# Angular analysis of charged and neutral $B \to K \mu^+\mu^-$ decays

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## Abstract

The angular distributions of the rare decays $B^+ \to K^+\mu^+\mu^-$ and $B^0 \to K^0_{\rm\scriptscriptstyle S}\mu^+\mu^-$ are studied with data corresponding to 3fb$^{-1}$ of integrated luminosity, collected in proton-proton collisions at 7 and 8TeV centre-of-mass energies with the LHCb detector. The angular distribution is described by two parameters, $F_{\rm H}$ and the forward-backward asymmetry of the dimuon system $A_{\rm FB}$, which are determined in bins of the dimuon mass squared. The parameter $F_{\rm H}$ is a measure of the contribution from (pseudo)scalar and tensor amplitudes to the decay width. The measurements of $A_{\rm FB}$ and $F_{\rm H}$ reported here are the most precise to date and are compatible with predictions from the Standard Model.

## Figures and captions

 Angular acceptance as derived from simulation in the dimuon mass squared ranges (a) $1.1< q^2 < 6.0 {\mathrm{ Ge V^2 /}c^4}$ and (b) $15.0< q^2 < 22.0 {\mathrm{ Ge V^2 /}c^4}$. The dip in the acceptance for $B ^+ \rightarrow K ^+ \mu ^+\mu ^-$ decays results from the veto used to reject $B ^+ \rightarrow \overline{ D }{} ^0 \pi ^+$ decays (see text). The acceptance is normalised to unit area to allow a comparison of the shape of the distributions. eff_1_to_6.pdf [15 KiB] HiDef png [262 KiB] Thumbnail [187 KiB] *.C file eff_15[..].pdf [15 KiB] HiDef png [221 KiB] Thumbnail [169 KiB] *.C file Top, reconstructed mass of $B ^+ \rightarrow K ^+ \mu ^+\mu ^-$ candidates in the ranges (a) $1.1 < q^2 < 6.0 {\mathrm{ Ge V^2 /}c^4}$ and (b) $15.0 < q^2 < 22.0 {\mathrm{ Ge V^2 /}c^4}$. Bottom, reconstructed mass of $B ^0 \rightarrow K ^0_{\rm\scriptscriptstyle S} \mu ^+\mu ^-$ candidates in the ranges (c) $1.1 < q^2 < 6.0 {\mathrm{ Ge V^2 /}c^4}$ and (d) $15.0 < q^2 < 22.0 {\mathrm{ Ge V^2 /}c^4}$. The data are overlaid with the result of the fit described in the text. The long and downstream $K ^0_{\rm\scriptscriptstyle S}$ categories are combined for presentation purposes. The shaded region indicates the background contribution in the fit. mass1to6Bp.pdf [20 KiB] HiDef png [181 KiB] Thumbnail [163 KiB] *.C file mass15[..].pdf [19 KiB] HiDef png [178 KiB] Thumbnail [161 KiB] *.C file mass1to6B0.pdf [19 KiB] HiDef png [236 KiB] Thumbnail [196 KiB] *.C file mass15[..].pdf [19 KiB] HiDef png [232 KiB] Thumbnail [194 KiB] *.C file Top, angular distribution of $B ^+ \rightarrow K ^+ \mu ^+\mu ^-$ candidates with (a) $1.1 < q^2 < 6.0 {\mathrm{ Ge V^2 /}c^4}$ and (b) $15.0 < q^2 < 22.0 {\mathrm{ Ge V^2 /}c^4}$. Bottom, angular distribution of $B ^0 \rightarrow K ^0_{\rm\scriptscriptstyle S} \mu ^+\mu ^-$ candidates with (c) $1.1 < q^2 < 6.0 {\mathrm{ Ge V^2 /}c^4}$ and (d) $15.0 < q^2 < 22.0 {\mathrm{ Ge V^2 /}c^4}$. Only candidates with a reconstructed mass within $\pm50 {\mathrm{ Me V /}c^2}$ of the known $B ^+$ or $B ^0$ mass are shown. The data are overlaid with the result of the fit described in the text. The long and downstream $K ^0_{\rm\scriptscriptstyle S}$ categories are combined for presentation purposes. The shaded region indicates the background contribution in the fit. costhe[..].pdf [16 KiB] HiDef png [151 KiB] Thumbnail [142 KiB] *.C file costhe[..].pdf [16 KiB] HiDef png [149 KiB] Thumbnail [141 KiB] *.C file costhe[..].pdf [15 KiB] HiDef png [131 KiB] Thumbnail [119 KiB] *.C file costhe[..].pdf [15 KiB] HiDef png [127 KiB] Thumbnail [117 KiB] *.C file Two-dimensional confidence regions for $A_{\rm FB}$ and $F_{\rm H}$ for the decay $B ^+ \rightarrow K ^+ \mu ^+\mu ^-$ in the $q^2$ ranges (a) $1.1 < q^2 < 6.0 {\mathrm{ Ge V^2 /}c^4}$ and (b) $15.0 < q^2 < 22.0 {\mathrm{ Ge V^2 /}c^4}$. The confidence intervals are determined using the Feldman-Cousins technique. The shaded (triangular) region illustrates the range of $A_{\rm FB}$ and $F_{\rm H}$ over which the signal angular distribution remains positive in all regions of phase-space. AFB_FH[..].pdf [16 KiB] HiDef png [231 KiB] Thumbnail [185 KiB] *.C file AFB_FH[..].pdf [16 KiB] HiDef png [238 KiB] Thumbnail [189 KiB] *.C file Dimuon forward-backward asymmetry, $A_{\rm FB}$, and the parameter $F_{\rm H}$ for the decay $B ^+ \rightarrow K ^+ \mu ^+\mu ^-$ as a function of the dimuon invariant mass squared, $q^2$ . The inner horizontal bars indicate the one-dimensional 68% confidence intervals. The outer vertical bars include contributions from systematic uncertainties (described in the text). The confidence intervals for $F_{\rm H}$ are overlaid with the SM theory prediction (narrow band). Data are not presented for the regions around the ${ J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ and $\psi {(2S)}$ resonances. cAFB.pdf [14 KiB] HiDef png [86 KiB] Thumbnail [84 KiB] *.C file cFH.pdf [18 KiB] HiDef png [126 KiB] Thumbnail [97 KiB] *.C file Results for the parameter $F_{\rm H}$ for the decay $B ^0 \rightarrow K ^0_{\rm\scriptscriptstyle S} \mu ^+\mu ^-$ as a function of the dimuon invariant mass squared, $q^2$ . The inner horizontal bars indicate the one-dimensional 68% confidence intervals. The outer vertical bars include contributions from systematic uncertainties (described in the text). The confidence intervals are overlaid with the SM theory prediction (narrow band). Data are not presented for the regions around the ${ J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ and $\psi {(2S)}$ resonances. cFHK0.pdf [17 KiB] HiDef png [89 KiB] Thumbnail [68 KiB] *.C file Two-dimensional confidence regions for $A_{\rm FB}$ and $F_{\rm H}$ for the decay $B ^+ \rightarrow K ^+ \mu ^+\mu ^-$ in the $q^2$ ranges (a) $0.10 < q^2 < 0.98 {\mathrm{ Ge V^2 /}c^4}$, (b) $1.10 < q^2 < 2.00 {\mathrm{ Ge V^2 /}c^4}$, (c) $2.00 < q^2 < 3.00 {\mathrm{ Ge V^2 /}c^4}$ and (d) $3.00 < q^2 < 4.00 {\mathrm{ Ge V^2 /}c^4}$. The confidence intervals are determined using the Feldman-Cousins technique and are purely statistical. The shaded (triangular) region illustrates the range of $A_{\rm FB}$ and $F_{\rm H}$ over which the signal angular distribution remains positive in all regions of phase-space. AFB_FH[..].pdf [17 KiB] HiDef png [270 KiB] Thumbnail [191 KiB] *.C file AFB_FH[..].pdf [16 KiB] HiDef png [262 KiB] Thumbnail [188 KiB] *.C file AFB_FH[..].pdf [16 KiB] HiDef png [261 KiB] Thumbnail [183 KiB] *.C file AFB_FH[..].pdf [16 KiB] HiDef png [188 KiB] Thumbnail [151 KiB] *.C file Two-dimensional confidence regions for $A_{\rm FB}$ and $F_{\rm H}$ for the decay $B ^+ \rightarrow K ^+ \mu ^+\mu ^-$ in the $q^2$ ranges (a) $4.00 < q^2 < 5.00 {\mathrm{ Ge V^2 /}c^4}$, (b) $5.00 < q^2 < 6.00 {\mathrm{ Ge V^2 /}c^4}$, (c) $6.00 < q^2 < 7.00 {\mathrm{ Ge V^2 /}c^4}$ and (d) $7.00 < q^2 < 8.00 {\mathrm{ Ge V^2 /}c^4}$. The confidence intervals are determined using the Feldman-Cousins technique and are purely statistical. The shaded (triangular) region illustrates the range of $A_{\rm FB}$ and $F_{\rm H}$ over which the signal angular distribution remains positive in all regions of phase-space. AFB_FH[..].pdf [15 KiB] HiDef png [217 KiB] Thumbnail [164 KiB] *.C file AFB_FH[..].pdf [16 KiB] HiDef png [239 KiB] Thumbnail [178 KiB] *.C file AFB_FH[..].pdf [16 KiB] HiDef png [206 KiB] Thumbnail [160 KiB] *.C file AFB_FH[..].pdf [16 KiB] HiDef png [185 KiB] Thumbnail [149 KiB] *.C file Two-dimensional confidence regions for $A_{\rm FB}$ and $F_{\rm H}$ for the decay $B ^+ \rightarrow K ^+ \mu ^+\mu ^-$ in the $q^2$ ranges (a) $11.00 < q^2 < 11.75 {\mathrm{ Ge V^2 /}c^4}$, (b) $11.75 < q^2 < 12.50 {\mathrm{ Ge V^2 /}c^4}$ and (c) $15.00 < q^2 < 16.00 {\mathrm{ Ge V^2 /}c^4}$. The confidence intervals are determined using the Feldman-Cousins technique and are purely statistical. The shaded (triangular) region illustrates the range of $A_{\rm FB}$ and $F_{\rm H}$ over which the signal angular distribution remains positive in all regions of phase-space. AFB_FH[..].pdf [15 KiB] HiDef png [247 KiB] Thumbnail [182 KiB] *.C file AFB_FH[..].pdf [16 KiB] HiDef png [211 KiB] Thumbnail [163 KiB] *.C file AFB_FH[..].pdf [16 KiB] HiDef png [261 KiB] Thumbnail [189 KiB] *.C file Two-dimensional confidence regions for $A_{\rm FB}$ and $F_{\rm H}$ for the decay $B ^+ \rightarrow K ^+ \mu ^+\mu ^-$ in the $q^2$ ranges (a) $16.00 < q^2 < 17.00 {\mathrm{ Ge V^2 /}c^4}$, (b) $17.00 < q^2 < 18.00 {\mathrm{ Ge V^2 /}c^4}$ and (c) $18.00 < q^2 < 19.00 {\mathrm{ Ge V^2 /}c^4}$. The confidence intervals are determined using the Feldman-Cousins technique and are purely statistical. The shaded (triangular) region illustrates the range of $A_{\rm FB}$ and $F_{\rm H}$ over which the signal angular distribution remains positive in all regions of phase-space. AFB_FH[..].pdf [15 KiB] HiDef png [230 KiB] Thumbnail [172 KiB] *.C file AFB_FH[..].pdf [16 KiB] HiDef png [248 KiB] Thumbnail [181 KiB] *.C file AFB_FH[..].pdf [17 KiB] HiDef png [287 KiB] Thumbnail [201 KiB] *.C file Two-dimensional confidence regions for $A_{\rm FB}$ and $F_{\rm H}$ for the decay $B ^+ \rightarrow K ^+ \mu ^+\mu ^-$ in the $q^2$ ranges (a) $19.00 < q^2 < 20.00 {\mathrm{ Ge V^2 /}c^4}$, (b) $20.00 < q^2 < 21.00 {\mathrm{ Ge V^2 /}c^4}$ and (c) $21.00 < q^2 < 22.00 {\mathrm{ Ge V^2 /}c^4}$. The confidence intervals are determined using the Feldman-Cousins technique and are purely statistical. The shaded (triangular) region illustrates the range of $A_{\rm FB}$ and $F_{\rm H}$ over which the signal angular distribution remains positive in all regions of phase-space. AFB_FH[..].pdf [16 KiB] HiDef png [239 KiB] Thumbnail [175 KiB] *.C file AFB_FH[..].pdf [16 KiB] HiDef png [249 KiB] Thumbnail [179 KiB] *.C file AFB_FH[..].pdf [15 KiB] HiDef png [175 KiB] Thumbnail [141 KiB] *.C file Animated gif made out of all figures. PAPER-2014-007.gif Thumbnail

## Tables and captions

 Forward-backward asymmetry, $A_{\rm FB}$, and $F_{\rm H}$ for the decay $B ^+ \rightarrow K ^+ \mu ^+\mu ^-$ in the $q^2$ bins used in this analysis. These parameters are also given in a wide bin at large ($1.1 < q^2 <6.0 {\mathrm{ Ge V^2 /}c^4}$) and low ($15.0 < q^2 < 22.0 {\mathrm{ Ge V^2 /}c^4}$) hadronic recoil. The column labelled stat is the 68% statistical confidence interval on $F_{\rm H}$ ($A_{\rm FB}$) when treating $A_{\rm FB}$ ($F_{\rm H}$) as a nuisance parameter. The column labelled syst is the systematic uncertainty. Table_1.pdf [37 KiB] HiDef png [230 KiB] Thumbnail [118 KiB] tex code The 68% confidence interval on the parameter $F_{\rm H}$ for the decay $B ^0 \rightarrow K ^0_{\rm\scriptscriptstyle S} \mu ^+\mu ^-$ in $q^2$ bins. In addition to the narrow binning used in the analysis, results are also given in wide bins at large ($1.1 < q^2 <6.0 {\mathrm{ Ge V^2 /}c^4}$) and low ($15.0 < q^2 < 22.0 {\mathrm{ Ge V^2 /}c^4}$) hadronic recoil. The column labelled stat is the 68% statistical confidence interval. The column labelled syst is the systematic uncertainty. Table_2.pdf [36 KiB] HiDef png [127 KiB] Thumbnail [63 KiB] tex code

Created on 21 October 2019.