Order alpha_s^2 magnetic penguin correction for B decay to light mesons

TL;DR

This paper calculates the order alpha_s^2 correction to magnetic penguin operators in B meson decays, confirming QCD factorization and showing significant impact on decay amplitude coefficients.

Contribution

It provides the first complete analytic calculation of the alpha_s^2 correction to magnetic penguin operators in B decays within QCD factorization.

Findings

Soft and collinear divergences cancel out, confirming QCD factorization.

Order alpha_s^2 correction reduces the penguin amplitude coefficient a^c_{4,I}.

The correction has a stronger effect on the imaginary part.

Abstract

We compute the order alpha_s^2 correction to the matrix element of magnetic penguin operator for B meson decaying to light mesons within the QCD factorization framework. We explicitly show that the soft and collinear divergences are canceled out, so that the validity of QCD factorization is confirmed. We present the result of the calculation in complete analytic forms. The result is also applied to B -> K pi decays, and we find that the order alpha_s^2 correction of magnetic penguin operator can considerably reduce the coefficient of penguin amplitude a^c_{4,I}. The reduction is stronger for the imaginary part.