Renormalon Effects in Quasi Parton Distributions

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 $$\mathcal{O}({\Lambda}<sup>2_{QCD}/x<sup>2P_z<sup>2)$$ effect, with $x$ the parton momentum fraction and $P_z$ the hadron momentum, together with a new $$\mathcal{O}(\delta(x)\Lambda<sup>2_{QCD}/P_z<sup>2)$$ 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.