Renormalon Effects in Quasi Parton Distributions

Wei-Yang Liu^1*, Jiunn-Wei Chen¹

¹Department of Physics, National Taiwan University, Taipei, Taiwan

* Presenter:Wei-Yang Liu, email:weiyangliuphys@gmail.com

We investigate the renormalon ambiguity from bubble-chain diagrams in the isovector quasi-parton distribution function of a hadron. We confirm the assertion by Braun, Vladimirov and Zhang [1] that the leading IR renormalon ambiguity is formally an O(Λ_QCD²/x²P_z² ) effect, with x the parton momentum fraction and P_z the hadron momentum. We also clarify how quark number conservation in the renormalon ambiguity is satisfied by identifying a δ(x) contribution with a divergent prefactor. To further quantify this effect, we study the bubble-chain diagrams to three- loops and find excellent convergence for the matching kernel between the RI/MOM renormalized quasi-parton distribution and the MS parton distribution. This suggests that renormalons do not cause a slow convergence to the perturbative kernel in this scheme at the three-loop order. The improvement of convergence using the R-scheme to remove the leading renormalon ambiguity is also demonstrated.

Keywords: lattice QCD, large momentum effective theory (LaMET), partonic structure, renormalon