Infrared factorization in inclusive B meson decays
G. P. Korchemsky, G. Sterman
TL;DR
The paper develops an infrared factorization framework for inclusive B decays near the end-points of photon and lepton spectra, decomposing differential rates into hard, jet, and soft functions that obey RG evolution to resum large logs. The soft function, described by Wilson lines, is universal and tied to the heavy-quark distribution within the B meson; IR renormalon analysis motivates a Gaussian nonperturbative model for this distribution. The authors derive resummed moment expressions for radiative and semileptonic decays, showing consistency with known one-loop results, and show that ratios of moments cancel nonperturbative inputs, yielding perturbatively calculable predictions. Together, these results provide a unified perturbative/nonperturbative treatment of end-point inclusive B decays and reveal a direct link between Wilson-line dynamics and the heavy-quark distribution in the B meson.
Abstract
We perform infrared factorization of differential rates of radiative and semileptonic inclusive decays of the B meson in the end-point region of photon and charged lepton spectrum, respectively, in the leading heavy quark mass limit. We find that the differential rates are expressed in terms of hard, jet and soft functions, which satisfy evolution equations. Solving these equations, we find expressions for the moments of the differential rates in their end-point regions, which take into account all leading and nonleading logarithmic corrections in perturbation theory, as well as large nonperturbative power corrections. Expanded to the one-loop level, our predictions coincide with the results of existing lowest order calculations for B->γX_s and B->l\barnu X_u. Nonperturbative corrections appear in our formalism from the boundary value of the soft function in the evolution equation. The soft function is a universal process-independent function, which describes the distribution of the b quark in the B meson. Its behavior in the end-point region is governed by the nonperturbative asymptotics of a Wilson line expectation value. By considering the contributions of infrared renormalons, we find an ansatz for the Wilson line, which leads to a Gaussian model for the heavy quark distribution function.