NNLO fermionic corrections to the charm quark mass dependent matrix elements in B -> X_s gamma

TL;DR

This paper calculates second-order quantum corrections involving charm quark loops to matrix elements in B -> X_s gamma decay, improving precision in theoretical predictions for this process.

Contribution

It provides the first detailed computation of NNLO fermionic corrections with charm quark mass dependence, including new results for b-quark loop insertions.

Findings

Results confirm previous massless quark loop calculations

Large deviations found for b-quark loop insertions

Noticeable differences observed for charm quark loops

Abstract

We compute the virtual O(alpha_s^2) fermionic contributions to the charm quark mass dependent matrix elements of the B -> X_s gamma decay. In the case of a massless quark loop insertion into the gluon propagator, our result obtained as an expansion in z=m_c^2/m_b^2 and an exact expression in terms of multi-fold MB integrals, confirms the findings of Bieri, Greub and Steinhauser [19]. We observe, however, large deviations in the case of a b-quark loop insertion.The charm quark loop shows smaller, but still noticeable differences.