Bremsstrahlung corrections to the decay $b\to s\gamma$

Abstract

We calculate the O(${\alpha }_s$) gluon Bremsstrahlung corrections to the inclusive decay $b\to s\gamma$, involving the full operator basis ${\hat{O}}_1$ -- ${\hat{O}}_8$. Confirming and extending earlier calculations of Ali and Greub, we give formulas for the total decay width as well as the perturbative photon spectrum, regarding the former as a necessary part of the forthcoming complete NLO analysis. We explore in detail the renormalization scale dependence of our results and find it considerably increased.

Comments: 23 pages, LaTeX, uses epsf.sty and rotate.sty. 4 figures (uuencoded postscript) appended as seperate file. A complete postscript version may be obtained from URL ftp://feynman.t30.physik.tu-muenchen.de/pub/preprints/tum-93-95.ps.gz Final version as to appear in Physical Review D. Some minor errors corrected, without changes in the numerical results. One reference added