# Differential branching fraction and angular moments analysis of the decay $B^0 \to K^+ \pi^- \mu^+ \mu^-$ in the $K^*_{0,2}(1430)^0$ region

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## Abstract

Measurements of the differential branching fraction and angular moments of the decay $B^0 \to K^+ \pi^- \mu^+ \mu^-$ in the $K^+\pi^-$ invariant mass range $1330<m(K^+ \pi^-)<1530 MeV/c^2$ are presented. Proton-proton collision data are used, corresponding to an integrated luminosity of 3 $fb^{-1}$ collected by the LHCb experiment. Differential branching fraction measurements are reported in five bins of the invariant mass squared of the dimuon system, $q^2$, between 0.1 and 8.0 $GeV^2/c^4$. For the first time, an angular analysis sensitive to the S-, P- and D-wave contributions of this rare decay is performed. The set of 40 normalised angular moments describing the decay is presented for the $q^2$ range 1.1--6.0 $GeV^2/c^4$.

## Figures and captions

 Background-subtracted $m( K ^+ \pi ^- )$ distribution for $B ^0 \!\rightarrow K ^+ \pi ^- \mu ^+\mu ^-$ decays in the range $1.1< q^2 <6.0 {\mathrm{\,Ge V^2\!/}c^4}$. The region $1330< m( K ^+ \pi ^- ) <1530 {\mathrm{\,Me V\!/}c^2}$ is indicated by the blue, hatched area. Fig1.pdf [17 KiB] HiDef png [189 KiB] Thumbnail [56 KiB] *.C file Angle conventions for (a) $\overline{ B }{} {}^0 \rightarrow K ^- \pi ^+ \mu ^- \mu ^+$ and (b) $B ^0 \rightarrow K ^+ \pi ^- \mu ^+ \mu ^-$, as described in Ref. [12]. The leptonic and hadronic frames are back-to-back with a common $\hat{y}$ axis. For the dihedral angle $\phi$ between the leptonic and hadronic decay planes, there is an additional sign flip $\phi\rightarrow -\phi$ compared to previous LHCb analyses [1,2,3,4]. Fig2a.pdf [19 KiB] HiDef png [251 KiB] Thumbnail [61 KiB] *.C file Fig2b.pdf [19 KiB] HiDef png [251 KiB] Thumbnail [61 KiB] *.C file Relative efficiency in $\cos{\theta_\ell}$ , $\cos{\theta_K}$ and $\phi'$ in the region $1.1< q^2 <6.0 {\mathrm{\,Ge V^2\!/}c^4}$ and $1330< m( K ^+ \pi ^- ) <1530 {\mathrm{\,Me V\!/}c^2}$ as determined from a moment analysis of simulated $B ^0 \!\rightarrow K ^+ \pi ^- \mu ^+\mu ^-$ decays, shown as a histogram. The efficiency function is shown by the blue, dashed line. Fig3a.pdf [13 KiB] HiDef png [110 KiB] Thumbnail [35 KiB] *.C file Fig3b.pdf [13 KiB] HiDef png [116 KiB] Thumbnail [36 KiB] *.C file Fig3c.pdf [14 KiB] HiDef png [105 KiB] Thumbnail [33 KiB] *.C file Invariant mass $m( K ^+ \pi ^- \mu ^+ \mu ^- )$ for (left) the control decay $B ^0 \!\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^{*0}$ and (right) the signal decay $B ^0 \!\rightarrow K ^+ \pi ^- \mu ^+\mu ^-$ in the bin $1.1 < q^2 < 6.0 {\mathrm{\,Ge V^2\!/}c^4}$. The solid black line represents the total fitted function. The individual components of the signal (blue, shaded area) and combinatorial background (red, hatched area) are also shown. Fig4a.pdf [20 KiB] HiDef png [154 KiB] Thumbnail [48 KiB] *.C file Fig4b.pdf [21 KiB] HiDef png [309 KiB] Thumbnail [85 KiB] *.C file Differential branching fraction of $B ^0 \!\rightarrow K ^+ \pi ^- \mu ^+\mu ^-$ in bins of $q^2$ for the range $1330< m( K ^+ \pi ^- ) <1530 {\mathrm{\,Me V\!/}c^2}$. The error bars indicate the sums in quadrature of the statistical and systematic uncertainties. Fig5.pdf [14 KiB] HiDef png [74 KiB] Thumbnail [33 KiB] *.C file Measurement of the normalised moments, $\overline{\Gamma}_{i}$, of the decay $B ^0 \!\rightarrow K ^+ \pi ^- \mu ^+\mu ^-$ in the range $1.1< q^2 <6.0 {\mathrm{\,Ge V^2\!/}c^4}$ and $1330< m( K ^+ \pi ^- ) <1530 {\mathrm{\,Me V\!/}c^2}$. The error bars indicate the sums in quadrature of the statistical and systematic uncertainties. Fig6a.pdf [15 KiB] HiDef png [88 KiB] Thumbnail [43 KiB] *.C file Fig6b.pdf [15 KiB] HiDef png [95 KiB] Thumbnail [45 KiB] *.C file The distributions of each of the decay angles within the signal region. The acceptance-corrected data is represented by the points with error bars. The estimated signal distribution is shown by the blue, shaded histogram. The projected background from the upper mass sideband is shown by the red, hatched histogram, which is stacked onto the signal histogram. Fig7a.pdf [15 KiB] HiDef png [339 KiB] Thumbnail [95 KiB] *.C file Fig7b.pdf [15 KiB] HiDef png [396 KiB] Thumbnail [109 KiB] *.C file Fig7c.pdf [15 KiB] HiDef png [401 KiB] Thumbnail [107 KiB] *.C file Invariant mass $m( K ^+ \pi ^- \mu ^+ \mu ^- )$ distributions of the signal decay $B ^0 \!\rightarrow K ^+ \pi ^- \mu ^+\mu ^-$ in each of the $q^2$ bins used for the differential branching fraction measurement. The solid black line represents the total fitted function. The individual components of the signal (blue, shaded area) and combinatorial background (red, hatched area) are also shown. Fig8a.pdf [20 KiB] HiDef png [251 KiB] Thumbnail [70 KiB] *.C file Fig8b.pdf [20 KiB] HiDef png [281 KiB] Thumbnail [79 KiB] *.C file Fig8c.pdf [20 KiB] HiDef png [285 KiB] Thumbnail [81 KiB] *.C file Fig8d.pdf [20 KiB] HiDef png [315 KiB] Thumbnail [88 KiB] *.C file Fig8e.pdf [20 KiB] HiDef png [354 KiB] Thumbnail [96 KiB] *.C file Fig8f.pdf [21 KiB] HiDef png [309 KiB] Thumbnail [85 KiB] *.C file Animated gif made out of all figures. PAPER-2016-025.gif Thumbnail

## Tables and captions

 Expected resonant contributions above the $K ^{*}(892)^{0}$ mass range. For each, the spin-parity, $J^P$, and branching fraction to $K \pi$, $\mathcal{B}(K\pi)$, are given (taken from Ref. [10]). Table_1.pdf [54 KiB] HiDef png [82 KiB] Thumbnail [14 KiB] tex code Differential branching fraction of $B ^0 \!\rightarrow K ^+ \pi ^- \mu ^+\mu ^-$ in bins of $q^2$ for the range $1330< m( K ^+ \pi ^- ) <1530 {\mathrm{\,Me V\!/}c^2}$. The first uncertainty is statistical, the second systematic and the third due to the uncertainty on the $B ^0 \!\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^{*}(892)^{0}$ and ${ J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \!\rightarrow \mu ^+\mu ^-$ branching fractions. Table_2.pdf [42 KiB] HiDef png [125 KiB] Thumbnail [22 KiB] tex code Measurement of the normalised moments, $\overline{\Gamma}_{i}$, of the decay $B ^0 \!\rightarrow K ^+ \pi ^- \mu ^+\mu ^-$ in the range $1.1< q^2 <6.0 {\mathrm{\,Ge V^2\!/}c^4}$ and $1330< m( K ^+ \pi ^- ) <1530 {\mathrm{\,Me V\!/}c^2}$. The first uncertainty is statistical and the second systematic. Table_3.pdf [44 KiB] HiDef png [237 KiB] Thumbnail [47 KiB] tex code Summary of the main sources of systematic uncertainty for the differential branching fraction and the angular moments analysis. Typical ranges are quoted for the different $q^2$ bins used in the differential branching fraction measurement, and for the moments measured in the angular analysis. The systematic uncertainties are significantly smaller than the statistical ones. Table_4.pdf [56 KiB] HiDef png [61 KiB] Thumbnail [9 KiB] tex code The transversity-basis moments of the 41 orthonormal angular functions $f_i(\Omega)$ in Eq. 1 [12]. The amplitudes correspond to the $\overline{ B }{} {}^0$ decay. Table_5.pdf [77 KiB] HiDef png [365 KiB] Thumbnail [60 KiB] tex code

## Supplementary Material [file]

 Supplementary material full pdf supple[..].pdf [108 KiB]

Created on 20 April 2019.Citation count from INSPIRE on 24 April 2019.