Hard-scattering factorization with heavy quarks: A general treatment

TL;DR

The paper provides a rigorous, all-orders proof of hard-scattering factorization in QCD that retains heavy-quark masses in the short-distance coefficient functions, enabling correct treatments across $Q oughly M$ and beyond. It builds a CWZ-based renormalization framework with a sequence of active-flavor subschemes, ensuring manifest decoupling and mass-parameter consistency with the $ar{MS}$ scheme. Through a 2PI-graph expansion and a carefully constructed remainder, the author demonstrates that all non-leading power corrections are uniformly suppressed by $igO(rac{\Lambda}{Q})^p$, while providing practical recursion relations and operator definitions for renormalized parton densities and coefficients. The framework unifies treatments from light to heavy quarks, includes matching conditions and evolution equations across flavor thresholds, and clarifies the relative roles of mass effects in coefficient functions versus parton densities, with broad applicability to DIS and other hard processes.

Abstract

A detailed proof of hard scattering factorization is given with the inclusion of heavy quark masses. Although the proof is explicitly given for deep-inelastic scattering, the methods apply more generally The power-suppressed corrections to the factorization formula are uniformly suppressed by a power of Λ/Q, independently of the size of heavy quark masses, M, relative to Q.

Figures (13)

• Figure 1: Regions for the leading power of structure functions have this structure.
• Figure 2: A graph with 4 decompositions of the form of Fig. \ref{['fig:leading.region']}.
• Figure 3: The handbag diagram that characterizes the only leading region in a super-renormalizable theory.
• Figure 4: Handbag diagram with the final-state interactions that make the current quark jet.
• Figure 5: Decomposition of structure function in terms of 2PI amplitudes.