 GeV2 /c4width, and in two larger bins 1.1< q2<6.0 GeV2 /c4and 15.0< q2<19.0 GeV2 /c4. The choice of q2bins is identical to that of ref. [27]. The measurements of FSallow the determination of the differential branching fraction of the B0→K∗(892)0µ+µ−decay. The differential branching fraction is determined by normalising the B0→K∗(892)0µ+µ−yield in each q2bin to the total event yield of the B0→J/ψ K∗0control channel, where the J/ψ →µ+µ−decay mode is used. The measurements are made using a pp-collision data sample recorded by the LHCb experiment in Run 1, corresponding to an integrated luminosity of 3 fb−1. These data were collected at centre-of-mass energies of 7 and 8 TeV during 2011 and 2012 respectively. The differential branching fraction measurement is complementary to the angular analysis presented in ref. [27], and supersedes that of ref. [21]. The latter analysis was performed on a 1 fb−1 subset of the Run 1 data sample. This paper is organised as follows. Section 2describes the angular and mKπ distributions of B0→K∗0µ+µ−decays with the K+π−system in a P- or S-wave state. Section 3 describes the LHCb detector and the procedure used to generate simulated data. The 1Inclusion of charge conjugate processes is implied throughout this paper unless otherwise noted. – 2 – JHEP11(2016)047 reconstruction and selection of B0→K+π−µ+µ−candidates are described in section 4. Section 5describes the parameterisation of the mass distributions and section 6describes the determination of FS, including the method used to correct for the detection and selection biases. The measurement of the differential branching fraction of B0→K∗(892)0µ+µ− decays is presented in section 7. The systematic uncertainties affecting the measurements are discussed in section 8. Finally, the conclusions are presented in section 9. 2 The angular distribution and FS The final state of the B0→K∗0µ+µ−decay is completely described by q2, and the three decay angles, ~ Ω≡(cos θK,cos θ`, φ) [21]. The angle between the µ+(µ−) and the direction opposite to that of the B0(B0) meson in the rest frame of the dimuon system is denoted by θ`. The angle between the direction of the K+(K−) and the B0(B0) meson in the rest frame of the K∗0(K∗0) is denoted by θK. The angle between the plane defined by the dimuon pair and the plane defined by the kaon and pion in the B0(B0) rest frame is denoted by φ. In the limit that the dimuon mass is large compared to the mass of the muons (q24m2 µ), this choice of the angular basis allows the differential decay rates of B0→K∗0µ+µ−and B0→K∗0µ+µ−decays to be written as d5(Γ + Γ) dmKπdq2d~ Ω=9 32πh(Is 1+¯ Is 1) sin2θK(1 + 3 cos 2θ`)+(Ic 1+¯ Ic 1) cos2θK(1 −cos 2θ`) + + (I3+¯ I3) sin2θKsin2θ`cos 2φ+ (I4+¯ I4) sin 2θKsin 2θ`cos φ+ +(I5+¯ I5) sin 2θKsin θ`cos φ+ (I6s+¯ I6s) sin2θKcos θ`+ +(I7+¯ I7) sin 2θKsin θ`sin φ+ (I8+¯ I8) sin 2θKsin 2θ`sin φ+ +(I9+¯ I9) sin2θKsin2θ`sin 2φ+ (I10 +¯ I10)(1 −cos 2θ`) + (2.1) +(I11 +¯ I11) cos θK(1 −cos 2θ`) + (I14 +¯ I14) sin θKsin 2θ`cos φ+ (I15 +¯ I15) sin θKsin θ`cos φ+ +(I16 +¯ I16) sin θKsin θ`sin φ+ (I17 +¯ I17) sin θKsin 2θ`sin φi, where Γ and Γ denote the decay rates of the B0and B0respectively. The 15 coefficients Ij(¯ Ij) are bilinear combinations of the K∗0(K∗0) decay amplitudes and vary with q2and mKπ. The numbering of the coefficients follows the convention used in ref. [27]. Coefficients Ijwith j≤9 involve P-wave amplitudes only, coefficient I10 involves S-wave amplitudes only and coefficients with 11 ≤j≤17 describe the interference between P- and S-wave amplitudes [28]. The polarity of the LHCb dipole magnet, discussed in section 3, is reversed periodically. Coupled with the fact that B0and B0decays are studied simultaneously, this results in a symmetric detection efficiency in φ. Therefore, the angular distribution is simplified by – 3 – JHEP11(2016)047 performing a transformation of the φangle such that φ0=(φ+πif φ < 0 φotherwise,(2.2) which results in the cancellation of terms in eq. (2.1) that have a sin φor cos φdependence. The remaining Ijand ¯ Ijcoefficients can be written in terms of the decay amplitudes given in ref. [27]. Defining ~ Ω0≡(cos θK,cos θ`, φ0), the resulting differential decay rate has the form d5(Γ + Γ) dmKπdq2d~ Ω0=1 4πGS|fLASS(mKπ)|2(1 −cos 2θ`) + +3 4πG0 P|fBW(mKπ)|2cos2θK(1 −cos 2θ`) + +√3 2πRe GRe SP +iGIm SPfLASS(mKπ)f∗ BW(mKπ)cos θK(1 −cos 2θ`)+ +9 16πG⊥k P|fBW(mKπ)|2sin2θK1 + 1 3cos 2θ`+ (2.3) +3 8πS3(G0 P+G⊥k P)|fBW(mKπ)|2sin2θKsin2θ`cos 2φ0+ +3 2πAFB(G0 P+G⊥k P)|fBW(mKπ)|2sin2θKcos θ`+ +3 4πS9(G0 P+G⊥k P)|fBW(mKπ)|2sin2θKsin2θ`sin 2φ0, where fBW(mKπ) denotes the mKπ dependence of the resonant P-wave component, which is modelled using a relativistic Breit-Wigner function. The S-wave component is modelled using the LASS parameterisation [29], fLASS(mKπ). The exact definitions of the P- and S-wave line shapes are given in appendix A. The real-valued coefficients GS,GRe SP,GIm SP, G0 Pand G⊥k Pare bilinear combinations of the q2-dependent parts of the K∗0(K∗0) helicity amplitudes AL,R i(q2) (AL,R i(q2)) and are given by GS=|AL S(q2)|2+|AR S(q2)|2+|AL S(q2)|2+|AR S(q2)|2, GRe SP +iGIm SP =AL SAL∗ 0+AR SAR∗ 0+AL SAL∗ 0+AR SAR∗ 0, G0 P=|AL 0(q2)|2+|AR 0(q2)|2+|AL 0(q2)|2+|AR 0(q2)|2,(2.4) G⊥k P=X i=⊥,k|AL i(q2)|2+|AR i(q2)|2+|AL i(q2)|2+|AR i(q2)|2, where Land Rdenote the (left- and right-handed) chiralities of the dimuon system. These coefficients are determined through the extended maximum likelihood fit described in section 6.2. The coefficients S3,AFB and S9are CP-averaged observables that are defined in ref. [27]. The integral of eq. (2.3) with respect to cos θ`and φ0is independent of these observables. However, detection effects that are either asymmetric or non-uniform in cos θ` and φ0introduce a residual dependence on these observables. In this analysis, S3,AFB and – 4 – JHEP11(2016)047 S9are set to their measured values [27]. The systematic uncertainty associated with this choice is negligible. Using the definitions of eq. (2.4), the S-wave fraction FSin the range a<mKπ < b can be determined from the coefficients GSand G0,⊥k P, through FS|b a=GSRb admKπ |fLASS(mKπ)|2 GSRb admKπ |fLASS(mKπ)|2+G0 P+G⊥k PRb admKπ |fBW(mKπ)|2.(2.5) 3 Detector and simulation The LHCb detector [30,31] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of particles containing bor cquarks. The detector includes a high-precision tracking system divided into three sub-systems: a silicon-strip vertex detector surrounding the pp interaction region, a large-area silicon-strip detector that is 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 situated downstream of the magnet. The tracking system provides a measurement of the momentum, p, of charged particles with a relative uncertainty that varies from 0.5% at low momentum to 1.0% at 200 GeV/c. The minimum distance of a track to a primary vertex (PV), the impact parameter, 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 (RICH) detectors. Photons, electrons and hadrons are identified by a calorimeter system consisting of scintillatingpad and preshower detectors, an electromagnetic calorimeter and a hadronic calorimeter. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers. The online event selection is performed by a trigger [32], which 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. A large sample of simulated events is used to determine the effect of the detector geometry, trigger, and the selection criteria on the angular distribution of the signal, and to determine the ratio of efficiencies between the signal and the B0→J/ψ K∗0normalisation mode. In the simulation, pp collisions are generated using Pythia [33,34] with a specific LHCb configuration [35]. The decay of the B0meson is described by EvtGen [36], which generates final-state radiation using Photos [37]. As described in ref. [38], the Geant4 toolkit [39,40] is used to implement the interaction of the generated particles with the detector and the detector response. Data-driven corrections are applied to the simulation following the procedure of ref. [27]. These corrections account for the small level of mismodelling of the detector occupancy, the B0momentum and vertex quality, and the particle identification (PID) performance. 4 Selection of signal candidates The B0→K∗0µ+µ−signal candidates are first required to pass the hardware trigger, which selects events containing at least one muon with transverse momentum pT>1.48 GeV/c in – 5 – JHEP11(2016)047 the 7 TeV data or pT>1.76 GeV/c in the 8 TeV data. In the subsequent software trigger, at least one of the final-state particles is required to have pT>1.7 GeV/c in the 7 TeV data or pT>1.6 GeV/c in the 8 TeV data, unless the particle is identified as a muon in which case pT>1.0 GeV/c is required. The final-state particles that satisfy these transverse momentum criteria are also required to have an impact parameter larger than 100 µm with respect to all PVs in the event. Finally, the tracks of two or more of the final-state particles are required to form a vertex that is significantly displaced from the PVs. Signal candidates are formed from a pair of oppositely charged tracks that are identified as muons, combined with a K∗0meson candidate. The K∗0candidate is formed from two oppositely charged tracks that are identified as a kaon and a pion. These signal candidates are required to pass a set of loose preselection requirements, which are identical to those described in ref. [27], with the exception that the K∗0candidate is required to have an invariant mass in the wider 644 < mKπ <1200 MeV/c2range. The preselection requirements exploit the decay topology of B0→K∗0µ+µ−transitions and restrict the data sample to candidates with good quality vertex and track fits. Candidates are required to have a reconstructed B0invariant mass (mKπµµ) in the range 5170 < mKπµµ <5780 MeV/c2. The backgrounds formed by combining particles from different b- and c-hadron decays are referred to as combinatorial. Such backgrounds are suppressed with the use of a Boosted Decision Tree (BDT) [41,42]. The BDT used for the present analysis is identical to that described in ref. [27] and the same working point is used. The BDT selection has a signal efficiency of 90% while removing 95% of the combinatorial background surviving the preselection. The efficiency of the BDT is uniform with respect to mKπµµ in the above mass range. Specific background processes can mimic the signal if their final states are misidentified or misreconstructed. The requirements of ref. [27] are reassessed and found to reduce the sum of all backgrounds from such decay processes to a level of less than 2% of the expected signal yield. The only requirement that is modified in the present analysis is that responsible for removing genuine B0→K∗0µ+µ−decays, where the track of the genuine pion is reconstructed with the kaon hypothesis and vice versa. These misidentified signal candidates occur more often in the wider mKπ window used for the present analysis, and are reduced by tightening the requirements made on the kaon and pion PID information provided by the RICH detectors. After the application of all the selection criteria, this specific background process is reduced to less than 1% of the level of the signal. 5 The K+π−µ+µ−and K+π−mass distributions The K+π−µ+µ−invariant mass is used to discriminate between signal and background. The distribution of the signal candidates is modelled using the sum of two Gaussian functions with a common mean, each with a power law tail on the lower side. The parameters describing this model are determined from fits to B0→J/ψ K∗0data in a q2range 9.22 < q2<9.96 GeV2 /c4and with an mKπ range of 644 < mKπ <1200 MeV/c2, shown in the left hand plot of figure 1. These parameters are fixed for the subsequent fits to the B0→ K∗0µ+µ−candidates in the same mKπ range. In samples of simulated B0→K∗0µ+µ− decays, the mKπµµ resolution is observed to differ from that in B0→J/ψ K∗0decays by 2 – 6 – JHEP11(2016)047 ] 2 c [MeV/ µµπ K m 5200 5400 5600 2 cCandidates / 15 MeV/ 0 50 100 3 10× LHCb *0 K ψ /J→ 0 B ] 2 c [MeV/ µµπ K m 5200 5400 5600 2 cCandidates / 15 MeV/ 0 500 1000 LHCb - µ + µ *0 K→ 0 B Figure 1. Invariant mass mKπµµ of (left) the B0→J/ψK∗0decay and (right) the signal decay B0→K∗0µ+µ−integrated over the q2regions described in the text. The individual signal (blue shaded area) and background (red hatched area) components are shown. The solid line denotes the total fitted distribution. to 8% depending on q2. A correction factor is therefore derived from the simulation and is applied to the widths of the Gaussian functions in the different q2bins. In the fits to B0→J/ψ K∗0decays, an additional component is included to account for the B0 s→J/ψ K∗0 process. The size of this additional component is taken to be 0.8% of the B0→J/ψK∗0 signal [43]. The fit to the B0→J/ψK∗0mode gives 389 577 ±649 decays. In the fits to B0→K∗0µ+µ−decays, shown in the right hand plot of figure 1, the B0 s→K∗0µ+µ− contribution is neglected. The systematic uncertainty related to ignoring this background process is negligible. For both B0→J/ψK∗0and B0→K∗0µ+µ−decays, the combinatorial background in the K+π−µ+µ−invariant mass spectrum is described by an exponential function. The B0→K∗0µ+µ−yield integrated over the q2ranges 0.1< q2<8.0 GeV2 /c4, 11.0< q2<12.5 GeV2 /c4and 15.0< q2<19.0 GeV2 /c4is determined to be 2593 ±60. The q2regions 8.0< q2<11.0 GeV2 /c4and 12.5< q2<15.0 GeV2 /c4are dominated by the contributions from B0→J/ψ K∗0and B0→ψ(2S)K∗0decays respectively and are therefore excluded in the fits to the signal B0→K∗0µ+µ−decays. As discussed in section 2, the K+π−invariant mass distribution of the signal candidates is modelled with two distributions. A relativistic Breit-Wigner function is used for the P-wave component and the LASS parameterisation for the S-wave component. The parameters of these functions are fixed to the values determined in B0→J/ψ K∗0decays using the model described in ref. [44]. A systematic uncertainty is assigned for this choice. The K+π−invariant mass distribution of the combinatorial background is modelled using an empirical threshold function of the form fbkg(mKπ)=(mKπ −mthr)1/α,(5.1) where mthr = 634 MeV/c2is given by the sum of the pion and kaon masses [45], and αis a parameter determined from fits to the data. This model has been validated on data from the upper mKπµµ sideband, defined as 5350 < mKπµµ <5780 MeV/c2, where no resonant structure in the mKπ spectrum is observed. – 7 – JHEP11(2016)047 0 0.2 0.4 0.6 0.8 K θ cos 1−0.5−0 0.5 1 ] 4 c/ 2 [GeV 2 q 5 10 15 LHCb simulation 0 0.2 0.4 0.6 0.8 ] 2 c [GeV/ π K m 800 1000 1200 ] 4 c/ 2 [GeV 2 q 5 10 15 LHCb simulation Figure 2. Two-dimensional projections of the efficiency (left) in the cos θK–q2plane and (right) in the mKπ–q2plane, determined from a principal moments analysis of simulated four-body B0→K+π−µ+µ−phase-space decays. The colour scale denotes the efficiency in arbitrary units. The lack of entries in the top right corner of the mKπ–q2distribution is due to the limited phase space available in the decay of the B0meson. 6 Determination of the S-wave fraction 6.1 Efficiency correction The trigger, selection, and detector geometry bias the distributions of the decay angles cos θK, cos θ`,φ0, as well as the q2and mKπ distributions. The dominant sources of bias are the geometrical acceptance of the detector and the requirements on the track momentum, the impact parameter, and the PID of the hadrons. The method for obtaining the efficiency correction, described in ref. [27], is extended to also include the mKπ dimension. The detection efficiency is expressed in terms of orthonormal Legendre polynomials of order n,Pn(x), as (q2, mKπ,~ Ω0) = X g,h,i,j,k cghijkPg(mKπ)Ph(cos θ`)Pi(cos θK)Pj(φ0)Pk(q2).(6.1) As the polynomials are orthonormal over the domain x∈[−1,1], the observables mKπ,φ0, and q2are linearly transformed to lie within this domain when evaluating the efficiency. The sum in eq. (6.1) runs up to 5th order for cos θKand φ0, and up to 8th, 7th and 6th order for cos θ`,q2and mKπ respectively. The coefficients cghijk are determined using a principal moment analysis of simulated four-body B0→K+π−µ+µ−phase-space decays. Two-dimensional projections of the detection efficiency as a function of cos θK–q2and mKπ–q2are shown in figure 2. 6.2 Fit to the mass and angular distributions An extended maximum likelihood fit to mKπµµ,mKπ and cos θKis performed in each bin of q2in order to determine the coefficients GS,GRe SP,GIm SP and G⊥k Paveraged over the q2bin. Given these coefficients, the S-wave fraction FSis extracted using eq. (2.5). The angular distribution of the signal is described by eq. (2.3) multiplied by the efficiency model – 8 – JHEP11(2016)047 dominant. The effect of neglecting a possible D-wave K+π−component, arising from the tail of the K∗ 2(1430)0, is also assessed and found to be negligible. 8.2 Systematic uncertainties on the differential branching fraction Systematic uncertainties affecting the differential branching fraction predominantly arise through: the knowledge of R, the ratio of the reconstruction and selection efficiencies described in section 7; the uncertainty of the branching fraction of the decay B0→J/ψ K∗0, which is shown as a separate systematic uncertainty in table 2; and systematic uncertainties related to the determination of FS, which are propagated to the differential branching fraction measurement. The imperfect knowledge of the B→K∗form-factor model used in the generation of the B0→K∗0µ+µ−simulated sample affects the determination of the ratio of efficiencies R. A systematic uncertainty is therefore assessed by weighting simulated events to account for the variations between the models described in refs. [50] and [54]. As described in section 8.1, after all corrections to the simulation are applied, a small difference remains in the momentum spectrum of the pions between simulated and genuine B0→J/ψ K∗0decays. The ratio R, and consequently dB/dq2, is therefore calculated by weighting the simulated B0→K∗(892)0µ+µ−and B0→J/ψ K∗(892)0decays to account for the observed differences. Other sources of systematic uncertainties affecting the determination of the signal yield, such as the choice of model to describe the mKπµµ distribution of the signal and the background components, the choice of the mKπ and cos θKmodels to describe the background, and the effect of residual specific backgrounds, are found to be negligible. 9 Conclusions This paper presents the first measurement of the S-wave fraction in the K+π−system of B0→K∗0µ+µ−decays using a data sample corresponding to an integrated luminosity of 3 fb−1collected at the LHCb experiment. Accounting for the measured S-wave fraction in the wide mKπ region, the first measurement of the P-wave component of the differential branching fraction of B0→K∗(892)0µ+µ−decays is reported in bins of q2. All previous measurements of the differential branching fraction have compared the combination of S- and P-wave components to the theory prediction, which is made purely for the resonant P- wave part of the K+π−system. The measurements of the S-wave fraction presented in this paper are compatible with theory predictions [18–20] and support previous estimates [21]. In the absence of any previous measurement, such estimates have been used to assign a systematic uncertainty for a possible S-wave component [21]. The measurements of the S- wave fraction presented in this paper allow these estimates to be replaced with an accurate assessment of the scalar component in B0→K∗0µ+µ−decays. The resulting measurements of the differential branching fraction of B0→K∗(892)0µ+µ−decays are the most precise to date and are in good agreement with the SM predictions. – 15 – JHEP11(2016)047 Acknowledgments We would like to thank Gudrun Hiller and Martin Jung for useful discussions regarding the treatment of the K+π−system. 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); NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy); FOM and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES and FANO (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). A The mKπ distribution of the signal The K+π−invariant mass distribution of the signal candidates is modelled by two distributions. For the P-wave component, a relativistic Breit-Wigner function is used, given by fBW(mKπ) = pkp k k892 B0 1(k, k892, d)B0 0(p, p892, d) m2 Kπ −m2 892 −im892Γ892(mKπ),(A.1) where √kp is the phase-space factor, Γ892(mKπ) is given by Γ892(mKπ)=Γ892B02 1(k, k892, d)k k892 3m892 mKπ ,(A.2) and B0are Blatt-Weisskopf barrier factors as defined in ref. [45]. The parameter dis the meson radius parameter and is set to 1.6 GeV−1c[44]. The systematic uncertainty associated with the choice of this value is negligible. The parameters m892 and Γ892 are the pole mass and width of the K∗(892)0resonance, and k(p) is the momentum of the K+ (K∗0) in the rest frame of the K∗0(B0) evaluated at a given mKπ. The parameters k892 and p892 are the values of kand pevaluated at the pole mass of the K∗(892)0resonance. In eq. (A.1), the orbital angular momentum between the K∗(892)0and the dimuon system is considered to be zero. The inclusion of a higher orbital angular momentum component has a negligible effect on the measurements. – 16 – JHEP11(2016)047 The S-wave component of the signal is modelled using the LASS parameterisation [29], given by fLASS(mKπ) = pkpB0 1(k, k1430, d)k k1430  1 cot δB−i+e2iδB1 cot δR−i,(A.3) where k1430 is the momentum of the K∗0in the B0rest frame, evaluated at the pole mass of the K∗ 0(1430)0resonance. The terms cot δBand cot δRare given by cot δB=1 ak +rk 2(A.4) and cot δR=m2 1430 −m2 Kπ m1430Γ1430(mKπ),(A.5) with the running width Γ1430(mKπ) in turn given by Γ1430(mKπ)=Γ1430 k k1430 m1430 mKπ .(A.6) The parameters m1430 and Γ1430 are the pole mass and width of the K∗ 0(1430)0resonance, and k1430 is the momentum of the kaon in the K∗0rest frame, evaluated at the pole mass of the K∗ 0(1430)0resonance. The second term of eq. (A.3) is equivalent to a Breit-Wigner function for the K∗ 0(1430)0. The first term of eq. (A.3) contains two empirical parameters {a, r}. These parameters are fixed to the values a= 3.83 GeV/c−1and r= 2.86 GeV/c−1, determined in B0→J/ψ K∗0decays using the model described in ref. [44]. In order to assess the systematic effect of this choice, these parameters are also fixed to values from the LASS experiment, a= 1.94 GeV/c−1and r= 1.76 GeV/c−1. The resulting systematic uncertainty is found to be negligible. B Likelihood fit projections Figures 6–9show the projections of the fitted probability density function on mKπµµ,mKπ and cos θK. Figure 6shows the wider q2bins of 1.1< q2<6.0 GeV2 /c4and 15.0< q2< 19.0 GeV2 /c4, figures 7–9show the mKπµµ,mKπ and cos θKprojections respectively for the finer q2bins. In all figures, the solid line denotes the total fitted distribution. The individual components, signal (blue shaded area) and background (red hatched area), are also shown. – 17 – JHEP11(2016)047 ] 2 c [MeV/ µµπ K m 5200 5400 5600 2 cCandidates / 15 MeV/ 0 100 200 300 LHCb 4 c/ 2 < 6.0 GeV 2 q1.1 < ] 2 c [MeV/ µµπ K m 5200 5400 5600 2 cCandidates / 15 MeV/ 0 100 200 300 LHCb 4 c/ 2 < 19.0 GeV 2 q15.0 < ] 2 c [MeV/ π K m 800 1000 1200 2 cCandidates / 28 MeV/ 0 100 200 300 LHCb 4 c/ 2 < 6.0 GeV 2 q1.1 < ] 2 c [MeV/ π K m 800 1000 1200 2 cCandidates / 28 MeV/ 0 100 200 300 400 LHCb 4 c/ 2 < 19.0 GeV 2 q15.0 < K θ cos 1−0.5−0 0.5 1 Candidates / 0.1 0 50 100 150 LHCb 4 c/ 2 < 6.0 GeV 2 q1.1 < K θ cos 1−0.5−0 0.5 1 Candidates / 0.1 0 20 40 60 80 LHCb 4 c/ 2 < 19.0 GeV 2 q15.0 < Figure 6. Angular and mass distributions for the q2bins 1.1< q2<6.0 GeV2 /c4(left) and 15.0< q2<19.0 GeV2 /c4(right). The distributions of cos θKand mKπ are shown for candidates in the signal mKπµµ window of ±50 MeV/c2around the known B0mass. – 18 – JHEP11(2016)047 ] 2 c [MeV/ µµπ K m 5200 5400 5600 2 cCandidates / 15 MeV/ 0 50 100 150 LHCb 4 c/ 2 < 0.98 GeV 2 q0.10 < ] 2 c [MeV/ µµπ K m 5200 5400 5600 2 cCandidates / 15 MeV/ 0 50 100 LHCb 4 c/ 2 < 2.5 GeV 2 q1.1 < ] 2 c [MeV/ µµπ K m 5200 5400 5600 2 cCandidates / 15 MeV/ 0 50 100 LHCb 4 c/ 2 < 4.0 GeV 2 q2.5 < ] 2 c [MeV/ µµπ K m 5200 5400 5600 2 cCandidates / 15 MeV/ 0 50 100 150 LHCb 4 c/ 2 < 6.0 GeV 2 q4.0 < ] 2 c [MeV/ µµπ K m 5200 5400 5600 2 cCandidates / 15 MeV/ 0 50 100 150 LHCb 4 c/ 2 < 8.0 GeV 2 q6.0 < ] 2 c [MeV/ µµπ K m 5200 5400 5600 2 cCandidates / 15 MeV/ 0 50 100 150 LHCb 4 c/ 2 < 12.5 GeV 2 q11.0 < ] 2 c [MeV/ µµπ K m 5200 5400 5600 2 cCandidates / 15 MeV/ 0 50 100 150 LHCb 4 c/ 2 < 17.0 GeV 2 q15.0 < ] 2 c [MeV/ µµπ K m 5200 5400 5600 2 cCandidates / 15 MeV/ 0 50 100 LHCb 4 c/ 2 < 19.0 GeV 2 q17.0 < Figure 7. The K+π−µ+µ−invariant mass distributions for the fine q2bins. – 19 – JHEP11(2016)047 ] 2 c [MeV/ π K m 800 1000 1200 2 cCandidates / 28 MeV/ 0 50 100 150 LHCb 4 c/ 2 < 0.98 GeV 2 q0.10 < ] 2 c [MeV/ π K m 800 1000 1200 2 cCandidates / 28 MeV/ 0 50 100 LHCb 4 c/ 2 < 2.5 GeV 2 q1.1 < ] 2 c [MeV/ π K m 800 1000 1200 2 cCandidates / 28 MeV/ 0 20 40 60 80 LHCb 4 c/ 2 < 4.0 GeV 2 q2.5 < ] 2 c [MeV/ π K m 800 1000 1200 2 cCandidates / 28 MeV/ 0 50 100 150 LHCb 4 c/ 2 < 6.0 GeV 2 q4.0 < ] 2 c [MeV/ π K m 800 1000 1200 2 cCandidates / 28 MeV/ 0 50 100 150 200 LHCb 4 c/ 2 < 8.0 GeV 2 q6.0 < ] 2 c [MeV/ π K m 800 1000 1200 2 cCandidates / 28 MeV/ 0 50 100 150 LHCb 4 c/ 2 < 12.5 GeV 2 q11.0 < ] 2 c [MeV/ π K m 800 1000 1200 2 cCandidates / 28 MeV/ 0 100 200 LHCb 4 c/ 2 < 17.0 GeV 2 q15.0 < ] 2 c [MeV/ π K m 800 1000 1200 2 cCandidates / 28 MeV/ 0 50 100 150 LHCb 4 c/ 2 < 19.0 GeV 2 q17.0 < Figure 8. The K+π−invariant mass distributions for the fine q2bins for candidates in the signal mKπµµ window of ±50 MeV/c2around the known B0mass. – 20 – JHEP11(2016)047 K θ cos 1−0.5−0 0.5 1 Candidates / 0.1 0 10 20 30 40 LHCb 4 c/ 2 < 0.98 GeV 2 q0.10 < K θ cos 1−0.5−0 0.5 1 Candidates / 0.1 0 10 20 30 40 LHCb 4 c/ 2 < 2.5 GeV 2 q1.1 < K θ cos 1−0.5−0 0.5 1 Candidates / 0.1 0 10 20 30 40 LHCb 4 c/ 2 < 4.0 GeV 2 q2.5 < K θ cos 1−0.5−0 0.5 1 Candidates / 0.1 0 20 40 60 LHCb 4 c/ 2 < 6.0 GeV 2 q4.0 < K θ cos 1−0.5−0 0.5 1 Candidates / 0.1 0 20 40 60 LHCb 4 c/ 2 < 8.0 GeV 2 q6.0 < K θ cos 1−0.5−0 0.5 1 Candidates / 0.1 0 10 20 30 40 LHCb 4 c/ 2 < 12.5 GeV 2 q11.0 < K θ cos 1−0.5−0 0.5 1 Candidates / 0.1 0 20 40 LHCb 4 c/ 2 < 17.0 GeV 2 q15.0 < K θ cos 1−0.5−0 0.5 1 Candidates / 0.1 0 10 20 30 LHCb 4 c/ 2 < 19.0 GeV 2 q17.0 < Figure 9. 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