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

Understand

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}.