Measurement of CP-averaged observables in the B0->K*0mu+mu- decay

An angular analysis of the B0 → K∗0(→ K+π−)μ+μ− decay is presented using a data set corresponding to an integrated luminosity of 4.7 fb−1 of pp collision data collected with the LHCb experiment. The full set of CP -averaged observables are determined in bins of the invariant mass squared of the dimuon system. Contamination from decays with the K+π− system in an S-wave configuration is taken into account. The tension seen between the previous LHCb results and the Standard Model predictions persists with the new data. The precise value of the significance of this tension depends on the choice of theory nuisance parameters. Submitted to Phys. Rev. Lett. c © 2020 CERN for the benefit of the LHCb collaboration, license CC BY 4.0 licence. †Authors are listed at the end of this paper. ar X iv :2 00 3. 04 83 1v 1 [ he pex ] 1 0 M ar 2 02 0

written as 1 d(Γ +Γ)/dq 2 d 4 (Γ +Γ) dq 2 d Ω P = 9 32π 3 4 (1 − F L ) sin 2 θ K + F L cos 2 θ K + 1 4 (1 − F L ) sin 2 θ K cos 2θ l −F L cos 2 θ K cos 2θ l + S 3 sin 2 θ K sin 2 θ l cos 2φ +S 4 sin 2θ K sin 2θ l cos φ + S 5 sin 2θ K sin θ l cos φ + 4 3 A FB sin 2 θ K cos θ l + S 7 sin 2θ K sin θ l sin φ +S 8 sin 2θ K sin 2θ l sin φ + S 9 sin 2 θ K sin 2 θ l sin 2φ , where F L is the fraction of the longitudinal polarisation of the K * 0 meson, A FB is the forward-backward asymmetry of the dimuon system and S i are other CP -averaged observables [1]. The K + π − system can also be in an S-wave configuration, which modifies the angular distribution to 1 d(Γ +Γ)/dq 2 d 4 (Γ +Γ) F S sin 2 θ l + 9 32π (S 11 + S 13 cos 2θ l ) cos θ K + 9 32π (S 14 sin 2θ l + S 15 sin θ l ) sin θ K cos φ + 9 32π (S 16 sin θ l + S 17 sin 2θ l ) sin θ K sin φ , where F S denotes the S-wave fraction and the coefficients S 11 , S 13 -S 17 arise from interference between the S-and P-wave amplitudes. Throughout this letter, F S and the interference terms between the S-and P-wave are treated as nuisance parameters. Additional sets of observables, for which the leading B 0 → K * 0 form-factor uncertainties cancel, can be built from F L , A FB and S 3 -S 9 . Examples of such optimised observables include the P The online event selection is performed by a trigger, which comprises a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage that applies a full event reconstruction [58]. Offline, signal candidates are formed from a pair of oppositely charged tracks that are identified as muons, combined with a K * 0 candidate.
The distribution of the reconstructed K + π − µ + µ − invariant mass, m(K + π − µ + µ − ), is used to discriminate signal from background. This distribution is fitted simultaneously with the three decay angles. The distribution of the reconstructed K + π − mass, m(K + π − ), depends on the K + π − angular-momentum configuration and is used to constrain the S-wave fraction. The analysis procedure is cross-checked by performing a fit of the b → ccs tree-level decay B 0 → J/ψK * 0 , with J/ψ → µ + µ − , which results in the same final-state particles. Hereafter, the B 0 → J/ψ(→ µ + µ − )K * 0 decay and the equivalent decay via the ψ(2S) resonance are denoted by B 0 → J/ψK * 0 and B 0 → ψ(2S)K * 0 , respectively.
Two types of backgrounds are considered: combinatorial background, where the selected particles do not originate from a single b-hadron decay; and peaking backgrounds, where a single decay is selected but with some of the final-state particles misidentified. The combinatorial background is distributed smoothly in m(K + π − µ + µ − ), whereas the peaking backgrounds can accumulate in specific regions of the reconstructed mass. In addition, the decays B 0 → J/ψK * 0 , B 0 → ψ(2S)K * 0 and B 0 → φ(1020)(→ µ + µ − )K * 0 are removed by rejecting events with q 2 in the ranges 8.0 < q 2 < 11.0 GeV 2 /c 4 , 12.5 < q 2 < 15.0 GeV 2 /c 4 or 0.98 < q 2 < 1.10 GeV 2 /c 4 .
The criteria used to select candidates from the Run 1 data are the same as those described in Ref. [1]. The selection of the 2016 data follows closely that of the Run 1 data. Candidates are required to have 5170 < m(K + π − µ + µ − ) < 5700 MeV/c 2 and 795.9 < m(K + π − ) < 995. 9 MeV/c 2 . The four tracks of the final-state particles are required to have significant impact parameter (IP) with respect to all primary vertices (PVs) in the event. The tracks are fitted to a common vertex, which is required to be of good quality. The IP of the B 0 candidate is required to be small with respect to one of the PVs. The vertex of the B 0 candidate is required to be significantly displaced from the same PV. The angle between the reconstructed B 0 momentum and the vector connecting this PV to the reconstructed B 0 decay vertex, θ DIRA , is also required to be small. To avoid the same track being used to construct more than one of the final state particles, the opening angle between every pair of tracks is required to be larger than 1 mrad.
Combinatorial background is reduced further using a boosted decision tree (BDT) algorithm [59,60]. The BDT is trained entirely on data with B 0 → J/ψK * 0 candidates used as a proxy for the signal and candidates from the upper-mass sideband 5350 < m(K + π − µ + µ − ) < 7000 MeV/c 2 used as a proxy for the background. The training uses a cross-validation technique [61]. The input variables used are the reconstructed B 0 decay-time and vertex-fit quality, the momentum and transverse momentum of the B 0 candidate, θ DIRA , PID information from the RICH detectors and the muon system, and variables describing the isolation of the final-state tracks [62]. The variables that are used in the BDT are chosen so as to induce the minimum possible distortion in the angular and q 2 distributions. A requirement is placed on the BDT output to maximise the signal significance. This requirement rejects more than 97% of the remaining combinatorial background, while retaining more than 85% of the signal. The signal efficiency of the BDT is uniform in the m(K + π − µ + µ − ) and m(K + π − ) distributions.
Peaking backgrounds from B 0 where the latter constitutes a background if the kaon from the K * 0 decay is misidentified as the pion and vice versa. In each case, at least one particle needs to be misidentified for the decay to be reconstructed as a signal candidate. Vetoes to reduce these peaking backgrounds are formed by placing requirements on the invariant mass of the candidates, recomputed with the relevant change in the particle mass hypotheses, and by using PID information. In addition, in order to avoid having a strongly peaking contribution to the cos θ K angular distribution in the upper mass sideband, B + → K + µ + µ − candidates with K + µ + µ − invariant mass within 60 MeV/c 2 of the B + mass are removed. The background from b-hadron decays with two hadrons misidentified as muons is negligible. The signal efficiency and residual peaking backgrounds are estimated using simulated events. The vetoes remove a negligible amount of signal. The largest residual backgrounds are from at the level of 1% or less of the expected signal yield. This is sufficiently small such that these backgrounds are neglected in the angular analysis and are considered only as sources of systematic uncertainty.
A simultaneous fit to the Run 1 data and the 2016 data is performed, with the angular observables as common fit parameters. For each data set, an unbinned maximum-likelihood fit to the distributions of m(K + π − µ + µ − ) and the three decay angles is used to determine the CP -averaged angular observables in bins of q 2 , in either the standard or optimised basis; and a simultaneous fit of the m(K + π − ) invariant mass distribution is used to constrain the S-wave fraction. The fitted probability density functions (PDFs) are of an identical form to those of Ref. [1], as are the q 2 bins used. In addition to the narrow q 2 bins, results are obtained for the wider bins 1.1 < q 2 < 6.0 GeV 2 /c 4 and 15.0 < q 2 < 19.0 GeV 2 /c 4 .
The angular distribution of the signal is described using Eq. (1). The P ( ) i observables are determined by reparameterising Eq. (1) using a basis comprising F L , P 1,2,3 and P 4,5,6,8 . The angular distribution is multiplied by an acceptance model used to account for the effect of the reconstruction and candidate selection. The acceptance function is parameterised in four dimensions, according to where the terms L h (x) denote Legendre polynomials of order h and the values of the angles and q 2 are rescaled to the range −1 < x < +1 when evaluating the polynomials. For the cos θ l , cos θ K and φ angles, the sum in Eq. (3) encompasses L h (x) up to fourth, fifth and sixth order, respectively. The q 2 parameterisation comprises L h (x) up to fifth order. Simulation indicates that the acceptance function can be assumed to be flat across m(K + π − ). The coefficients c ijmn are determined using a principal moment analysis of simulated B 0 → K * 0 µ + µ − decays. As all of the relevant kinematic variables needed to describe the decay are used in this parameterisation, the acceptance function does not depend on the decay model used in the simulation. In the narrow q 2 bins, the acceptance is taken to be constant across each bin and is included in the fit by multiplying Eq. (2) by the acceptance function evaluated with the value of q 2 fixed at the bin centre. In the wider q 2 bins, the shape of the acceptance can vary significantly across the bin. In the likelihood, candidates are therefore weighted by the inverse of the acceptance function and parameter uncertainties are obtained using a bootstrapping technique [63]. The background angular distribution is modelled with second-order polynomials in cos θ l , cos θ K and φ, with the angular coefficients allowed to vary in the fit. This angular distribution is assumed to factorise in the three decay angles, which is confirmed to be the case for candidates in the upper mass sideband of the data.
The m(K + π − µ + µ − ) 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 low mass side. The parameters describing the signal mass shape are determined from a fit to the B 0 → J/ψK * 0 decay in the data and are subsequently fixed when fitting the B 0 → K * 0 µ + µ − candidates. For each of the q 2 bins, a scale factor that is determined from simulation is included to account for the difference in resolution between the B 0 → J/ψK * 0 and B 0 → K * 0 µ + µ − decay modes. A component is included in the B 0 → J/ψK * 0 fit to account for B 0 s → J/ψK * 0 decays, which are at the level of ∼ 1% of the B 0 → J/ψK * 0 signal yield. The background from the equivalent Cabibbo-suppressed penguin decay, B 0 s → K * 0 µ + µ − [64], is negligible and is ignored in the fit of the signal decay. The combinatorial background is described well by an exponential distribution in m(K + π − µ + µ − ).
The K * 0 signal component in the m(K + π − ) distribution is modelled using a relativistic Breit-Wigner function for the P-wave component and the LASS parameterisation [65] for the S-wave component. The combinatorial background is described by a linear function in m(K + π − ).
The decay B 0 → J/ψK * 0 is used to cross-check the analysis procedure in the region 8.0 < q 2 < 11.0 GeV 2 /c 4 . This decay is selected in the data with negligible background contamination. The angular structure has been determined by measurements made by the BaBar, Belle and LHCb collaborations [66][67][68]. The B 0 → J/ψK * 0 angular observables obtained from the Run 1 and 2016 LHCb data, using the acceptance correction derived as described above, are in good agreement with these previous measurements. Figure 1 shows the projection of the fitted PDF on the K + π − µ + µ − mass distribution. The B 0 → K * 0 µ + µ − yield, integrated over the q 2 ranges 0.10 < q 2 < 0.98 GeV 2 /c 4 , 1.1 < q 2 < 8.0 GeV 2 /c 4 , 11.0 < q 2 < 12.5 GeV 2 /c 4 and 15.0 < q 2 < 19.0 GeV 2 /c 4 , is determined to be 2398 ± 57 for the Run 1 data, and 2187 ± 53 for the 2016 data.
Pseudoexperiments, generated using the results of the best fit to data, are used to assess the bias and coverage of the fit. The majority of observables have a bias of less than 10% of their statistical uncertainty, with the largest bias being 17%, and all observables have an uncertainty estimate within 10% of the true uncertainty. The biases are driven by boundary effects in the observables. The largest effect comes from requiring that F S ≥ 0, which can bias F S to larger values. This can then result in a bias in the P-wave observables (see Eq. 2). The statistical uncertainty is corrected to account for any underor over-coverage and a systematic uncertainty equal to the size of the observed bias is assigned.
The size of other sources of systematic uncertainty is estimated using pseudoexperiments, in which one or more parameters are varied and the angular observables are determined with and without this variation. The systematic uncertainty is then taken as the average of the difference between the two models. The pseudoexperiments are generated with signal yields many times larger than the data, in order to render statistical fluctuations negligible.
The size of the total systematic uncertainty varies depending on the angular observable and the q 2 bin. The majority of observables in both the S i and P ( ) i basis have a total systematic uncertainty between 5% and 25% of the statistical uncertainty. For F L , the systematic uncertainty tends to be larger, typically between 20% and 50%. The systematic uncertainties are given in Table 3 of the Supplemental Material.
The dominant systematic uncertainties arise from the peaking backgrounds that are neglected in the analysis, the bias correction, and, for the narrow q 2 bins, from the uncertainty associated with evaluating the acceptance at a fixed point in q 2 . For the peaking backgrounds, the systematic uncertainty is evaluated by injecting additional candidates, drawn from the angular distributions of the background modes, into the pseudoexperiment data. The systematic uncertainty for the bias correction is determined directly from the pseudoexperiments used to validate the fit. The systematic uncertainty from the variation of the acceptance with q 2 is determined by moving the point in q 2 at which the acceptance is evaluated to halfway between the bin centre and the upper and the lower edge. The largest deviation is taken as the systematic uncertainty. Examples of further sources of systematic uncertainty investigated include the m(K + π − ) lineshape for the S-wave contribution, the assumption that the acceptance function is flat across the m(K + π − ) mass, and the effect of the B + → K + µ + µ − veto on the angular distribution of the background. These sources make a negligible contribution to the total uncertainty. With respect to the analysis of Ref. [1], the systematic uncertainty from residual differences between data and simulation is significantly reduced, owing to an improved decay model for B 0 → J/ψK * 0 decays [67].
The CP -averaged observables F L , A FB , S 5 and P 5 that are obtained from the S i and P The SM predictions are based on the prescription of Ref. [44], which combines light-cone sum rule calculations [43], valid in the low-q 2 region, with lattice determinations at high q 2 [71,72] to yield more precise determinations of the form factors over the full q 2 range. For the P ( ) i observables, predictions from Ref. [69] are shown using form factors from Ref. [70]. These predictions are restricted to the region q 2 < 8.0 GeV 2 /c 4 . The results from Run 1 and the 2016 data are in excellent agreement. A stand-alone fit to the Run 1 data reproduces exactly the central values of the observables obtained in Ref. [1].
Considering the observables individually, the results are largely in agreement with the The data are compared to SM predictions based on the prescription of Refs. [43,44], with the exception of the P 5 distribution, which is compared to SM predictions based on Refs. [69,70]. SM predictions. The local discrepancy in the P 5 observable in the 4.0 < q 2 < 6.0 GeV 2 /c 4 and 6.0 < q 2 < 8.0 GeV 2 /c 4 bins reduces from the 2.8 and 3.0 σ observed in Ref.
[1] to 2.5 and 2.9 σ. However, as discussed below, the overall tension with the SM is observed to increase mildly.
Using the Flavio software package [42], a fit of the angular observables is performed varying the parameter Re(C 9 ). The default Flavio SM nuisance parameters are used, including form-factor parameters and subleading corrections to account for long-distance QCD interference effects with the charmonium decay modes [43,44]. The same q 2 bins as in Ref. [1] are included. The 3.0 σ discrepancy with respect to the SM value of Re(C 9 ) obtained with the Ref. [1] data set changes to 3.3 σ with the data set used here. The best fit to the angular distribution is obtained with a shift in the SM value of Re(C 9 ) by −0.99 +0. 25 −0.21 . The tension observed in any such fit will depend on the effective coupling(s) varied, the handling of the SM nuisance parameters and the q 2 bins that are included in the fit. For example, the 6.0 < q 2 < 8.0 GeV 2 /c 4 bin is known to be associated with larger theoretical uncertainties [46]. Neglecting this bin, a Flavio fit gives a tension of 2.4 σ using the observables from Ref. [1] and 2.7 σ tension with the measurements reported here.
In summary, using 4.7 fb −1 of pp collision data collected with the LHCb experiment during the years 2011, 2012 and 2016, a complete set of CP -averaged angular observables has been measured for the B 0 → K * 0 µ + µ − decay. These are the most precise measurements of these quantities to date.

Supplemental Material
This supplemental material includes additional information to that already provided in the main letter. A full set of results for the nominal analysis is presented in both graphical and tabular form in Sec. 1. A complete description of the corresponding systematic uncertainties is given in Sec. 2. The correlations between the angular observables are presented for the S i observables in Sec. 3 and for the P

Results
The values of S 3 , S 4 and S 7 -S 9 obtained from the simultaneous fit are shown in Fig. 3. The data are compared to theoretical predictions based on the prescription of Ref. [44]. The predictions combine light-cone sum rule calculations [43] with lattice determinations [71,72] of the B 0 → K * 0 form factors. Figure 4 shows the values of the optimised observables, P ( ) i , obtained from the fit. The data are compared to predictions based on the prescription in Ref. [69]. These predictions use form factors from Ref. [70]. The values of the observables in the standard and optimised basis are given in Tables 1 and 2, respectively. The statistical correlation between the observables in each q 2 bin is provided in Tables 4-13  and Tables 14-23. i  iii Table 1: Results for the CP -averaged observables F L , A FB and S 3 -S 9 . The first uncertainties are statistical and the second systematic.