Tree-level contributions to B -> Xs gamma

TL;DR

This paper evaluates tree-level contributions to the B -> Xs gamma decay, showing they can significantly affect the branching ratio at low photon energy cutoffs, with implications for theoretical predictions.

Contribution

It provides a detailed calculation of CKM-suppressed tree-level and QCD penguin contributions, highlighting their potential impact on the inclusive branching ratio.

Findings

Tree-level contributions can increase the branching ratio by over 10% at low photon energy cutoffs.

The effect diminishes to less than 0.4% for higher energy cutoffs due to phase-space suppression.

Results depend on light quark mass assumptions, with variations from 10 to 50 in m_b/m_q ratio.

Abstract

Weak radiative decay B -> X_s gamma is known to be a loop-generated process. However, it does receive tree-level contributions from CKM-suppressed b -> u ubar s gamma transitions. In the present paper, we evaluate such contributions together with similar ones from the QCD penguin operators. For a low value of the photon energy cutoff E_0 ~ m_b/20 that has often been used in the literature, they can enhance the inclusive branching ratio by more than 10%. For E_0 = 1.6 GeV or higher, the effect does not exceed 0.4%, which is due to phase-space suppression. Our perturbative results contain collinear logarithms that depend on the light quark masses m_q (q=u,d,s). We have allowed m_b/m_q to vary from 10 to 50, which corresponds to values of m_q that are typical for the constituent quark masses. Such a rough method of estimation may be improved in the future with the help of fragmentation functions once the considered effects begin to matter in the overall error budget for BR(B -> X_s gamma).