Renormalization group equation improved analysis of $B \to \pi$ form factors from Light-Cone Sum Rules

TL;DR

This paper improves the analysis of $B o \pi$ form factors by incorporating one-loop QCD corrections and renormalization group evolution within light-cone sum rules, leading to more scale-independent results.

Contribution

It introduces a complete renormalization group equation evolution in the analysis of $B o \pi$ form factors, enhancing the precision and scale stability of the results.

Findings

Form factors become nearly independent of the factorization scale.

The method allows reliable extrapolation across the entire $q^2$ region.

Results are consistent with other theoretical studies.

Abstract

Within the framework of $B$-meson light-cone sum rules, we compute the one-loop level QCD corrections to $B\to \pi$ transition form factors at small $ q^{2}$ region, in implement of a complete renormalization group equation evolution. To solve the renormalization group equations, we work at the "dual" space where the anomalous dimensions of the jet function and the light-cone distribution amplitudes are diagonal. With the complete renormalization group equation evolution, the form factors are almost independent of the factorization scale, which is shown numerically. We also extrapolate the results of the form factors to the whole $q^2$ region, and compare their behavior with other studies.