Renormalization-Mass Scale Dependence in QCD Contributions to Semileptonic $b \to u$ Decay

Details Renormalization-Mass Scale Dependence in QCD Contributions to Semileptonic $b \to u$ Decay Renormalization-Mass Scale Dependence in QCD Contributions to Semileptonic $b \to u$ Decay

2002-08-30

arxiv.org/abs/hep-ph/0209001v1

Nucl.Phys.Proc.Suppl. 115 (2003) 85-88

Physics

High Energy Physics

High Energy Physics - Phenomenology

4 pages, latex using espcrc2.sty. Write-up of talk given at BEACH 2002, Vancouver

Scientific paper

10.1016/S0920-5632(02)01959-X

QCD contributions to the $b \to u \ell^- \bar{\nu}_\ell$ decay rate, which are known to two-loop order in the $\bar{MS}$ scheme, exhibit sufficient dependence on the renormalization mass $\mu$ to compromise phenomenological predictions for inclusive semileptonic $B \to X_u$ 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 $B \to X_u$ inclusive rate.

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