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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Animated gif made out of all figures.

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.

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.