Description
We derive and solve the renormalization-group (RG) equation for the shape function $ g_{17}(\omega,\omega_1;\mu) $, which appears at subleading power in the factorization of the inclusive decays $ \bar{B} \to X_s \gamma $ and $ \bar{B} \to X_s \ell^+ \ell^- $.
Our results provide the first key ingredient for a next-to-leading order analysis of the resolved-photon $ Q_1^c - Q_{7\gamma} $ interference contribution, whose current uncertainties rank among the largest in both inclusive penguin modes.
We examine the renormalization of this function and demonstrate that, for amplitude-level soft functions, the analytic properties of the anomalous dimension enable a much simpler “reduced” evolution equation. This simplification will play a crucial role in various inclusive and exclusive B decays beyond leading power in the heavy-quark and large-energy expansions.
| Secondary track | T05 - QCD and Hadronic Physics |
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