Heavy-to-light form factors to three loops

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 lig...

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Bibliographic Details
Published in:arXiv.org 2024-09
Main Authors: Fael, Matteo, Huber, Tobias, Lange, Fabian, Müller, Jakob, Schönwald, Kay, Steinhauser, Matthias
Format: Article
Language:English
Subjects:
Form factors
Mathematical analysis
Momentum transfer
Quarks
Tensors
Online Access:Get full text
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Summary: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.
ISSN:2331-8422