SCALE UNCERTAINTIES IN THE B-]X-S-GAMMA DECAY

We analyze the theoretical uncertainties in Br(B --> X-s gamma) due to the choice of the high energy matching scale mu(w) = O(M-w) and the s cale mu(t) at which the running top quark mass is defined: (m) over ba r(t)( mu(t)). To this end we have repeated the calculation of the init ial conditions confirming the final results of Adel and Yao and Greub and Hurth and generalizing them to include the dependences on mu(t) an d mu(w) with mu(t) not equal mu(w). In the leading order the mu(w), an d mu(t) uncertainties in Br(B --> X-s gamma) turn out to be +/- 13% an d +/- 3% respectively. We show analytically how these uncertainties ar e reduced after including next-to-leading QCD corrections. They amount to +/- 0.4% and +/- 0.3% respectively. Reanalyzing the uncertainties due to the scale mu(b) = O(m(b)) we find that after the inclusion of N LO effects they amount to +/- 3.2% which is smaller by a factor of two than claimed in the literature. Including the uncertainties due to in put parameters as well as the non-perturbative 1/m(b)(2) and 1/m(c)(2) corrections we find Br(B --> X-s gamma) = (3.48 +/- 0.31) X 10(-4) wh ere the error is dominated by uncertainties in the input parameters. T his should be compared with (3.28 +/- 0.33) X 10(-4) found by Chetyrki n et al. where the error is shared evenly between the scale and parame tric uncertainties. (C) 1997 Elsevier Science B.V.