Renormalon Effects in Quasi Parton Distributions

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
$\mathcal{O}({\Lambda}^2_{QCD}/x^2P_z^2)$ 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.