$B\to K^* \ell^+ \ell^-$ decays at large recoil in the Standard Model: a theoretical reappraisal

Abstract

We critically reassess the theoretical uncertainties in the Standard Model calculation of the $B \to K^* \ell^+ \ell^-$ observables, focusing on the low $q^2$ region. We point out that even optimized observables are affected by sizable uncertainties, since hadronic contributions generated by current-current operators with charm are difficult to estimate, especially for $q^2 \sim 4 m_c^2\simeq 6.8$ GeV$^2$. We perform a detailed numerical analysis and present both predictions and results from the fit obtained using most recent data. We find that non-factorizable power corrections of the expected order of magnitude are sufficient to give a good description of current experimental data within the Standard Model. We discuss in detail the $q^2$ dependence of the corrections and their possible interpretation as shifts of the Standard Model Wilson coefficients.