Renormalon effect of quasi-PDF in gradient flow formalism

TL;DR

This work analyzes how gradient flow affects the renormalon structure of flowed quasi-PDFs within the LaMET framework. By performing a bubble-chain (large $β_0$) analysis at zero external momentum, it finds that UV renormalons are eliminated by finite flow time, while IR renormalons are altered but persist, with flow-induced corrections depending on the scale $\sqrt{8t}$. The explicit Borel results show the UV $w=\tfrac{1}{2}$ singularity disappears for flowed quasi-PDFs and the IR $w=2$ singularity picks up a $t$-dependent term, making higher-dimensional operator contributions more prominent at finite $t$. These findings imply that while gradient flow improves UV behavior and scheme matching, finite flow time can enhance power corrections, which has important implications for lattice extractions of PDFs and related observables.

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 $β_0$ 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.

Figures (2)

• Figure 1: The bubble chain diagrams correspond to changing a gluon propagator to gluon propagators dressed with fermion loops.
• Figure 2: Bubble diagrams contributing to the quasi-PDF. The black square denotes the flowed gluon field, the double line represents the Wilson line, and the gray bubble represents the bubble chain.