Renormalon effect of quasi-PDF in gradient flow formalism

TL;DR

This paper studies how gradient flow affects renormalon ambiguities in quasi-PDFs, showing UV renormalons are eliminated while IR renormalons are modified, with implications for operator contributions at small flow times.

Contribution

It demonstrates the impact of gradient flow on renormalon structures in quasi-PDFs, revealing UV renormalon elimination and IR renormalon modifications.

Findings

UV renormalons are eliminated by gradient flow.

IR renormalons are modified but persist at finite flow time.

Flowed operators can enhance power-suppressed contributions.

Abstract

We investigate the behavior of renormalon ambiguities in the context of quasi-parton distribution functions (quasi-PDFs) defined using gradient-flowed fields. We examine how this impacts the UV and IR renomalons. Using the large $\beta_0$ approximation, we find that UV renormalons for zero external momentum quasi-PDF are eliminated by the flow, while IR renormalons persist but are modified at finite flow time. Moreover, we observe that large numerical coefficients associated with flowed operators can enhance power-suppressed contributions, making higher-dimensional operators non-negligible even at small flow times.