Heavy fermions and two loop electroweak corrections to $b\rightarrow s+\gamma$

TL;DR

This paper calculates electroweak two-loop corrections involving heavy fermions to the rare decay process $b ightarrow s+\gamma$, showing potential 5% deviations from Standard Model predictions at new physics scales around 200 GeV.

Contribution

It provides a detailed analysis of two-loop electroweak corrections with heavy fermions to $b ightarrow s+\gamma$, verifying decoupling behavior and estimating their impact on decay rates.

Findings

Two-loop corrections can alter the branching ratio by up to 5%.

Decoupling theorem is explicitly verified in the heavy fermion limit.

Corrections are significant at new physics scales around 200 GeV.

Abstract

Applying effective Lagrangian method and on-shell scheme, we analyze the electroweak corrections to the rare decay $b\rightarrow s+\gamma$ from some special two loop diagrams in which a closed heavy fermion loop is attached to the virtual charged gauge bosons or Higgs. At the decoupling limit where the virtual fermions in inner loop are much heavier than the electroweak scale, we verify the final results satisfying the decoupling theorem explicitly when the interactions among Higgs and heavy fermions do not contain the nondecoupling couplings. Adopting the universal assumptions on the relevant couplings and mass spectrum of new physics, we find that the relative corrections from those two loop diagrams to the SM theoretical prediction on the branching ratio of $B\rightarrow X_{_s}\gamma$ can reach 5% as the energy scale of new physics $\Lambda_{_{\rm NP}}=200$ GeV.