Wei-Yang LiuJIUNN-WEI CHEN2022-12-232022-12-232020-10-142470-0010https://scholars.lib.ntu.edu.tw/handle/123456789/62674316 pages, 5 figuresWe 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.High Energy Physics - Phenomenology; High Energy Physics - Phenomenologyjournal article10.1103/PhysRevD.104.0945012-s2.0-85119127026WOS:000716446500002http://arxiv.org/abs/2010.06623v6