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

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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

CERN-EP-2016-141 LHCb-PAPER-2016-012 15 June 2016

Measurements of the S-wave fraction in

B

0

→ K

+

π

µ

+

µ

decays and the

B

0

→ K

(892)

0

µ

+

µ

differential branching

fraction

The LHCb collaboration†

Abstract

A measurement of the differential branching fraction of the decay

B0 → K∗(892)0µ+µis presented together with a determination of the

S-wave fraction of the K+πsystem in the decay B0 → K+πµ+µ. The analysis

is based on pp-collision data corresponding to an integrated luminosity of 3 fb−1

collected 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 q2 region 1.1 < q2 < 6.0 GeV2/c4. In this q2 region, for the K+π− invariant

mass range 796 < mKπ < 996 MeV/c2, the S-wave fraction of the K+π− system in

B0 → K+πµ+µdecays is found to be

FS = 0.101 ± 0.017(stat) ± 0.009(syst),

and the differential branching fraction of B0 → K∗(892)0µ+µdecays is determined

to be

dB/dq2 = (0.342+0.017−0.017(stat) ± 0.009(syst) ± 0.023(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.

Published in JHEP 11 (2016) 047

c

CERN on behalf of the LHCb collaboration, licence CC-BY-4.0.

Authors are listed at the end of this paper.

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1

Introduction

The decay B0→ K∗0µ+µproceeds 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].

In this paper, the symbol K∗0 denotes any neutral strange meson in an excited state that decays to a K+ and a π.1 For invariant masses of the K+πsystem in the range

considered in this analysis, the K∗0 decay products are predominantly found in a P- or S-wave state. The fractional size of the scalar (S-S-wave) component of the K+πsystem (F

S)

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 q2 range

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)0 Breit–Wigner function around the corresponding pole mass.

In all previous determinations of the differential branching fraction of B0→ K∗(892)0µ+µdecays [21–25], the K(892)0 was selected by requiring a window of

size 80–380 MeV/c2 around the known K(892)0 mass, but no correction was made for the

scalar fraction. This fraction was assumed to be small and was treated as a systematic un-certainty. 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+µdecays is

critical.

In this paper, the first measurement of FS in 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

pre-vious estimates of the S-wave fraction [18–21], FS is also determined in a narrower

window of 796 < mKπ < 996 MeV/c2. The values of FS are reported in eight bins of q2

of approximately 2 GeV2/c4 width, and in two larger bins 1.1 < q2 < 6.0 GeV2/c4 and 15.0 < q2 < 19.0 GeV2/c4. The choice of q2 bins is identical to that of Ref. [27].

The measurements of FS allow 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+µyield in each q2 bin to the total event yield of

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the B0→ J/ψ K∗0 control channel, where the J/ψ → µ+µdecay 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 2 describes the angular and mKπdistributions

of B0 → K∗0µ+µdecays with the K+πsystem in a P- or S-wave state. Section 3

describes the LHCb detector and the procedure used to generate simulated data. The reconstruction and selection of B0→ K+πµ+µcandidates are described in Sec. 4.

Section 5 describes the parameterisation of the mass distributions and Sec. 6 describes 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 Sec. 7. The systematic uncertainties affecting the measurements are discussed in Sec. 8. Finally, the conclusions are presented in Sec. 9.

2

The angular distribution and F

S

The final state of the B0→ K∗0µ+µdecay 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+µand B0→ K∗0µ+µdecays to be written as

d5(Γ + Γ) dmKπdq2d~Ω = 9 32π h (I1s+ ¯I1s) sin2θK(1 + 3 cos 2θ`) + (I1c+ ¯I c 1) cos 2 θK(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`) +

(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 φ

i ,

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where Γ and Γ denote the decay rates of the B0 and B0 respectively. The 15 coefficients Ij ( ¯Ij) are bilinear combinations of the K∗0 (K∗0) decay amplitudes and vary with q2

and mKπ. The numbering of the coefficients follows the convention used in Ref. [27].

Coefficients Ij with 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 Sec. 3, is reversed periodically. Coupled with the fact that B0 and B0 decays are studied simultaneously, this results in a

symmetric detection efficiency in φ. Therefore, the angular distribution is simplified by performing a transformation of the φ angle such that

φ0 = (

φ + π if φ < 0

φ otherwise, (2)

which results in the cancellation of terms in Eq. 1 that have a sin φ or cos φ dependence. The remaining Ij and ¯Ij coefficients 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 4πG 0 P|fBW(mKπ)|2cos2θK(1 − cos 2θ`) + √ 3 2πRe 

GReSP+ iGImSP fLASS(mKπ)fBW∗ (mKπ) cos θK(1 − cos 2θ`) +

9 16πG ⊥k P |fBW(mKπ)|2sin2θK  1 + 1 3cos 2θ`  + 3 8πS3(G 0 P+ G ⊥k P ) |fBW(mKπ)| 2

sin2θKsin2θ`cos 2φ0+

3 2πAFB(G 0 P+ G ⊥k P ) |fBW(mKπ)| 2 sin2θKcos θ`+ 3 4πS9(G 0 P+ G ⊥k P ) |fBW(mKπ)| 2

sin2θKsin2θ`sin 2φ0,

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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, GImSP,

G0

P and G ⊥k

P are bilinear combinations of the q2-dependent parts of the K

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amplitudes AL,Ri (q2) (AL,R

i (q2)) and are given by

GS = |ALS(q2)|2+ |ARS(q2)|2+ |ALS(q2)|2+ |ARS(q2)|2, GReSP+ iGImSP = ALSAL∗0 + ARSAR∗0 + ALSAL∗0 + ARSAR∗0 , G0P = |AL0(q2)|2+ |AR0(q2)|2+ |AL0(q2)|2+ |AR0(q2)|2, (4) G⊥kP = X i=⊥,k |ALi (q2)|2+ |ARi (q2)|2 + |ALi (q2)|2+ |ARi (q2)|2,

where L and R denote the (left- and right-handed) chiralities of the dimuon system. These coefficients are determined through the extended maximum likelihood fit described in Sec. 6.2. The coefficients S3, AFB and S9 are CP -averaged observables that are defined

in Ref. [27]. The integral of Eq. 3 with respect to cos θ` and φ0 is independent of these

observables. However, detection effects that are either asymmetric or non-uniform in cos θ`

and φ0 introduce a residual dependence on these observables. In this analysis, S3, AFB

and S9 are set to their measured values [27]. The systematic uncertainty associated with

this choice is negligible.

Using the definitions of Eq. 4, the S-wave fraction FS in the range a < mKπ < b can

be determined from the coefficients GS and G0,⊥kP , through

FS|ba= GS RabdmKπ|fLASS(mKπ)| 2 GS Rb a dmKπ|fLASS(mKπ)| 2 +  G0 P+ G ⊥k P  Rb a dmKπ|fBW(mKπ)| 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 b or c quarks. 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 pT is 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 scintillating-pad 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

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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∗0 normalisation

mode. In the simulation, pp collisions are generated using Pythia [33] with a specific LHCb configuration [34]. The decay of the B0 meson is described by EvtGen [35], which generates final-state radiation using Photos [36]. As described in Ref. [37], the Geant4 toolkit [38] 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 B0 momentum and vertex quality, and the

particle identification (PID) performance.

4

Selection of signal candidates

The B0→ K∗0µ+µsignal 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

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∗0 meson candidate. The K∗0 candidate 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∗0 candidate is required to have an invariant mass in the wider 644 < mKπ < 1200 MeV/c2 range. The preselection

requirements exploit the decay topology of B0→ K∗0µ+µtransitions and restrict the

data sample to candidates with good quality vertex and track fits. Candidates are required to have a reconstructed B0 invariant mass (m

Kπµµ) 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) [39, 40]. 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

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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+µdecays, 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+πµ+µinvariant 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∗0 data in a q2

range 9.22 < q2 < 9.96 GeV2/c4 and with an mKπ range of 644 < mKπ < 1200 MeV/c2,

shown in Fig. 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∗0 decays by 2 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 q2 bins. In the fits to B0→ J/ψ K∗0

decays, an additional component is included to account for the B0s→ J/ψ K∗0process. The

size of this additional component is taken to be 0.8% of the B0→ J/ψ K∗0 signal [41]. The

fit to the B0→ J/ψ K∗0 mode gives 389 577 ± 649 decays. In the fits to B0→ K∗0µ+µ

decays, the B0s→ K∗0µ+µcontribution is neglected. The systematic uncertainty related to

ignoring this background process is negligible. For both B0→ J/ψ K∗0 and B0→ K∗0µ+µ

decays, the combinatorial background in the K+πµ+µinvariant mass spectrum is

described by an exponential function. The B0→ K∗0µ+µyield integrated over the q2

ranges 0.1 < q2 < 8.0 GeV2/c4, 11.0 < q2 < 12.5 GeV2/c4 and 15.0 < q2 < 19.0 GeV2/c4 is

determined to be 2593 ± 60. The q2 regions 8.0 < q2 < 11.0 GeV2/c4 and 12.5 < q2 <

15.0 GeV2/c4 are dominated by the contributions from B0→ J/ψ K∗0 and B0→ ψ(2S)K∗0

decays respectively and are therefore excluded in the fits to the signal B0→ K∗0µ+µ

decays.

As discussed in Sec. 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∗0 decays

using the model described in Ref. [42]. A systematic uncertainty is assigned for this choice. The K+πinvariant mass distribution of the combinatorial background is modelled

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] 2 c [MeV/ µ µ π K m 5200 5400 5600 2c Candidates / 15 MeV/ 0 50 100 3 10 × LHCb *0 K ψ / J → 0 B ] 2 c [MeV/ µ µ π K m 5200 5400 5600 2c Candidates / 15 MeV/ 0 500 1000 LHCb -µ + µ *0 K → 0 B

Figure 1: Invariant mass mKπµµ of (left) the B0→ J/ψ K∗0decay and (right) the signal decay

B0→ K∗0µ+µ− integrated over the q2 regions 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.

using an empirical threshold function of the form

fbkg(mKπ) = (mKπ− mthr)1/α, (6)

where mthr= 634 MeV/c2 is given by the sum of the pion and kaon masses [43], and α is 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.

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 q2 and 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). (7)

As the polynomials are orthonormal over the domain x ∈ [−1, 1], the observables mKπ, φ0,

and q2 are linearly transformed to lie within this domain when evaluating the efficiency. The sum in Eq. 7 runs up to 5th order for cos θ

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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–q2 plane and (right)

in the mKπ–q2 plane, determined from a principal moments analysis of simulated four-body

B0→ K+πµ+µphase-space decays. The colour scale denotes the efficiency in arbitrary units.

The lack of entries in the top right corner of the mKπ–q2 distribution is due to the limited phase

space available in the decay of the B0 meson.

order for cos θ`, q2 and mKπ respectively. The coefficients cghijk are determined using a

principal moment analysis of simulated four-body B0→ K+πµ+µphase-space decays.

Two-dimensional projections of the detection efficiency as a function of cos θK–q2 and

mKπ–q2 are shown in Fig. 2.

6.2

Fit to the mass and angular distributions

An extended maximum likelihood fit to mKπµµ, mKπ and cos θK is performed in each bin

of q2 in order to determine the coefficients G

S, GReSP, GImSP and G ⊥k

P averaged over the q2

bin. Given these coefficients, the S-wave fraction FS is extracted using Eq. 5. The angular

distribution of the signal is described by Eq. 3 multiplied by the efficiency model evaluated at the centre of the q2 bin (q2

bc). Integrating over cos θ` and φ0 simplifies the fit, while

retaining the sensitivity to the parameters related to FS. The resulting angular and mKπ

distribution of the signal, Psig, within a bin qmin2 < q2 < q2max, is given by

Psig(mKπ, cos θK) = Z qmax2 q2 min Z π 0 Z 1 −1 dcos θ`dφ0dq2  d5(Γ + Γ) dmKπdq2d~Ω0 × (qbc2 , mKπ, ~Ω0)  , (8)

The overall scale of Psig is set by fixing the parameter G0Pto an arbitrary value. The mKπµµ

distribution of the signal is assumed to factorise with Psig(mKπ, cos θK). This assumption

is validated using simulated events.

The cos θK distribution of the combinatorial background is modelled with a second-order

polynomial where all parameters are allowed to vary in the fit. The mKπ, mKπµµand cos θK

distributions of the combinatorial background are assumed to factorise. This assumption has been validated on data from the upper mKπµµsideband. Figure 3 shows the projections

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] 2 c [MeV/ µ µ π K m 5200 5400 5600 2c Candidates / 15 MeV/ 0 100 200 300 LHCb 4 c / 2 < 6.0 GeV 2 q 1.1 < ] 2 c [MeV/ π K m 800 1000 1200 2c Candidates / 28 MeV/ 0 100 200 300 LHCb 4 c / 2 < 6.0 GeV 2 q 1.1 < 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 q 1.1 <

Figure 3: Angular and mass distributions for the q2 bin 1.1 < q2< 6.0 GeV2/c4. The distributions

of cos θK and mKπ are shown for candidates in the signal mKπµµwindow of ±50 MeV/c2 around

the known B0 mass. The solid line denotes the total fitted distribution. The individual

components, signal (blue shaded area) and background (red hatched area), are also shown.

of the probability distribution function on the angular and mass distributions for the q2

bin 1.1 < q2 < 6.0 GeV2/c4. Projections of other q2 bins are provided in Appendix B.

6.3

Result for F

S

Using Eq. 5, FS is determined in the full mKπ region of the fit, FS|1200644 , and in the

narrow mKπ region, FS| 996

796. The statistical uncertainty on FS is determined using the

following procedure. Values of the parameters of the fit are generated according to a multi-dimensional bifurcated Gaussian distribution. This distribution is constructed out of the correlation matrix of the fit and the asymmetric uncertainties obtained from a profile likelihood. For each generated set of parameters of the fit, a value of FS is

computed. The 68% confidence interval is defined by taking the 16th–84th percentiles of

the resulting distribution of FS. The correct coverage of this method is validated using

pseudoexperiments generated with a wide range of FS values.

Figure 4 shows the values of FS|1200644 and FS|996796 in each q2 bin. The uncertainties

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] 4 c / 2 [GeV 2 q 0 5 10 15 1200 644 |S F 0 0.1 0.2 0.3 0.4 LHCb ] 4 c / 2 [GeV 2 q 0 5 10 15 996 796 |S F 0 0.05 0.1 0.15 0.2 LHCb

Figure 4: Results for the S-wave fraction (FS) in bins of q2 in the range (left) 644 < mKπ <

1200 MeV/c2 and (right) 796 < mKπ< 996 MeV/c2. The uncertainties shown are the quadratic

sum of the statistical and systematic uncertainties. The shape of FS is found to be compatible

with the smoothly varying distribution of FL, as measured in Ref. [27].

reported in Table 1. The sources of systematic uncertainty are detailed in Sec. 8. As expected, the shape of the measured FS distribution is found to be compatible with the

smoothly varying distribution of FL measured in Ref. [27].

Table 1: S-wave fraction (FS) in bins of q2for two mKπregions. The first uncertainty is statistical

and the second systematic.

q2 bin (GeV2/c4) FS| 996 796 FS| 1200 644 0.10 < q2 < 0.98 0.021+0.015 −0.011± 0.009 0.052+0.035−0.027± 0.013 1.1 < q2 < 2.5 0.144+0.035−0.030± 0.010 0.304+0.058−0.053± 0.013 2.5 < q2 < 4.0 0.029+0.031 −0.020± 0.010 0.071+0.069−0.049± 0.015 4.0 < q2 < 6.0 0.117+0.027 −0.023± 0.008 0.254+0.048−0.044± 0.012 6.0 < q2 < 8.0 0.033+0.022−0.019± 0.009 0.082+0.049−0.045± 0.016 11.0 < q2 < 12.5 0.021+0.021 −0.016± 0.007 0.049+0.048−0.039± 0.014 15.0 < q2 < 17.0 −0.008+0.033 −0.014± 0.006 −0.016+0.069−0.030± 0.012 17.0 < q2 < 19.0 0.018+0.013−0.017± 0.009 0.034+0.024−0.032± 0.019 1.1 < q2 < 6.0 0.101+0.017−0.017± 0.009 0.224+0.032−0.033± 0.013 15.0 < q2 < 19.0 0.010+0.017 −0.014± 0.007 0.019+0.030−0.025± 0.015

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The presence of a nonresonant P-wave component in the K+π− system has been suggested in Refs. [44, 45]. However, no evidence for such a component was found in the current data sample. The effect of neglecting a nonresonant P-wave contribution with a relative phase and magnitude varied within the statistical uncertainties determined in this analysis, was found to be negligible.

7

Differential

branching

fraction

of

the

decay

B

0

→ K

(892)

0

µ

+

µ

The differential branching fraction of the decay B0→ K∗(892)0µ+µis estimated by

normalising the signal yield, nK∗0µ+µ−, obtained from the fit described in Sec. 6.2, to

the total event yield of the decay B0→ J/ψ K∗0, n

J/ψ K∗0. The number of B0→ J/ψ K∗0

events is obtained from a fit to the mKπµµ spectrum using the same q2 range as for

the fit to determine the mKπµµ mass shape parameters (Sec. 5), but for an mKπ range

796 < mKπ < 996 MeV/c2. This yield has to be corrected for the S-wave fraction within the

narrow mKπ window of B0→ J/ψ K∗0 decays, F J/ψ K∗0

S . The value of F J/ψ K∗0

S is obtained

from Ref. [46] and is adjusted to the mKπ range 796 < mKπ < 996 MeV/c2. The ratio of

B0→ K∗0µ+µand B0→ J/ψ K∗0 events is corrected for the relative efficiency between

the two decays, R = J/ψK∗0/K∗0µ+µ−. This ratio is determined using simulated samples

of B0→ K∗(892)0µ+µand B0→ J/ψ K(892)0 decays. The angular distributions of these

samples are corrected to account for the presence of P- and S-wave components with a relative abundance given by the measurements of Sec. 6.3 and Ref. [46]. The systematic uncertainty associated with this correction is determined by varying the components within the uncertainties of the measured values and recalculating R. The resulting uncertainty

on R is negligible.

The differential branching fraction of B0→ K∗(892)0µ+µdecays in a q2 bin of width

(q2

max− qmin2 ) is given by

dB dq2 = R (q2 max− qmin2 ) (1 − FS| 1200 644 )nK∗0µ+µ− (1 − FSJ/ψ K∗0)nJ/ψ K∗0 B(B0→ J/ψ K∗0 )B(J/ψ → µ+µ−), (9)

where FS|1200644 , R and nK∗0µ+µ− correspond to quantities measured within the relevant q2

bin. The branching fraction B(B0 → J/ψ K(892)0) obtained from Ref. [47] is

B(B0 → J/ψ K∗(892)0) = (1.19 ± 0.01 ± 0.08) × 10−3,

where the first uncertainty is statistical and the second systematic. The branching fraction for J/ψ → µ+µ− decays is taken from Ref. [43]. The resulting differential branching fraction is shown in Fig. 5. The uncertainties given are a quadratic sum of statistical and systematic uncertainties and the bands shown indicate the SM prediction from Refs. [48,49]. The results are also reported in Table 2. The various sources of systematic uncertainties are described in Sec. 8.

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]

4

c

/

2

[GeV

2

q

0

5

10

15

]

2

/GeV

4

c

[

2

q

/d

B

d

0

0.05

0.1

0.15

6 −

10

×

LHCb

Figure 5: Differential branching fraction of B0→ K∗(892)0µ+µdecays as a function of q2. The

data are overlaid with the SM prediction from Refs. [48, 49]. No SM prediction is included in the

region close to the narrow c¯c resonances. The result in the wider q2 bin 15.0 < q2 < 19.0 GeV2/c4

is also presented. The uncertainties shown are the quadratic sum of the statistical and systematic

uncertainties, and include the uncertainty on the B0→ J/ψ K∗0 and J/ψ → µ+µbranching

fractions.

Table 2: Differential branching fraction of B0→ K∗(892)0µ+µdecays in bins of q2. The first

uncertainty is statistical, the second systematic and the third due to the uncertainty on the

B0→ J/ψ K∗0 and J/ψ → µ+µ− branching fractions.

q2 bin (GeV2/c4) dB/dq2× 10−7 (c4/ GeV2) 0.10 < q2 < 0.98 1.016+0.067 −0.073± 0.029 ± 0.069 1.1 < q2 < 2.5 0.326+0.032 −0.031± 0.010 ± 0.022 2.5 < q2 < 4.0 0.334+0.031−0.033± 0.009 ± 0.023 4.0 < q2 < 6.0 0.354+0.027 −0.026± 0.009 ± 0.024 6.0 < q2 < 8.0 0.429+0.028 −0.027± 0.010 ± 0.029 11.0 < q2 < 12.5 0.487+0.031−0.032± 0.012 ± 0.033 15.0 < q2 < 17.0 0.534+0.027 −0.037± 0.020 ± 0.036 17.0 < q2 < 19.0 0.355+0.027 −0.022± 0.017 ± 0.024 1.1 < q2 < 6.0 0.342+0.017 −0.017± 0.009 ± 0.023 15.0 < q2 < 19.0 0.436+0.018−0.019± 0.007 ± 0.030

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The total branching fraction of the B0→ K∗(892)0µ+µdecay is obtained from the

sum over the eight q2 bins. To account for the fraction of signal events in the vetoed q2

regions, a correction factor of 1.532 ± 0.001(stat) ± 0.010(syst) is applied. This factor is determined using the calculation in Ref. [50] and form factors from Ref. [51]. The systematic uncertainty is determined by recalculating the extrapolation factor using the form factors from Ref. [52] and taking the difference to the nominal value. The resulting total branching fraction is

B(B0→ K

(892)0µ+µ−) = (0.904+0.016−0.015± 0.010 ± 0.006 ± 0.061) × 10−6,

where the uncertainties, from left to right, are statistical, systematic, from the extrapolation to the full q2region and due to the uncertainty of the branching fraction of the normalisation mode.

8

Systematic uncertainties

The sources of systematic uncertainty considered can alter the angular and mass distribu-tions, as well as the ratio of efficiencies between the signal and control channels. In general, the systematic uncertainties are significantly smaller than the statistical uncertainties. The various sources of systematic uncertainty are discussed in detail below and are summarised in Table 3. Motivated by Eq. 9, the systematic uncertainty for FS is presented for the mKπ

region 644 < mKπ < 1200 MeV/c2. Typical ranges are quoted in order to summarise the

effect the systematic uncertainties have across the various q2 bins. Sources of systematic uncertainty that can affect both FS and the differential branching fraction are treated as

100% correlated.

Table 3: Summary of the main sources of systematic uncertainty on FS|1200644 and dB/dq2. Typical

ranges are quoted in order to summarise the effect the systematic uncertainties have across the

various q2 bins. Source FS| 1200 644 dB/dq 2 ×10−7(c4/GeV2 ) Data-simulation differences 0.008–0.013 0.004–0.021 Efficiency model 0.001–0.010 0.001–0.012 S-wave mKπ model 0.001–0.017 0.001–0.015 B0 → K(892)0 form factors 0.003–0.017 B(B0→ J/ψ (→ µ+µ)K∗0) 0.025–0.079

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8.1

Systematic uncertainties on the S-wave fraction

The impact of each source of systematic uncertainty on FS is estimated using

pseudoex-periments, where samples are generated varying one or more parameters. The value of FS is determined using both the nominal model and the alternative model. For every

pseudoexperiment, the difference between the two values of FSis computed. In general, the

systematic uncertainty is then taken as the average of this difference over a large number of pseudoexperiments. The exception to this is the statistical uncertainty of the efficiency correction. In order to account for this statistical variation, the standard deviation of the difference between the two values of FS from each pseudoexperiment is used instead.

The systematic uncertainty is evaluated in each q2 bin separately. The pseudodata are

generated with signal and background yields many times larger than those of the data, rendering statistical effects negligible. The main systematic uncertainties on FS originate

from the efficiency correction function and the choice of model used to describe the S-wave component of the mKπ distribution of the signal.

There are two main systematic uncertainties associated with the efficiency correction function used for determining FS. Firstly, an uncertainty arises from residual

data-simulation differences. After all corrections to the data-simulation are applied, a difference at the level of 10% remains in the momentum spectrum of the pions between simulated and genuine B0→ J/ψ K∗0 decays. A new efficiency correction is derived after weighting the

simulated phase-space sample to account for this difference. The second main systematic uncertainty associated with the efficiency correction is due to the order of the polynomials used to describe the efficiency function. To evaluate this uncertainty, a new efficiency correction is derived in which the polynomial order in q2 is increased by two. This change

is motivated by a small residual difference between the q2 dependence of the nominal efficiency correction and the simulated phase-space sample, near the upper kinematic edge of the q2 range. Uncertainties due to the limited size of the simulation sample used to

derive the efficiency correction, as well as due to the evaluation of the efficiency correction at the centre of the q2 bin are also assessed and are found to be negligible.

To assess the modelling of the S-wave component in the mKπ distribution,

pseudoex-periments are produced where the LASS line shape is exchanged for the sum of resonant K0∗(800)0 (also known as the κ resonance) and K

0(1430)0 contributions. An additional

variation is considered where the parameters of the LASS distribution, determined in B0 → J/ψ K∗0 decays using the model described in Ref. [42], are exchanged for those

measured by the LASS collaboration [29]. The largest of the two variations is taken as the systematic uncertainty on the S-wave model. Systematic uncertainties associated with the modelling of the P-wave mKπ distribution of the signal are found to be negligible.

Integrating the differential decay rate given in Eq. 3 over cos θ` and φ0 results in the

cancellation of terms involving the angular observables S3, AFB and S9. However the

integral of the product of the differential decay rate with the efficiency correction, given in Eq. 8, results in a residual dependence of the signal distribution on these angular observables. By generating pseudoexperiments with observables S3, AFB and S9 either set

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on FS is assessed. Even considering the largest variation observed, the resulting systematic

uncertainty is negligible.

All other sources of systematic uncertainties described in Ref. [27], such as the modelling of the mKπµµ distribution of the signal and background, the choice of the mKπ and cos θK

background models and the effect of residual specific backgrounds, are found to be sub-dominant. The effect of neglecting a possible D-wave K+πcomponent, arising from the

tail of the K2∗(1430)0, is also assessed and found to be negligible.

8.2

Systematic uncertainties on the differential branching

frac-tion

Systematic uncertainties affecting the differential branching fraction predominantly arise through: the knowledge of R, the ratio of the reconstruction and selection efficiencies

described in Sec. 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. [48] and [52].

As described in Sec. 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∗0 decays. 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)0 decays 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 θK models 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+πsystem of

B0→ K∗0µ+µdecays using a data sample corresponding to an integrated luminosity of

3 fb−1 collected 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+µdecays is reported in bins of q2. All previous

measurements of the differential branching fraction have compared the combination of S-and wave components to the theory prediction, which is made purely for the resonant P-wave part of the K+πsystem. The measurements of the S-wave fraction presented in this

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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+µdecays. The resulting

measurements of the differential branching fraction of B0→ K(892)0µ+µdecays are the

most precise to date and are in good agreement with the SM predictions.

Acknowledgements

We would like to thank Gudrun Hiller and Martin Jung for useful discussions regarding the treatment of the K+πsystem. 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 (USA). 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 (USA). 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).

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Appendices

A

The m

distribution of the signal

The K+πinvariant mass distribution of the signal candidates is modelled by two

distri-butions. For the P-wave component, a relativistic Breit-Wigner function is used, given by fBW(mKπ) = p kp  k k892  B10(k, k892, d)B00(p, p892, d) m2 Kπ− m2892− im892Γ892(mKπ) , (10)

where√kp is the phase-space factor, Γ892(mKπ) is given by

Γ892(mKπ) = Γ892B10 2(k, k892, d)  k k892 3 m 892 mKπ  , (11)

and B0 are Blatt–Weisskopf barrier factors as defined in Ref. [43]. The parameter d is the meson radius parameter and is set to 1.6 GeV−1c [42]. 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)0 resonance, and k (p) is the momentum of the K+ (K∗0) in the rest frame of the K∗0 (B0) evaluated at a given m

Kπ. The parameters k892

and p892 are the values of k and p evaluated at the pole mass of the K∗(892)0 resonance.

In Eq. 10, the orbital angular momentum between the K∗(892)0 and the dimuon system is considered to be zero. The inclusion of a higher orbital angular momentum component has a negligible effect on the measurements.

The S-wave component of the signal is modelled using the LASS parameterisation [29], given by fLASS(mKπ) = p kpB10(k, k1430, d)  k k1430   1 cot δB− i + e2iδB 1 cot δR− i  , (12)

where k1430 is the momentum of the K∗0 in the B0 rest frame, evaluated at the pole mass

of the K0∗(1430)0 resonance. The terms cot δB and cot δR are given by

cot δB = 1 ak + rk 2 (13) and cot δR= m2 1430− m2Kπ m1430Γ1430(mKπ) , (14)

with the running width Γ1430(mKπ) in turn given by

Γ1430(mKπ) = Γ1430 k k1430 m1430 mKπ . (15)

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The parameters m1430 and Γ1430 are the pole mass and width of the K0∗(1430)0 resonance,

and k1430 is the momentum of the kaon in the K∗0 rest frame, evaluated at the pole mass

of the K0∗(1430)0 resonance. The second term of Eq. 12 is equivalent to a Breit–Wigner

function for the K0∗(1430)0. The first term of Eq. 12 contains two empirical parameters {a, r}. These parameters are fixed to the values a = 3.83 GeV/c−1 and r = 2.86 GeV/c−1, determined in B0→ J/ψ K∗0 decays using the model described in Ref. [42].

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−1 and r = 1.76 GeV/c−1. The resulting systematic uncertainty is found to be negligible.

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B

Likelihood fit projections

Figures 6–9 show the projections of the fitted probability density function on mKπµµ,

mKπ and cos θK. Figure 6 shows the wider q2 bins of 1.1 < q2 < 6.0 GeV2/c4 and 15.0 <

q2 < 19.0 GeV2/c4, Figs. 7–9 show the m

Kπµµ, mKπ and cos θK projections respectively for

the finer q2 bins. 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. ] 2 c [MeV/ µ µ π K m 5200 5400 5600 2 c Candidates / 15 MeV/ 0 100 200 300 LHCb 4 c / 2 < 6.0 GeV 2 q 1.1 < ] 2 c [MeV/ µ µ π K m 5200 5400 5600 2 c Candidates / 15 MeV/ 0 100 200 300 LHCb 4 c / 2 < 19.0 GeV 2 q 15.0 < ] 2 c [MeV/ π K m 800 1000 1200 2 c Candidates / 28 MeV/ 0 100 200 300 LHCb 4 c / 2 < 6.0 GeV 2 q 1.1 < ] 2 c [MeV/ π K m 800 1000 1200 2 c Candidates / 28 MeV/ 0 100 200 300 400 LHCb 4 c / 2 < 19.0 GeV 2 q 15.0 < 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 q 1.1 < 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 q 15.0 <

Figure 6: Angular and mass distributions for the q2 bins 1.1 < q2 < 6.0 GeV2/c4 (left) and

15.0 < q2< 19.0 GeV2/c4 (right). The distributions of cos θK and mKπ are shown for candidates

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] 2 c [MeV/ µ µ π K m 5200 5400 5600 2 c Candidates / 15 MeV/ 0 50 100 150 LHCb 4 c / 2 < 0.98 GeV 2 q 0.10 < ] 2 c [MeV/ µ µ π K m 5200 5400 5600 2 c Candidates / 15 MeV/ 0 50 100 LHCb 4 c / 2 < 2.5 GeV 2 q 1.1 < ] 2 c [MeV/ µ µ π K m 5200 5400 5600 2 c Candidates / 15 MeV/ 0 50 100 LHCb 4 c / 2 < 4.0 GeV 2 q 2.5 < ] 2 c [MeV/ µ µ π K m 5200 5400 5600 2 c Candidates / 15 MeV/ 0 50 100 150 LHCb 4 c / 2 < 6.0 GeV 2 q 4.0 < ] 2 c [MeV/ µ µ π K m 5200 5400 5600 2 c Candidates / 15 MeV/ 0 50 100 150 LHCb 4 c / 2 < 8.0 GeV 2 q 6.0 < ] 2 c [MeV/ µ µ π K m 5200 5400 5600 2 c Candidates / 15 MeV/ 0 50 100 150 LHCb 4 c / 2 < 12.5 GeV 2 q 11.0 < ] 2 c [MeV/ µ µ π K m 5200 5400 5600 2 c Candidates / 15 MeV/ 0 50 100 150 LHCb 4 c / 2 < 17.0 GeV 2 q 15.0 < ] 2 c [MeV/ µ µ π K m 5200 5400 5600 2 c Candidates / 15 MeV/ 0 50 100 LHCb 4 c / 2 < 19.0 GeV 2 q 17.0 <

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] 2 c [MeV/ π K m 800 1000 1200 2 c Candidates / 28 MeV/ 0 50 100 150 LHCb 4 c / 2 < 0.98 GeV 2 q 0.10 < ] 2 c [MeV/ π K m 800 1000 1200 2 c Candidates / 28 MeV/ 0 50 100 LHCb 4 c / 2 < 2.5 GeV 2 q 1.1 < ] 2 c [MeV/ π K m 800 1000 1200 2 c Candidates / 28 MeV/ 0 20 40 60 80 LHCb 4 c / 2 < 4.0 GeV 2 q 2.5 < ] 2 c [MeV/ π K m 800 1000 1200 2 c Candidates / 28 MeV/ 0 50 100 150 LHCb 4 c / 2 < 6.0 GeV 2 q 4.0 < ] 2 c [MeV/ π K m 800 1000 1200 2 c Candidates / 28 MeV/ 0 50 100 150 200 LHCb 4 c / 2 < 8.0 GeV 2 q 6.0 < ] 2 c [MeV/ π K m 800 1000 1200 2 c Candidates / 28 MeV/ 0 50 100 150 LHCb 4 c / 2 < 12.5 GeV 2 q 11.0 < ] 2 c [MeV/ π K m 800 1000 1200 2 c Candidates / 28 MeV/ 0 100 200 LHCb 4 c / 2 < 17.0 GeV 2 q 15.0 < ] 2 c [MeV/ π K m 800 1000 1200 2 c Candidates / 28 MeV/ 0 50 100 150 LHCb 4 c / 2 < 19.0 GeV 2 q 17.0 <

Figure 8: The K+πinvariant mass distributions for the fine q2 bins for candidates in the signal

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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 q 0.10 < 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 q 1.1 < 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 q 2.5 < 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 q 4.0 < 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 q 6.0 < 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 q 11.0 < K θ cos 1 − −0.5 0 0.5 1 Candidates / 0.1 0 20 40 LHCb 4 c / 2 < 17.0 GeV 2 q 15.0 < 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 q 17.0 <

Figure 9: The cos θK angular distributions for the fine q2 bins for candidates in the signal mKπµµ

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R. Aaij39, B. Adeva38, M. Adinolfi47, Z. Ajaltouni5, S. Akar6, J. Albrecht10, F. Alessio39,

M. Alexander52, S. Ali42, G. Alkhazov31, P. Alvarez Cartelle54, A.A. Alves Jr58, S. Amato2,

S. Amerio23, Y. Amhis7, L. An40, L. Anderlini18, G. Andreassi40, M. Andreotti17,g,

J.E. Andrews59, R.B. Appleby55, O. Aquines Gutierrez11, F. Archilli1, P. d’Argent12,

A. Artamonov36, M. Artuso60, E. Aslanides6, G. Auriemma26,s, M. Baalouch5, S. Bachmann12,

J.J. Back49, A. Badalov37, C. Baesso61, W. Baldini17, R.J. Barlow55, C. Barschel39, S. Barsuk7,

W. Barter39, V. Batozskaya29, V. Battista40, A. Bay40, L. Beaucourt4, J. Beddow52,

F. Bedeschi24, I. Bediaga1, L.J. Bel42, V. Bellee40, N. Belloli21,i, K. Belous36, I. Belyaev32,

E. Ben-Haim8, G. Bencivenni19, S. Benson39, J. Benton47, A. Berezhnoy33, R. Bernet41,

A. Bertolin23, M.-O. Bettler39, M. van Beuzekom42, S. Bifani46, P. Billoir8, T. Bird55,

A. Birnkraut10, A. Bitadze55, A. Bizzeti18,u, T. Blake49, F. Blanc40, J. Blouw11, S. Blusk60,

V. Bocci26, T. Boettcher57, A. Bondar35, N. Bondar31,39, W. Bonivento16, S. Borghi55,

M. Borisyak67, M. Borsato38, F. Bossu7, M. Boubdir9, T.J.V. Bowcock53, E. Bowen41,

C. Bozzi17,39, S. Braun12, M. Britsch12, T. Britton60, J. Brodzicka55, E. Buchanan47, C. Burr55,

A. Bursche2, J. Buytaert39, S. Cadeddu16, R. Calabrese17,g, M. Calvi21,i, M. Calvo Gomez37,m,

P. Campana19, D. Campora Perez39, L. Capriotti55, A. Carbone15,e, G. Carboni25,j,

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V. Cogoni16,f, L. Cojocariu30, G. Collazuol23,o, P. Collins39, A. Comerma-Montells12,

A. Contu39, A. Cook47, S. Coquereau8, G. Corti39, M. Corvo17,g, B. Couturier39, G.A. Cowan51,

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T. Humair54, M. Hushchyn67, N. Hussain56, D. Hutchcroft53, M. Idzik28, P. Ilten57,

R. Jacobsson39, A. Jaeger12, J. Jalocha56, E. Jans42, A. Jawahery59, M. John56, D. Johnson39,

C.R. Jones48, C. Joram39, B. Jost39, N. Jurik60, S. Kandybei44, W. Kanso6, M. Karacson39,

T.M. Karbach39,†, S. Karodia52, M. Kecke12, M. Kelsey60, I.R. Kenyon46, M. Kenzie39,

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A.K. Kuonen40, K. Kurek29, T. Kvaratskheliya32,39, D. Lacarrere39, G. Lafferty55,39, A. Lai16,

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K. Petridis47, A. Petrolini20,h, A. Petrov66, M. Petruzzo22,q, E. Picatoste Olloqui37, B. Pietrzyk4,

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Figure

Figure 1: Invariant mass m Kπµµ of (left) the B 0 → J/ψ K ∗0 decay and (right) the signal decay B 0 → K ∗0 µ + µ − integrated over the q 2 regions described in the text
Figure 2: Two-dimensional projections of the efficiency (left) in the cos θ K –q 2 plane and (right) in the m Kπ –q 2 plane, determined from a principal moments analysis of simulated four-body B 0 → K + π − µ + µ − phase-space decays
Figure 3: Angular and mass distributions for the q 2 bin 1.1 &lt; q 2 &lt; 6.0 GeV 2 /c 4
Table 1: S-wave fraction (F S ) in bins of q 2 for two m Kπ regions. The first uncertainty is statistical and the second systematic.
+7

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