The benefits of $ \bar{B} \to {\bar{K}^*}{l^{+} }{l^{-} } $ decays at low recoil

Abstract

Using the heavy quark effective theory framework put forward by Grinstein and Pirjol we work out predictions for \( \bar{B} \to {\bar{K}^*}{l^{+} }{l^{-} } \), l = e, μ, decays for a softly recoiling \( {\bar{K}^*} \), i.e., for large dilepton masses \( \sqrt {{{q^2}}} \) of the order of the b-quark mass m b . We work to lowest order in Λ/Q, where \( Q = \left( {{m_b}\sqrt {{{q^2}}} } \right) \) and include the next-to-leading order corrections from the charm quark mass m c and the strong coupling at \( \mathcal{O}\left( {{{{m_c^2}} \left/ {{{Q^2},{\alpha_s}}} \right.}} \right) \). The leading Λ/m b corrections are parametrically suppressed. The improved Isgur-Wise form factor relations correlate the \( \bar{B} \to {\bar{K}^*}{l^{+} }{l^{-} } \) transversity amplitudes, which simplifies the description of the various decay observables and provides opportunities for the extraction of the electroweak short distance couplings. We propose new angular observables which have very small hadronic uncertainties. We exploit existing data on \( \bar{B} \to {\bar{K}^*}{l^{+} }{l^{-} } \) distributions and show that the low recoil region provides powerful additional information to the large recoil one. We find disjoint best-fit solutions, which include the Standard Model, but also beyond-the-Standard Model ones. This ambiguity can be accessed with future precision measurements.