From Ds → γ in lattice QCD to Bs → μμγ at high q2

Abstract

We use a recent lattice determination of the vector and axial Ds → γ form factors at high squared momentum transfer q2 to infer their Bs → γ counterparts. To this end, we introduce a phenomenological approach summarized as follows. First, we describe the lattice data with different fit templates motivated by vector-meson dominance, that is expected to hold in the high-q2 region considered. We identify reference fit ansaetze with one or two physical poles, that we validate against alternative templates. Then, the pole residues can be unambiguously related to the appropriate couplings involving the pseudoscalar, the vector mesons concerned, and the photon — or tri-couplings — and the latter can be expressed as sums over quark magnetic moments, weighed by their e.m. charges. This description obeys a well-defined heavy-quark scaling, that allows to parametrically scale up the form factors to the Bs → γ case. We discuss a number of cross-checks of the whole approach, whose validation rests ultimately in a first-principle determination, e.g. in lattice QCD. Finally, we use our obtained form factors to reassess the SM prediction of ℬ(Bs → μ+μ−γ) in the range sqrt{q^2}in [4.2, 5.0] GeV, where an experimental measurement is awaited.