Renormalon Effects in Quasi Parton Distributions

TL;DR

This paper analyzes the renormalon ambiguities in quasi-PDFs, confirming their expected form and exploring their impact on perturbative matching, with findings suggesting good convergence in certain schemes despite potential issues at small x.

Contribution

It provides a detailed analysis of renormalon effects in quasi-PDFs, including new contributions and implications for perturbative matching convergence.

Findings

Leading IR renormalon ambiguity is $rac{ ext{const}}{x^2 P_z^2}$

Good convergence observed in R-scheme and RI/MOM scheme

Potential failure of perturbative matching at small x

Abstract

We investigate the renormalon ambiguity from bubble-chain diagrams in the isovector unpolarized quasi-parton distribution function (PDF) of a hadron. We confirm the assertion by Braun, Vladimirov and Zhang (arXiv:1810.00048) that the leading IR renormalon ambiguity is formally an $\mathcal{O}({\Lambda}^2_{QCD}/x^2P_z^2)$ effect, with $x$ the parton momentum fraction and $P_z$ the hadron momentum, together with a new $\mathcal{O}(\delta(x)\Lambda^2_{QCD}/P_z^2)$ contribution such that the quark number is conserved. This implies the convergence of the perturbative matching kernel between a quasi-PDF and a PDF would eventually fail for small $x$. However, in both the R-scheme designed to cancel the leading IR renormalon and the typically used RI/MOM scheme in lattice QCD for the same quasi-PDF, we find good convergence in the kernel based on three-loop bubble-chain diagram analyses. These results are encouraging for the quasi-PDF program. However, firm conclusions can only be drawn after the complete higher loop QCD calculations are carried out.