QCD sum rules for quark-gluon three-body components in the B meson

TL;DR

This paper refines QCD sum rule calculations for B-meson parameters by including higher-order corrections, improving stability and providing updated values for quark-gluon matrix elements.

Contribution

It introduces new radiative and power corrections to the sum rules for $$ and $_H$, enhancing their accuracy and stability.

Findings

Radiative corrections improve sum rule stability.

Values of  and _H are reduced with corrections.

Updated parameters align better with theoretical expectations.

Abstract

We discuss the QCD sum rule calculation of the heavy-quark effective theory parameters, $\lambda_E$ and $\lambda_H$, which correspond to matrix elements representing quark-gluon three-body components in the $B$-meson wavefunction. We derive the sum rules for $\lambda_{E,H}$ calculating the new higher-order QCD corrections, i.e., the order $\alpha_s$ radiative corrections to the Wilson coefficients associated with the dimension-5 quark-gluon mixed condensates, and the power corrections due to the dimension-6 vacuum condensates. We find that the new radiative corrections significantly improve the stability of the corresponding Borel sum rules and lead to the reduction of the values of $\lambda_{E,H}$. We also discuss the renormalization-group improvement for the sum rules and present update on the values of $\lambda_{E,H}$.