Isospin Breaking in B -> K^* gamma Decays

TL;DR

This paper analyzes isospin breaking in $B\to K^*\gamma$ decays within the QCD factorization framework. It shows that leading isospin violation arises at order $\Lambda/m_b$ from spectator-dependent processes, with soft form-factor differences being small. The dominant contribution comes from 4-quark penguin operators (notably $Q_6$), leading to a predicted $\Delta_{0-}$ around 8% with quantified uncertainties. The authors also discuss how New Physics in penguin and dipole sectors could modify $\Delta_{0-}$, and argue that precise measurements could constrain such scenarios, testing QCD factorization for power corrections.

Abstract

A calculation of the leading isospin-breaking contributions to the B -> K^* gamma decay amplitudes based on the QCD factorization approach is presented. They arise at order Lambda/m_b in the heavy-quark expansion and are due to annihilation contributions from 4-quark operators, the chromo-magnetic dipole operator, and charm penguins. In the Standard Model the decay rate for B^0 -> K^{*0} gamma is predicted to be about 10-20 % larger than that for B^- -> K^{*-} gamma. Isospin-breaking effects are a sensitive probe of the penguin sector of the effective weak Hamiltonian. New Physics models in which the hierarchy of B -> K^* gamma decay rates is either flipped or greatly enhanced could be ruled out with more precise data.

Figures (2)

• Figure 1: Spectator-dependent contributions from local 4-quark operators (left), the chromo-magnetic dipole operator (center), and the charm penguin (right). Crosses denote alternative photon attachments.
• Figure 2: Prediction for the quantity $\Delta_{0-}$ as a function of the renormalization scale, assuming $T_1^{B\to K^*}=0.3$. The dark lines refer to $\mu_0=m_b$ (solid), $m_b/2$ (upper dashed) and $2m_b$ (lower dashed). The band shows the theoretical uncertainty.