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2020

Renormalon Effects in Quasi Parton Distributions

Liu, Wei-Yang, Chen, Jiunn-Wei

Understand

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.