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Measurements of the S-wave fraction in $B^{0}\rightarrow K^{+}\pi^{-}\mu^{+}\mu^{-}$ decays and the $B^{0}\rightarrow K^{\ast}(892)^{0}\mu^{+}\mu^{-}$ differential branching fraction

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Abstract

A measurement of the differential branching fraction of the decay ${B^{0}\rightarrow K^{\ast}(892)^{0}\mu^{+}\mu^{-}}$ is presented together with a determination of the S-wave fraction of the $K^+\pi^-$ system in the decay $B^{0}\rightarrow K^{+}\pi^{-}\mu^{+}\mu^{-}$. 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, $q^2$. Precise theoretical predictions for the differential branching fraction of $B^{0}\rightarrow K^{\ast}(892)^{0}\mu^{+}\mu^{-}$ decays are available for the $q^2$ region $1.1<q^2<6.0 {\rm GeV}^2/c^4$. In this $q^2$ region, for the $K^+\pi^-$ invariant mass range $796 < m_{K\pi} < 996 {\rm MeV}/c^2$, the S-wave fraction of the $K^+\pi^-$ system in $B^{0}\rightarrow K^{+}\pi^{-}\mu^{+}\mu^{-}$ decays is found to be \begin{equation*} F_{\rm S} = 0.101\pm0.017({\rm stat})\pm0.009 ({\rm syst}), \end{equation*} and the differential branching fraction of $B^{0}\rightarrow K^{\ast}(892)^{0}\mu^{+}\mu^{-}$ decays is determined to be \begin{equation*} {\rm d}\mathcal{B}/{\rm d} q^2 = (0.342_{ -0.017}^{ +0.017}({\rm stat})\pm{0.009}({\rm syst})\pm0.023({\rm norm}))\times 10^{-7}c^{4}/{\rm GeV}^{2}. \end{equation*} The differential branching fraction measurements presented are the most precise to date and are found to be in agreement with Standard Model predictions.

Figures and captions

Invariant mass $ m_{K\pi\mu\mu} $ of (left) the $ B ^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^{*0} $ decay and (right) the signal decay $ B ^0 \rightarrow K ^{*0} \mu ^+ \mu ^- $ integrated over the $ q^2 $ 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.

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Two-dimensional projections of the efficiency (left) in the $\cos{\theta_K} $--$ q^2 $ plane and (right) in the $ m_{K\pi} $--$ q^2 $ plane, determined from a principal moments analysis of simulated four-body $ { B ^0 \rightarrow K ^+ \pi ^- \mu ^+\mu ^- } $ phase-space decays. The colour scale denotes the efficiency in arbitrary units. The lack of entries in the top right corner of the $ m_{K\pi} $--$ q^2 $ distribution is due to the limited phase space available in the decay of the $ B ^0 $ meson.

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Angular and mass distributions for the $ q^2 $ bin $1.1< q^2 <6.0 {\mathrm{ Ge V^2 /}c^4} $. The distributions of $\cos{\theta_K} $ and $ m_{K\pi} $ are shown for candidates in the signal $ m_{K\pi\mu\mu} $ window of $\pm50 {\mathrm{ Me V /}c^2} $ around the known $ B ^0 $ mass. The solid line denotes the total fitted distribution. The individual components, signal (blue shaded area) and background (red hatched area), are also shown.

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Results for the S-wave fraction ($F_{\rm S}$) in bins of $ q^2$ in the range (left) $644< m_{K\pi} <1200 {\mathrm{ Me V /}c^2} $ and (right) $796< m_{K\pi} <996 {\mathrm{ Me V /}c^2} $. The uncertainties shown are the quadratic sum of the statistical and systematic uncertainties. The shape of $F_{\rm S}$ is found to be compatible with the smoothly varying distribution of $F_{\rm L}$, as measured in Ref. [27].

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Differential branching fraction of $ { B ^0 \rightarrow K ^{*}(892)^{0} \mu ^+ \mu ^- }$ decays as a function of $ q^2 $. The data are overlaid with the SM prediction from Refs. [50,51]. No SM prediction is included in the region close to the narrow $c\bar{c}$ resonances. The result in the wider $ q^2$ bin $15.0< q^2 <19.0 {\mathrm{ Ge V^2 /}c^4} $ is also presented. The uncertainties shown are the quadratic sum of the statistical and systematic uncertainties, and include the uncertainty on the $ { B ^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^{*0} } $ and $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \rightarrow \mu^+\mu^-$ branching fractions.

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Angular and mass distributions for the $ q^2 $ bins $1.1< q^2 <6.0 {\mathrm{ Ge V^2 /}c^4} $ (left) and $15.0< q^2 <19.0 {\mathrm{ Ge V^2 /}c^4} $ (right). The distributions of $\cos{\theta_K} $ and $ m_{K\pi} $ are shown for candidates in the signal $ m_{K\pi\mu\mu} $ window of $\pm50 {\mathrm{ Me V /}c^2} $ around the known $ B ^0 $ mass.

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The $K^+\pi^-\mu^+\mu^-$ invariant mass distributions for the fine $ q^2 $ bins.

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The $ K ^+ \pi ^- $ invariant mass distributions for the fine $ q^2 $ bins for candidates in the signal $ m_{K\pi\mu\mu} $ window of $\pm50 {\mathrm{ Me V /}c^2} $ around the known $ B ^0 $ mass.

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The $\cos{\theta_K}$ angular distributions for the fine $ q^2 $ bins for candidates in the signal $ m_{K\pi\mu\mu} $ window of $\pm50 {\mathrm{ Me V /}c^2} $ around the known $ B ^0 $ mass.

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Tables and captions

S-wave fraction ($F_{\rm S}$) in bins of $ q^2 $ for two $ m_{K\pi} $ regions. The first uncertainty is statistical and the second systematic.

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Differential branching fraction of $ { B ^0 \rightarrow K ^{*}(892)^{0} \mu ^+ \mu ^- } $ decays in bins of $ q^2 $. The first uncertainty is statistical, the second systematic and the third due to the uncertainty on the $ { B ^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^{*0} } $ and $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \rightarrow \mu^+\mu^-$ branching fractions.

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Summary of the main sources of systematic uncertainty on $\left.F_{\rm S}\right|_{644}^{1200} $ and $\textrm{d} \mathcal{B}/\textrm{d} q^2 $. Typical ranges are quoted in order to summarise the effect the systematic uncertainties have across the various $ q^2 $ bins.

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Created on 21 October 2019.