Extracting short distance information fromb→sℓ+ℓ−effectively

Abstract

We point out that in inclusive $B\ensuremath{\rightarrow}{X}_{s}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ decay an angular decomposition provides a third (${q}^{2}$ dependent) observable sensitive to a different combination of Wilson coefficients than the rate and the forward-backward asymmetry. Since a precise measurement of ${q}^{2}$ dependence requires large data sets, it is important to consider the data integrated over regions of ${q}^{2}$. We develop a strategy to extract all measurable Wilson coefficients in $B\ensuremath{\rightarrow}{X}_{s}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ from a few simple integrated rates in the low ${q}^{2}$ region. A similar decomposition in $B\ensuremath{\rightarrow}{K}^{*}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$, together with the $B\ensuremath{\rightarrow}{K}^{*}\ensuremath{\gamma}$ rate, also provides a determination of the Wilson coefficients, without reliance on form factor models and without having to measure the zero of the forward-backward asymmetry.