A complete non-perturbative renormalization prescription for quasi-PDFs

Abstract

In this work we present, for the first time, the non-perturbative renormalization for the unpolarized, helicity and transversity quasi-PDFs, in an RI' scheme. The proposed prescription addresses simultaneously all aspects of renormalization: logarithmic divergences, finite renormalization as well as the linear divergence which is present in the matrix elements of fermion operators with Wilson lines. Furthermore, for the case of the unpolarized quasi-PDFs, we describe how to eliminate the unwanted mixing with the twist-3 scalar operator. We utilize perturbation theory for the one-loop conversion factor that brings the renormalization functions to the MS-scheme at a scale of 2 GeV. We also explain how to improve the estimates on the renormalization functions by eliminating lattice artifacts. The latter can be computed in one-loop perturbation theory and to all orders in the lattice spacing. We apply the methodology for the renormalization to an ensemble of twisted mass fermions with Nf=2+1+1 dynamical light quarks, and a pion mass of around 375 MeV.Comment: 24 pages, 10 figures, 2 Tables, Section 3 largely expanded compared to v1. Version accepted for publication in Nucl. Phys. B (invited Frontiers Article

Note on lattice regularization and equal-time correlators for parton distribution functions

“…An important property, stemming from eqs. (1) and (9), is that the support of f (ω, q 2 ) in the variable ω is given by eq. (4).…”

Pion distribution amplitude from Euclidean correlation functions

“…This last proposal received the most attention, despite added complications due to the renormalization of the Wilson line [9,10], see Refs. [11][12][13][14][15][16][17][18] for recent discussions, the reason being that it allows for a more direct momentum space interpretation in the framework of the large-momentum effective theory [14,19] (LaMET). The corresponding correlation functions, transformed into the longitudinal momentum fraction representation, have become known as quasi-parton-distributions [4].…”

Progress in computing parton distribution functions from the quasi-PDF approach

“…Hence, addressing them is of utmost importance for the robustness of the whole research programme. After the LATTICE 2017 conference, we have indeed addressed the systematic effects shortly described here and we refer to our paper [34] for more details. In short, we have investigated there several "diagonal" scales and estimated the magnitude of lattice artifacts as well as of truncation effects.…”

“…In these proceedings, we recapitulate the results of our extensive analysis that can be found in Ref. [34].…”

“…Arguably the most important of these effects is the influence of the pion mass. So far, our computations [13,15,34] have focused on an ensemble of N f = 2 + 1 + 1 twisted mass fermions at a non-physical pion mass of around 375 MeV. However, as shown e.g.…”