The angular distribution and differential branching fraction of the decay $B^{0} \to K^{*0} \mu^{+}\mu^{}$ are studied using a data sample, collected by the LHCb experiment in $pp$ collisions at $\sqrt{s}=7 {\rm TeV}$, corresponding to an integrated luminosity of $1.0 {\rm fb}^{1}$. Several angular observables are measured in bins of the dimuon invariant mass squared, $q^{2}$. A first measurement of the zerocrossing point of the forwardbackward asymmetry of the dimuon system is also presented. The zerocrossing point is measured to be $q_{0}^{2} = 4.9 \pm 0.9 {\rm GeV}^{2}/c^{4}$, where the uncertainty is the sum of statistical and systematic uncertainties. The results are consistent with the Standard Model predictions.
Distribution of $\mu ^+\mu ^ $ versus $ K ^+ \pi ^ \mu ^+\mu ^ $ invariant mass of selected $ B ^0 \rightarrow K ^{*0} \mu ^+\mu ^ $ candidates. The vertical lines indicate a $\pm 50 {\mathrm{ Me V /}c^2} $ signal mass window around the nominal $ B ^0$ mass. The horizontal lines indicate the two veto regions that are used to remove $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ and $\psi {(2S)} \rightarrow \mu ^+\mu ^ $ decays. The $ B ^0 \rightarrow K ^{*0} \mu ^+\mu ^ $ signal is clearly visible outside of the $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ and $\psi {(2S)} \rightarrow \mu ^+\mu ^ $ windows. 
plot2D.pdf [24 KiB] HiDef png [287 KiB] Thumbnail [321 KiB] *.C file 

Invariant mass distributions of $ K ^+ \pi ^ \mu ^+\mu ^ $ candidates in the six $ q^2$ bins used in the analysis. The candidates have been weighted to account for the detector acceptance (see text). Contributions from exclusive (peaking) backgrounds are negligible after applying the vetoes described in Sec. 4. 
mass0.pdf [20 KiB] HiDef png [176 KiB] Thumbnail [171 KiB] *.C file 

mass1.pdf [21 KiB] HiDef png [144 KiB] Thumbnail [137 KiB] *.C file 

mass2.pdf [21 KiB] HiDef png [168 KiB] Thumbnail [160 KiB] *.C file 

mass3.pdf [20 KiB] HiDef png [157 KiB] Thumbnail [149 KiB] *.C file 

mass4.pdf [19 KiB] HiDef png [127 KiB] Thumbnail [124 KiB] *.C file 

mass5.pdf [20 KiB] HiDef png [143 KiB] Thumbnail [135 KiB] *.C file 

Differential branching fraction of the $ B ^0 \rightarrow K ^{*0} \mu ^+\mu ^ $ decay as a function of the dimuon invariant mass squared. The data are overlaid with a SM prediction (see text) for the decay (lightblue band). A rate average of the SM prediction across each $ q^2$ bin is indicated by the dark (purple) rectangular regions. No SM prediction is included in the region close to the narrow $ c \overline c $ resonances. 
cWidth.pdf [18 KiB] HiDef png [132 KiB] Thumbnail [109 KiB] *.C file 

Fraction of longitudinal polarisation of the $ K ^{*0}$ , $F_{\rm L}$, dimuon system forwardbackward asymmetry, $A_{\rm FB}$ and the angular observables $S_3$ and $A_9$ from the $ B ^0 \rightarrow K ^{*0} \mu ^+\mu ^ $ decay as a function of the dimuon invariant mass squared, $ q^2$ . The lowest $ q^2$ bin has been corrected for the threshold behaviour described in Sec. 7.2. The experimental data points overlay the SM prediction described in the text. A rate average of the SM prediction across each $ q^2$ bin is indicated by the dark (purple) rectangular regions. No theory prediction is included for $A_9$, which is vanishingly small in the SM. 
cFL.pdf [18 KiB] HiDef png [119 KiB] Thumbnail [98 KiB] *.C file 

cAFB.pdf [17 KiB] HiDef png [105 KiB] Thumbnail [93 KiB] *.C file 

cS3.pdf [17 KiB] HiDef png [97 KiB] Thumbnail [90 KiB] *.C file 

cA9.pdf [14 KiB] HiDef png [72 KiB] Thumbnail [72 KiB] *.C file 

Transverse asymmetries $A_{\rm T}^{2}$ and $A_{\rm T}^{\rm Re}$ as a function of the dimuon invariant mass squared, $ q^2$ , in the $ B ^0 \rightarrow K ^{*0} \mu ^+\mu ^ $ decay. The lowest $ q^2$ bin has been corrected for the threshold behaviour described in Sec. 7.2. The experimental data points overlay the SM prediction that is described in the text. A rate average of the SM prediction across each $ q^2$ bin is indicated by the dark (purple) rectangular regions. 
cAT2.pdf [17 KiB] HiDef png [104 KiB] Thumbnail [93 KiB] *.C file 

cATRE.pdf [19 KiB] HiDef png [131 KiB] Thumbnail [106 KiB] *.C file 

Dimuon invariant mass squared, $ q^2$ , distribution of forwardgoing (left) and backwardgoing (right) candidates in the $ K ^+ \pi ^ \mu ^+\mu ^ $ invariant mass window $5230 < m( K ^+ \pi ^ \mu ^+\mu ^ ) < 5330 {\mathrm{ Me V /}c^2} $. The polynomial fit to the signal and background distributions in $ q^2$ is overlaid. 
forward.pdf [17 KiB] HiDef png [152 KiB] Thumbnail [149 KiB] *.C file 

backward.pdf [17 KiB] HiDef png [160 KiB] Thumbnail [158 KiB] *.C file 

Graphical representation of the angular basis used for $ B ^0 \rightarrow K ^{*0} \mu ^+\mu ^ $ and $\overline{ B }{} ^0 \rightarrow \overline{ K }{} ^{*0} \mu ^+\mu ^ $ decays in this paper. The notation $\hat{n}_{ab}$ is used to represent the normal to the plane containing particles $a$ and $b$ in the $ B ^0 $ (or $\overline{ B }{} ^0$ ) rest frame. An explicit description of the angular basis is given in the text. 
anglephi.pdf [88 KiB] HiDef png [256 KiB] Thumbnail [224 KiB] *.C file 

Animated gif made out of all figures. 
PAPER2013019.gif Thumbnail 
Signal yield ($N_{\text{sig}}$) and differential branching fraction ($\mathrm{d}\cal B /\mathrm{d} q^2 $) of the $ B ^0 \rightarrow K ^{*0} \mu ^+\mu ^ $ decay in the six $ q^2$ bins used in this analysis. Results are also presented in the $1 < q^2 < 6\mathrm{ Ge V} ^{2}/c^{4}$ range where theoretical uncertainties are best controlled. The first and second uncertainties are statistical and systematic. The third uncertainty comes from the uncertainty on the $ B ^0 \rightarrow K ^{*0} { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} $ and $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \rightarrow \mu ^+\mu ^ $ branching fractions. The final uncertainty on $\mathrm{d}\cal B /\mathrm{d} q^2 $ comes from an estimate of the pollution from non $ K ^{*0}$ $ B ^0 \rightarrow K ^+ \pi ^ \mu ^+\mu ^ $ decays in the $792 < m({ K ^+ \pi ^ }) < 992 {\mathrm{ Me V /}c^2} $ mass window (see Sec. 7.3.2). 
Table_1.pdf [51 KiB] HiDef png [123 KiB] Thumbnail [68 KiB] tex code 

Fraction of longitudinal polarisation of the $ K ^{*0}$ , $F_{\rm L}$, dimuon system forwardbackward asymmetry, $A_{\rm FB}$ and the angular observables $S_3$, $S_9$ and $A_9$ from the $ B ^0 \rightarrow K ^{*0} \mu ^+\mu ^ $ decay in the six bins of dimuon invariant mass squared, $ q^2$ , used in the analysis. The lower table includes the transverse observables $A_{\rm T}^{\rm Re}$ and $A_{\rm T}^{2}$, which have reduced formfactor uncertainties. Results are also presented in the $1 < q^2 < 6\mathrm{ Ge V} ^{2}/c^{4}$ range where theoretical uncertainties are best controlled. In the largerecoil bin, $0.1 < q^2 < 2.0\mathrm{ Ge V} ^{2}/c^{4}$, two results are given to highlight the size of the correction needed to account for changes in the angular distribution that occur when $ q^2 \raise.15em\hbox{$<$} \lower.35em\hbox{$\sim$} 1\mathrm{ Ge V} ^{2}/c^{4}$ (see Sec. 7.2). The value of $F_{\rm L}$ is independent of this correction. The final column contains the pvalue for the SM point (see text). No SM prediction, and consequently no pvalue, is available for the $10.09 < q^2 < 12.86\mathrm{ Ge V} ^{2}/c^{4}$ range. 
Table_2.pdf [56 KiB] HiDef png [266 KiB] Thumbnail [113 KiB] tex code 

Systematic contributions to the angular observables. The values given are the magnitude of the maximum contribution from each source of systematic uncertainty, taken across the six principal $ q^2$ bins used in the analysis. 
Table_3.pdf [42 KiB] HiDef png [92 KiB] Thumbnail [40 KiB] tex code 
README for supplementary information. A comparison of \lhcb's differential branching fraction measurement with earlier measurements from \babar~\cite{Aubert:2006vb,:2012vw}, \belle~\cite{:2009zv} and CDF~\cite{Aaltonen:2011ja} is provided in Fig.~\ref{fig:Supplementary:branching}. This figure also includes the recent CMS preliminary result~\cite{CMSPASBPH11009}. A comparison of the angular observables is provided in Fig.~\ref{fig:Supplementary:afb}. There is good agreement between the measurements of the experiments in every \qsq bin. The parameters $S_3$ and $S_9$ have not been previously measured. Fig1supp: Differential branching fraction of \decay{\Bz}{\Kstarz\mumu} as a function of the dimuon invariant mass squared, \qsq. The SM theory prediction is given as the continuous cyan (light) band and the rateaverage of this prediction across each $q^{2}$ bin is indicated by the purple (dark) rectangular regions. No SM prediction is included for the regions close to the narrow \ccbar resonances. Previous results from \babar~\cite{:2012vw}, \belle~\cite{:2009zv} and CDF~\cite{Aaltonen:2011ja} are included for reference, as is the recent CMS preliminary result~\cite{CMSPASBPH11009}. The bin centres of the data points have been offset for graphical purposes. Fig2supp (a)(d): Dimuon forwardbackward asymmetry, $A_{\rm FB}$, longitudinal polarisation fraction, $F_{\rm L}$ and angular observables $A_{T}^{2}$ and $A_9$ for the decay \decay{\Bz}{\Kstarz\mumu} as a function of the dimuon invariant mass squared, \qsq. The values of these observables measured by \babar~\cite{Aubert:2006vb,:2012vw}, \belle~\cite{:2009zv}, CDF~\cite{Aaltonen:2011ja} and recent preliminary results from ATLAS~\cite{ATLASCONF2013038} and CMS~\cite{CMSPASBPH11009} are included for reference. The SM theory prediction is given as the continuous cyan (light) band and the rateaverage of this prediction across each $q^{2}$ bin is indicated by the purple (dark) rectangular regions. No SM prediction is included for the regions close to the narrow \ccbar resonances. The bin centres of the data points have been offset for graphical purposes. References: Ref CMSPASBPH11009: CMS collaboration, Angular analysis and branching ratio measurement of the decay $B^{0} \to K^{*0} \mu^{+}\mu^{}$, CMSPASBPH11009 Ref ATLASCONF2013038: ATLAS collaboration, Angular analysis of $B_{d} \to K^{\ast 0}\mu^{+}\mu^{}$ with the ATLAS experiment, ATLASCONF2013038 Ref :2009zv: Belle collaboration, J.T. Wei et al., Measurement of the differential branching fraction and forwardbackword asymmetry for $B \to K^{(*)} \ell^+\ell^$, Phys. Rev. Lett. 103 (2009) 171801, arXiv:0904.0770 Ref Aubert:2006vb: BaBar collaboration, B.~Aubert et al., Measurements of branching fractions, rate asymmetries, and angular distributions in the rare decays $B \to K \ell^{+} \ell^{}$ and $B \to K^{*} \ell^{+} \ell^{}$, Phys. Rev. D. 73. 092001 arXiv:hepex/0604007. Ref Aaltonen:2011ja: CDF collaboration, T. Aaltonen et al., Measurements of the angular distributions in the decays $B \to K^{(*)} \mu^+ \mu^$ at CDF, Phys. Rev. Lett. 108 081807, arXiv:1108.0695. 
Fig1supp.pdf [20 KiB] HiDef png [204 KiB] Thumbnail [153 KiB] *C file 

Fig2asupp.pdf [20 KiB] HiDef png [219 KiB] Thumbnail [158 KiB] *C file 

Fig2bsupp.pdf [20 KiB] HiDef png [205 KiB] Thumbnail [152 KiB] *C file 

Fig2csupp.pdf [18 KiB] HiDef png [114 KiB] Thumbnail [96 KiB] *C file 

Fig2dsupp.pdf [14 KiB] HiDef png [81 KiB] Thumbnail [76 KiB] *C file 
Created on 17 August 2019.Citation count from INSPIRE on 23 August 2019.