Perturbative hysteresis and emergent resummation scales

TL;DR

This paper explores hysteresis phenomena in the perturbative solutions of RGEs, proposing resummation scales to better estimate theoretical uncertainties in QCD calculations relevant to collider physics.

Contribution

It introduces the concept of perturbative hysteresis and emergent resummation scales to improve the understanding of RGE solutions in QCD.

Findings

Resummation scales help quantify uncertainties in RGE solutions.

Hysteresis effects are observed in the perturbative evolution of PDFs.

Application to the $F_2$ structure function demonstrates practical relevance.

Abstract

We investigate hysteresis effects in the perturbative solution of renormalisation group equations (RGEs). We present examples for the QCD running coupling and proton's parton distribution functions (PDFs), relevant to precision physics at the Large Hadron Collider (LHC) and future collider experiments. We propose the use of resummation scales to take into account the theoretical uncertainties from the solution of the RGEs. As a case study, we consider the $F_2$ structure function in a region relevant to the extraction of PDFs.