The Resummed Rate for B -> X_s gamma

TL;DR

This paper examines the impact of resumming threshold logarithms on the B -> X_s gamma decay rate, finding that such resummation is unnecessary at current energy cuts, thus improving prediction prospects.

Contribution

It provides a detailed analysis of threshold log resummation effects on the decay rate and assesses their significance relative to non-perturbative effects and higher-order corrections.

Findings

Resummation of threshold logs is not necessary at current energy cuts.

Two-loop corrections can be as large as expected dominant terms.

Predictions for B -> X_s gamma rate are promising with current cuts.

Abstract

In this paper we investigate the effect of the resummation of threshold logs on the rate for B -> X_s gamma. We calculate the differential rate dGamma/dE_gamma including the infinite set of terms of the form alpha_s^n log^{n+1}(1-x) and alpha_s^n log^n(1-x) in the Sudakov exponent. The resummation is potentially important since these logs turn into log(2E_{cut}/m_b), when the rate is integrated from the lower cut x=2E_{cut}/m_b to 1. The resummed rate is then convolved with models for the structure function to study whether or not the logs will be enhanced due to the fermi motion of the heavy quark. A detailed discussion of the accuracy of the calculation with and without the inclusion of the non-perturbative effects dictated by the B meson structure function is given. We also investigate the first moment with respect to (1-x), which can be used to measure \bar\Lambda and lambda_1. It is shown that there are some two loop corrections which are just as large as the alpha_s^2 beta_0 term, which are usually expected to dominate. We conclude that, for the present energy cut, the threshold logs do not form a dominant sub-series and therefore their resummation is unnecessary. Thus, the prospects for predicting the rate for B -> X_s gamma accurately, given the present energy cut, are promising.