Implications of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>CP</mml:mi></mml:math>asymmetry in semileptonic<i>B</i>decay

Recent experimental searches for ${A}_{\mathrm{SL}},$ the $\mathrm{CP}$ asymmetry in semileptonic B decay, have reached an accuracy of the order of one percent. Consequently, they give meaningful constraints on new physics. We find that cancellations between the standard model (SM) and new physics contributions to ${B}^{0}\ensuremath{-}{B}^{0}$ mixing cannot be as strong as was allowed prior to these measurements. The predictions for this asymmetry within the SM and within models of minimal flavor violation (MFV) are below the reach of present and near future measurements. Including order ${m}_{c}^{2}{/m}_{b}^{2}$ and ${\ensuremath{\Lambda}}_{\mathrm{QCD}}{/m}_{b}$ corrections we obtain the SM prediction $\ensuremath{-}1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}&lt;{A}_{\mathrm{SL}}&lt;\ensuremath{-}0.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}.$ Future measurements can exclude not only the SM, but MFV as well, if the sign of the asymmetry is opposite to the SM or if it is the same sign but much enhanced. We also comment on the $\mathrm{CP}$ asymmetry in semileptonic ${B}_{s}$ decay, and update the range of the angle ${\ensuremath{\beta}}_{s}$ in the SM: $0.026&lt;\mathrm{sin}2{\ensuremath{\beta}}_{s}&lt;0.048.$