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arXiv · 2406.08182

Heavy-to-light form factors to three loops

Matteo Fael·Tobias Huber·Fabian Lange·Jakob Müller·Kay Schönwald·Matthias Steinhauser
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Abstract

We compute three-loop corrections of $\mathcal{O}(\alpha_{s}^3)$ 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 $\bar B \to X_s \gamma$ to three loops.

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Matteo Fael, Tobias Huber, Fabian Lange, Jakob Müller, Kay Schönwald, Matthias Steinhauser. 2024-06-12. Heavy-to-light form factors to three loops. https://arxiv.org/abs/2406.08182

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