Papers › Heavy-to-light form factors to three loops
Heavy-to-light form factors to three loops
Matteo Fael, Tobias Huber, Fabian Lange, Jakob Müller, Kay Schönwald, Matthias Steinhauser
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We compute three-loop corrections of 𝒪(αₛ³) to form factors with one massive and one massless quark coupling to an external vector, axialvector, scalar, pseudoscalar, or tensor current. We obtain analytic results for the color-planar contributions, for the contributions of light-quark loops, and the contributions with two heavy-quark loops. For the computation of the remaining master integrals we use the "expand and match" approach which leads to semi-analytic results for the form factors. We implement our results in a {\tt Mathematica} and a {\tt Fortran} code which allows for fast and precise numerical evaluations in the physically relevant phase space. The form factors are used to compute the hard matching coefficients in Soft-Collinear Effective Theory for all currents. The tensor coefficients at light-like momentum transfer are used to extract the hard function in B̅ →Xₛ γ to three loops.
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