Two-loop QCD corrections to charged-Higgs-mediated $b\to sγ$ decay

TL;DR

This paper computes the two-loop QCD corrections to the charged-Higgs-mediated contribution to the $b\to s\gamma$ transition in gauge-mediated SUSY models. Using na"ive dimensional regularization and MSbar, the authors perform an on-shell matching between the full theory and the effective theory, employing Heavy Mass Expansion to handle heavy $m_H$ and $m_t$ scales. They derive an explicit expression for the NLO Wilson coefficient $C_{71}$ and show that, for realistic parameters, the two-loop correction reduces the LO charged-Higgs effect by about 10–20% when $\bar{\mu}\approx m_t$, with detailed limiting cases provided. The results imply that in GM scenarios the charged-Higgs/top contribution remains a key, well-defined SUSY effect in B-physics, and the authors discuss agreement with a concurrent work and the relative usefulness of $C_7(\bar{\mu}\approx m_t)$ for phenomenology.

Abstract

The charged-Higgs-mediated contribution to the Wilson coefficient of the $b\to sγ$ magnetic penguin is expected to be one of the more promising candidates for a supersymmetric effect in B physics, probably the only one in gauge-mediated models. We compute the two-loop QCD correction to it. With naive dimensional regularization and MSbar subtraction, for reasonable values of the charged Higgs mass and for mu-bar = m_top, we find a (10--20)% reduction of the corresponding one-loop effect.

Figures (2)

• Figure 1: The 16 two-loop Feynman graphs (we show on a single diagrams all possible attachment of the photon and write near to it the name we give to the diagram) that we have to compute. The symbol $\otimes$ denotes the vertex $\bar{b}_R t_L H_-$.
• Figure 2: The Feynman graph that accounts for the renormalization of the mass and kinetic terms that mix the $b$ and $s$ quarks.