Evolution of the Light Cone Distribution Function for a Heavy Quark

TL;DR

This paper addresses the endpoint region in inclusive heavy-quark decays where nonperturbative effects are encapsulated by a universal light-cone shape function f(k_+). It derives and analytically solves the one-loop evolution equation for f(k_+, μ), providing an RG-improved framework that connects perturbative infrared structure to a nonperturbative distribution. The authors compute the one-loop evolution kernel in a tailored MS′ scheme and discuss how the shape function’s moments evolve and how a hard cutoff relates to the pole mass. The result enables consistent resummation of Sudakov-type logs in hadronic invariant-mass spectra, offering a practical pathway to incorporate radiative corrections in B-decay endpoint phenomenology.

Abstract

We compute the one-loop anomalous dimension for the light cone distribution function of a heavy quark and solve the corresponding evolution equation analytically. Some implications of the results for inclusive $B$ decays are discussed.

Figures (1)

• Figure 1: Renormalization of the structure function. The plain line denotes a massive or massless QCD propagator, the double plain line a heavy quark propagator, the dotted line a light--cone propagator. The shaded blob on the r.h.s. symbolizes the insertion of the structure function as a nonlocal operator.