cern.ch

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

[to restricted-access page]

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 3$ $fb$^{-1}$ of integrated luminosity, collected in proton-proton collisions at 7 and 8$ $TeV 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{\,GeV^2\!/}c^4} $ and (b) $15.0< q^2 < 22.0 {\mathrm{\,GeV^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 [243 KiB]
Thumbnail [70 KiB]
*.C file
eff_1_to_6.pdf
eff_15[..].pdf [15 KiB]
HiDef png [204 KiB]
Thumbnail [65 KiB] *.C file
eff_15_to_22.pdf

Top, reconstructed mass of $ B ^+ \!\rightarrow K ^+ \mu ^+\mu ^- $ candidates in the ranges (a) $1.1 < q^2 < 6.0 {\mathrm{\,GeV^2\!/}c^4} $ and (b) $15.0 < q^2 < 22.0 {\mathrm{\,GeV^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{\,GeV^2\!/}c^4} $ and (d) $15.0 < q^2 < 22.0 {\mathrm{\,GeV^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 [173 KiB]
Thumbnail [64 KiB]
*.C file
mass1to6Bp.pdf
mass15[..].pdf [19 KiB]
HiDef png [170 KiB]
Thumbnail [64 KiB] *.C file
mass15to22Bp.pdf
mass1to6B0.pdf [19 KiB]
HiDef png [213 KiB]
Thumbnail [78 KiB] *.C file
mass1to6B0.pdf
mass15[..].pdf [19 KiB]
HiDef png [210 KiB]
Thumbnail [77 KiB] *.C file
mass15to22B0.pdf

Top, angular distribution of $ B ^+ \!\rightarrow K ^+ \mu ^+\mu ^- $ candidates with (a) $1.1 < q^2 < 6.0 {\mathrm{\,GeV^2\!/}c^4} $ and (b) $15.0 < q^2 < 22.0 {\mathrm{\,GeV^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{\,GeV^2\!/}c^4} $ and (d) $15.0 < q^2 < 22.0 {\mathrm{\,GeV^2\!/}c^4} $. Only candidates with a reconstructed mass within $\pm50 {\mathrm{\,MeV\!/}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 [141 KiB]
Thumbnail [58 KiB]
*.C file
costhetal1to6Bp.pdf
costhe[..].pdf [16 KiB]
HiDef png [140 KiB]
Thumbnail [58 KiB] *.C file
costhetal15to22Bp.pdf
costhe[..].pdf [15 KiB]
HiDef png [127 KiB]
Thumbnail [50 KiB] *.C file
costhetal1to6B0.pdf
costhe[..].pdf [15 KiB]
HiDef png [124 KiB]
Thumbnail [49 KiB] *.C file
costhetal15to22B0.pdf

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{\,GeV^2\!/}c^4} $ and (b) $15.0 < q^2 < 22.0 {\mathrm{\,GeV^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 [227 KiB]
Thumbnail [68 KiB]
*.C file
AFB_FH_2D_1_to_6.pdf
AFB_FH[..].pdf [16 KiB]
HiDef png [234 KiB]
Thumbnail [70 KiB] *.C file
AFB_FH_2D_15_to_22.pdf

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 [84 KiB]
Thumbnail [39 KiB]
*.C file
cAFB.pdf
cFH.pdf [18 KiB]
HiDef png [123 KiB]
Thumbnail [45 KiB] *.C file
cFH.pdf

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 [87 KiB]
Thumbnail [31 KiB]
*.C file
cFHK0.pdf

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{\,GeV^2\!/}c^4} $, (b) $1.10 < q^2 < 2.00 {\mathrm{\,GeV^2\!/}c^4} $, (c) $2.00 < q^2 < 3.00 {\mathrm{\,GeV^2\!/}c^4} $ and (d) $3.00 < q^2 < 4.00 {\mathrm{\,GeV^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 [268 KiB]
Thumbnail [70 KiB]
*.C file
AFB_FH_0_to_1.pdf
AFB_FH[..].pdf [16 KiB]
HiDef png [259 KiB]
Thumbnail [69 KiB] *.C file
AFB_FH_1_to_2.pdf
AFB_FH[..].pdf [16 KiB]
HiDef png [258 KiB]
Thumbnail [67 KiB] *.C file
AFB_FH_2_to_3.pdf
AFB_FH[..].pdf [16 KiB]
HiDef png [185 KiB]
Thumbnail [56 KiB] *.C file
AFB_FH_3_to_4.pdf

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{\,GeV^2\!/}c^4} $, (b) $5.00 < q^2 < 6.00 {\mathrm{\,GeV^2\!/}c^4} $, (c) $6.00 < q^2 < 7.00 {\mathrm{\,GeV^2\!/}c^4} $ and (d) $7.00 < q^2 < 8.00 {\mathrm{\,GeV^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 [214 KiB]
Thumbnail [61 KiB]
*.C file
AFB_FH_4_to_5.pdf
AFB_FH[..].pdf [16 KiB]
HiDef png [237 KiB]
Thumbnail [65 KiB] *.C file
AFB_FH_5_to_6.pdf
AFB_FH[..].pdf [16 KiB]
HiDef png [203 KiB]
Thumbnail [59 KiB] *.C file
AFB_FH_6_to_7.pdf
AFB_FH[..].pdf [16 KiB]
HiDef png [182 KiB]
Thumbnail [55 KiB] *.C file
AFB_FH_7_to_8.pdf

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{\,GeV^2\!/}c^4} $, (b) $11.75 < q^2 < 12.50 {\mathrm{\,GeV^2\!/}c^4} $ and (c) $15.00 < q^2 < 16.00 {\mathrm{\,GeV^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 [244 KiB]
Thumbnail [67 KiB]
*.C file
AFB_FH_11_to_11.pdf
AFB_FH[..].pdf [16 KiB]
HiDef png [208 KiB]
Thumbnail [60 KiB] *.C file
AFB_FH_11_to_12.pdf
AFB_FH[..].pdf [16 KiB]
HiDef png [259 KiB]
Thumbnail [69 KiB] *.C file
AFB_FH_15_to_16.pdf

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{\,GeV^2\!/}c^4} $, (b) $17.00 < q^2 < 18.00 {\mathrm{\,GeV^2\!/}c^4} $ and (c) $18.00 < q^2 < 19.00 {\mathrm{\,GeV^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 [227 KiB]
Thumbnail [63 KiB]
*.C file
AFB_FH_16_to_17.pdf
AFB_FH[..].pdf [16 KiB]
HiDef png [245 KiB]
Thumbnail [67 KiB] *.C file
AFB_FH_17_to_18.pdf
AFB_FH[..].pdf [17 KiB]
HiDef png [284 KiB]
Thumbnail [73 KiB] *.C file
AFB_FH_18_to_19.pdf

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{\,GeV^2\!/}c^4} $, (b) $20.00 < q^2 < 21.00 {\mathrm{\,GeV^2\!/}c^4} $ and (c) $21.00 < q^2 < 22.00 {\mathrm{\,GeV^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 [236 KiB]
Thumbnail [64 KiB]
*.C file
AFB_FH_19_to_20.pdf
AFB_FH[..].pdf [16 KiB]
HiDef png [246 KiB]
Thumbnail [66 KiB] *.C file
AFB_FH_20_to_21.pdf
AFB_FH[..].pdf [15 KiB]
HiDef png [173 KiB]
Thumbnail [53 KiB] *.C file
AFB_FH_21_to_22.pdf

Animated gif made out of all figures.

PAPER-2014-007.gif
Thumbnail
thumbnail_PAPER-2014-007.gif

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{\,GeV^2\!/}c^4} $) and low ($15.0 < q^2 < 22.0 {\mathrm{\,GeV^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 [192 KiB]
Thumbnail [31 KiB]
tex code
Table_1.pdf

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{\,GeV^2\!/}c^4} $) and low ($15.0 < q^2 < 22.0 {\mathrm{\,GeV^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 [101 KiB]
Thumbnail [17 KiB]
tex code
Table_2.pdf

Created on 09 December 2018.Citation count from INSPIRE on 18 December 2018.