Rates and asymmetries ofB→πℓ+ℓ−decays

Abstract

The LHCb experiment observed ${B}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ decay with $1.0\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ data, which is the first measurement of a flavor changing neutral current $b\ensuremath{\rightarrow}d{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ decay ($\ensuremath{\ell}=e,\ensuremath{\mu}$). Based on QCD factorization, we give standard model predictions for the branching ratios, direct CP asymmetries, and isospin asymmetry for $B\ensuremath{\rightarrow}\ensuremath{\pi}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ decays, in the kinematic region where the dilepton invariant mass is small. We find that the contribution from weak annihilation enhances the direct CP asymmetry for low ${\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ pair mass. Anticipating improved measurements, we assess the utility of ${B}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ observables, when combined with ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\ell}}^{+}\ensuremath{\nu}$ and ${B}^{+}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$, for determining Cabibbo-Kobayashi-Maskawa matrix parameters in the future.