Renormalization-mass scale dependence in qcd contributions to semileptonic b → u decay

Abstract

QCD contributions to the b --> ul(-)v(l) decay rate, which are known to two-loop order in the MS scheme, exhibit sufficient dependence on the renormalization mass mu to compromise phenomenological predictions for inclusive semileptonic B --> X-u processes. Such scale dependence is ameliorated by the renormalization-group (RG) extraction and summation of all leading and RG-accessible subleading logarithms occurring subsequent to two-loop order in the perturbative series. This optimal RG-improvement of the known portion of the perturbative series virtually eliminates mu-dependence as a source of theoretical uncertainty in the predicted semileptonic B --> X-u inclusive rate.