Differential branching fraction and angular analysis of the $B^{+} \rightarrow K^{+}μ^{+}μ^{-}$ decay

TL;DR

This work measures the differential branching fraction $\mathrm{d}{\cal B}/\mathrm{d}q^2$ and the angular observables $A_{\rm FB}$ and $F_{\rm H}$ for the rare decay $B^{+} \rightarrow K^{+}\mu^{+}\mu^{-}$ using 1.0 fb$^{-1}$ of LHCb data at $\sqrt{s}=7$ TeV, normalising to $B^{+} \rightarrow K^{+}J/\psi$ to control systematics. The angular distribution is modeled by $\frac{1}{\Gamma}\frac{\mathrm{d}\Gamma}{\mathrm{d}\cos\theta_\ell}=\frac{3}{4}(1-F_{\rm H})(1-\cos^2\theta_\ell)+\frac{1}{2}F_{\rm H}+A_{\rm FB}\cos\theta_\ell$, with SM predicting $A_{\rm FB}=0$ and $F_{\rm H}\approx0$; the measurements across seven $q^2$ bins are consistent with these expectations. The differential branching fraction distribution is compatible with SM, and the total branching fraction is ${\cal B}(B^{+}\rightarrow K^{+}\mu^{+}\mu^{-})=(4.36\pm0.15\pm0.18)\times10^{-7}$, more precise than the previous world average. Together, these results constrain possible new-physics contributions in the vector/axial-vector and scalar/tensor operators governing $b\to s\mu\mu$ transitions and provide a stringent test of the SM in rare $B$ decays.

Abstract

The angular distribution and differential branching fraction of the decay $B^{+} \rightarrow K^{+}μ^{+}μ^{-}$ are studied with a dataset corresponding to $1.0\,\mathrm{fb}^{-1}$ of integrated luminosity, collected by the LHCb experiment. The angular distribution is measured in bins of dimuon invariant mass squared and found to be consistent with Standard Model expectations. Integrating the differential branching fraction over the full dimuon invariant mass range yields a total branching fraction of $\mathcal{B}(B^{+} \rightarrow K^{+}μ^{+}μ^{-}) = (4.36 \pm 0.15 \pm 0.18)\times 10^{-7}$. These measurements are the most precise to date of the $B^{+} \rightarrow K^{+}μ^{+}μ^{-}$ decay.

Figures (3)

• Figure 1: Invariant mass of selected $\mathrm{B}\xspace\xspace^+\xspace\xspace\!\rightarrow\xspace \mathrm{K}\xspace\xspace^+\xspace\upmu\xspace^+\upmu\xspace^-\xspace$ candidates with $0.05 < q^{2} < 22.00\mathrm{\,Ge V}\xspace^{2}/c^{4}$. Candidates with a dimuon invariant mass consistent with that of the ${\mathrm{J}\xspace / \uppsi\xspace }$ or $\uppsi\xspace{(2S)}$ are excluded. The peaking background contribution from the decays $\mathrm{B}\xspace\xspace^+\xspace\xspace\!\rightarrow\xspace \mathrm{K}\xspace\xspace^+\xspace\uppi\xspace\xspace^+\xspace\uppi\xspace\xspace^-\xspace$ and $\mathrm{B}\xspace\xspace^+\xspace\xspace\!\rightarrow\xspace \uppi\xspace\xspace^+\xspace\upmu\xspace^+\upmu\xspace^-\xspace$ is indicated in the figure.
• Figure 2: Differential branching fraction of $\mathrm{B}\xspace\xspace^+\xspace\xspace\!\rightarrow\xspace \mathrm{K}\xspace\xspace^+\xspace\upmu\xspace^+\upmu\xspace^-\xspace$ as a function of the dimuon invariant mass squared, $q^{2}$. The SM theory prediction (see text) is given as the continuous cyan (light) band and the rate-average of this prediction across the $q^{2}$ bin is indicated by the purple (dark) region. No SM prediction is included for the regions close to the narrow $\mathrm{c}\xspace\xspace\overline \mathrm{c}\xspace\xspace\xspace$ resonances.
• Figure 3: Dimuon forward-backward asymmetry, $A_{\rm FB}$, and the parameter $F_{\rm H}$ for $\mathrm{B}\xspace\xspace^+\xspace\xspace\!\rightarrow\xspace \mathrm{K}\xspace\xspace^+\xspace\upmu\xspace^+\upmu\xspace^-\xspace$ as a function of the dimuon invariant mass squared, $q^2$. The SM theory prediction (see text) for $F_{\rm H}$ is given as the continuous cyan (light) band and the rate-average of this prediction across the $q^2$ bin is indicated by the purple (dark) region. No SM prediction is included for the regions close to the narrow $\mathrm{c}\xspace\xspace\overline \mathrm{c}\xspace\xspace\xspace$ resonances.