Completing the Calculation of BLM corrections to B -> Xs gamma

TL;DR

This paper completes the calculation of BLM corrections to the B -> Xs gamma decay rate by including missing interference contributions and confirms previous results on spectrum corrections, enhancing theoretical precision.

Contribution

It provides the first complete calculation of the interference contribution from current-current and gluonic dipole operators in BLM corrections for B -> Xs gamma decay.

Findings

Calculated the missing interference contribution to BLM corrections.

Confirmed previous results for photon energy spectrum corrections.

Validated recent findings on gluonic dipole operator self-interference.

Abstract

Perturbative O(alpha_s^2) corrections to BR(B -> Xs gamma) in the BLM approximation receive contributions from two-, three- and four-body final states. While all the two-body results are well established by now, the other ones have remained incomplete for several years. Here, we calculate the last contribution that has been missing to date, namely the one originating from interference of the current-current and gluonic dipole operators (K_18^{(2)beta_0} and K_{28}^{(2)beta_0}). Moreover, we confirm all the previously known results for BLM corrections to the photon energy spectrum that involve the current-current operators (e.g., K_{22}^{(2)beta_0} and K_{27}^{(2)beta_0}). Finally, we also confirm the recent findings of Ferroglia and Haisch on self-interference of the gluonic dipole operator (K_{88}^{(2)beta_0}).