On B -> V l l at small dilepton invariant mass, power corrections, and new physics

Abstract

We investigate rare semileptonic \bar B -> \bar K^* l^+ l^- decays, providing a comprehensive treatment of theoretical uncertainties in the low-q^2 region as needed for interpreting current and future LHCb and B-factory data in terms of the new physics search. We go beyond the usual focus on form-factor uncertainties, paying proper attention to non-factorizable terms. A central point is the systematic exploitation of the V-A structure of SM weak interactions, which leads to the suppression of two helicity amplitudes and some of the angular coefficients. We review how this works at the level of (helicity) form factors, and show that the hierarchies extend to non-factorizable terms. For virtual charm effects, we give an argument for it in terms of light-cone QCD sum rules that continues to hold at the level of "long-distance" Lambda_QCD^2/m_c^2 power corrections, reducing an important source of theoretical uncertainty in any \bar B, \bar B_s -> V l^+ l^- (or \bar B -> V gamma) decay. The contributions of the remaining hadronic weak Hamiltonian respect a similar hierarchy. We employ a resonance model to preclude (in the \bar B -> \bar K^* case) large long-distance corrections to this. A phenomenological part pays particular attention to the region of lowest dilepton mass, 4 m_l^2 <= q^2 <= 2 GeV^2. Two observables remain theoretically clean, implying a (theoretical) sensitivity to the real (imaginary) part of the "right-handed" Wilson coefficient C_7' to 10% (1%) of C_7^SM, both in the muonic and the electronic mode. We also show that there are two near-exact relations between angular coefficients, even in the presence of new physics and when lepton masses are not neglected.