Rapidity Divergences and Deep Inelastic Scattering in the Endpoint Region

TL;DR

This paper investigates rapidity divergences in deep inelastic scattering near the endpoint region, showing that different factors require distinct scales and that rapidity running is non-perturbative, with implications for defining parton distribution functions.

Contribution

It introduces a rapidity regulator for endpoint DIS, analyzes the scale dependence of factorized components, and discusses the operator definition of PDFs in this regime.

Findings

Individual factors have rapidity divergences in the endpoint region.

Different factors require separate scales to minimize large logarithms.

Rapidity running in this context is non-perturbative.

Abstract

The deep inelastic scattering cross section in the endpoint region, $x \sim 1$, has been subjected to extensive analysis. We revisit this process, and show that in the endpoint individual factors in the factorized hadronic tensor have rapidity divergences. We regulate these divergences using a recently introduced rapidity regulator, and find that each factor requires a different scale to minimize large rapidity logarithms. Interestingly, in this case running in rapidity is non-perturbative. In addition, we give an operator definition of the parton distribution function in the endpoint region, and remark on the issues that should be considered in constructing this function.