Photonic penguins at two loops and m_t-dependence of BR[ B -> X_s l^+ l^-]

TL;DR

This paper computes two-loop corrections for B -> X_s l^+ l^- decay in the Standard Model, significantly reducing theoretical uncertainties related to top-quark mass dependence and providing a precise branching ratio estimate.

Contribution

It presents the first complete two-loop matching calculation for all relevant operators in B decay, refining the theoretical prediction and reducing uncertainties.

Findings

Branching ratio estimated at 1.46 x 10^-6 for specified dilepton mass range.

Reduced the uncertainty in decay spectrum from 16% to a lower value.

Remaining perturbative uncertainty around 13%, with smaller non-perturbative effects.

Abstract

We calculate two-loop matching conditions for all the operators that are relevant to B -> X_s l^+ l^- decay in the Standard Model. In effect, we are able to remove the +_16% uncertainty in the decay spectrum, which was mainly due to the renormalization-scale dependence of the top-quark mass. We find 1.46 * 10^-6 for the branching ratio integrated in the domain 0.05 < m_{l^+l^-}^2/m_b^2 < 0.25, for l= e or mu. There remains around 13% perturbative uncertainty in this quantity, while the non-perturbative effects are expected to be smaller.