Reduction of charm quark mass scheme dependence in [formula omitted] at the NNLL level

H.M Asatrian,C Greub,A Hovhannisyan,T Hurth,V Poghosyan

doi:10.1016/j.physletb.2005.05.080

Abstract

The uncertainty of the theoretical prediction of the B¯→Xsγ branching ratio at NLL level is dominated by the charm mass renormalization scheme ambiguity. In this Letter we calculate those NNLL terms which are related to the renormalization of mc, in order to get an estimate of the corresponding uncertainty at the NNLL level. We find that these terms significantly reduce (by typically a factor of two) the error on BR(B¯→Xsγ) induced by the definition of mc. Taking into account the experimental accuracy of around 10% and the future prospects of the B factories, we conclude that a NNLL calculation would increase the sensitivity of the observable B¯→Xsγ to possible new degrees of freedom beyond the SM significantly.

Highlights

The branching ratio of B → Xsγ is a very sensitive probe for new degrees of freedom beyond the standard model (SM)
In the present paper we try to give such a motivation: By calculating those NNLL terms which are induced by renormalizing the charm quark mass in the next-toleading logarithmic (NLL) expressions, i.e. those terms which are sensitive to the definition of the charm quark mass, we show that the large error at the NLL level related to the mc definition gets significantly reduced
The infinities induced by the 1/ǫ terms in δmc get cancelled in a full NNLL calculation, in particular by self-energy diagrams depicted in the right frame of Fig. 1

Summary

Introduction

The branching ratio of B → Xsγ is a very sensitive probe for new degrees of freedom beyond the standard model (SM) (for a review, see [1]). In the present paper we try to give such a motivation: By calculating those NNLL terms which are induced by renormalizing the charm quark mass in the NLL expressions, i.e. those terms which are sensitive to the definition of the charm quark mass, we show that the large error at the NLL level related to the mc definition gets significantly reduced. As this error is the dominant one at the NLL level (see eq (3)), we conclude that a complete NNLL calculation will drastically improve the theoretical prediction of the branching ratio.

NNLL terms related to mc renormalization

Analytical results

Findings

Numerical results