Renormalon effects on quasi-PDFs in the gradient flow formalism

We investigate renormalon ambiguities in quasiparton distribution functions (quasi-PDFs) defined using gradient-flowed fields. Focusing on both ultraviolet (UV) and infrared (IR) renormalons, we perform an explicit calculation of bubble chain diagrams to analyze their dependence on the flow time. We find that the gradient flow eliminates UV renormalon in quasi-PDFs. In the small flow-time expansion, the linear renormalons cancel exactly between the matching kernel and the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mover accent="true"> <a:mi>MS</a:mi> <a:mo stretchy="true">¯</a:mo> </a:mover> </a:math> quasi-PDF. Meanwhile, IR renormalons persist but are modified at finite flow time. The deformation of the renormalon structure induced by the gradient flow suggests an altered infrared behavior, with enhanced contributions from higher-twist effects even at small flow time.