The Radiative Decays B -> V gamma at Next-to-Leading Order in QCD

TL;DR

The paper develops a model-independent QCD factorization framework for exclusive radiative B decays B→K*γ and B→ργ in the heavy-quark limit, separating short-distance hard-scattering kernels from universal form factors and light-cone distribution amplitudes. It treats charm and up-quark loop effects as leading-power perturbative contributions, computes the amplitudes at next-to-leading order, and includes calculable spectator-scattering and annihilation power corrections, enabling systematic predictions beyond leading logs. The authors provide explicit factorization formulas, numerical results for key amplitudes, and predictions for branching ratios, CP asymmetries, and isospin/U-spin breaking, highlighting the remaining form-factor uncertainties and the sensitivity to CKM parameters. This framework strengthens the ability to test the Standard Model with exclusive radiative decays and lays groundwork for improved constraints from future data and lattice/QCD inputs.

Abstract

We provide a model-independent framework for the analysis of the radiative B-meson decays B -> K* gamma and B -> rho gamma. In particular, we give a systematic discussion of the various contributions to these exclusive processes based on the heavy-quark limit of QCD. We propose a novel factorization formula for the consistent treatment of B -> V gamma matrix elements involving charm (or up-quark) loops, which contribute at leading power in Lambda_QCD/m_B to the decay amplitude. Annihilation topologies are shown to be power suppressed. In some cases they are nevertheless calculable. The approach is similar to the framework of QCD factorization that has recently been formulated for two-body non-leptonic B decays. These results allow us, for the first time, to compute exclusive b -> s(d) gamma decays systematically beyond the leading logarithmic approximation. We present results for these decays complete to next-to-leading order in QCD and to leading order in the heavy-quark limit. Phenomenological implications for various observables of interest are discussed, including direct CP violation, and isospin and U-spin breaking effects.

Figures (11)

• Figure 1: Contribution of the magnetic penguin operator $Q_7$ described by $B\to V$ form factors. All possible gluon exchanges between the quark lines are included in the form factors and have not been drawn explicitly.
• Figure 2: ${\cal O}(\alpha_s)$ contribution to the hard-scattering kernels $T^I_{i}$ from four-quark operators $Q_i$. The crosses indicate the places where the emitted photon can be attached.
• Figure 3: ${\cal O}(\alpha_s)$ contribution to the hard-scattering kernels $T^I_{8}$ from chromomagnetic penguin operator $Q_8$.
• Figure 4: ${\cal O}(\alpha_s)$ contribution to the hard-scattering kernels $T^{II}_i$ from four-quark operators $Q_i$ (left) and from $Q_8$.
• Figure 5: Annihilation contribution to $\bar{B}\to V\gamma$ decay. The dominant mechanism is the radiation of the photon from the light quark in the $B$ meson, as shown. This amplitude is suppressed by one power of $\Lambda_{QCD}/m_b$, but it is still calculable in QCD factorization. Radiation of the photon from the remaining three quark lines is suppressed by $(\Lambda_{QCD}/m_b)^2$ for operators $Q_{1,2}$.