Resummed rate for B -> X-s gamma - art. no. 074006

In this paper we investigate the effect of the resummation of threshold log s on the rate for B --> X-s gamma. We calculate the differential rate d Gam ma/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 resummati on is potentially important since these logs turn into log(2E(cut)/m(b)), w hen the rate is integrated from the lower cut x = 2E(cut)/m(b) to 1. The re summed rate is then convolved with models for the structure function to stu dy 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 wi th respect to (1-x), which can be used to measure <(Lambda)over bar> and la mbda(I). It is shown that there are some two loop corrections which are jus t as large as the alpha(s)(2)beta(0) term, which are usually expected to do minate. We conclude that, for the present energy cut, the threshold logs do not form a dominant sub-series and therefore their resummation is unnecess ary. Thus the prospects for predicting the rate for B --> X-s gamma accurat ely, given the present energy cut, are promising.