Parton distribution function with nonperturbative renormalization from lattice QCD

Abstract

We present lattice results for the isovector unpolarized parton distribution with nonperturbative RI/MOM-scheme renormalization on the lattice. In the framework of large-momentum effective field theory (LaMET), the full Bjorken-x dependence of a momentum-dependent quasi-distribution is calculated on the lattice and matched to the ordinary lightcone parton distribution at one-loop order, with power corrections included. The important step of RI/MOM renormalization that connects the lattice and continuum matrix elements is detailed in this paper. A few consequences of the results are also addressed here.

Finite continuum quasi distributions from lattice QCD

“…Our results for diagrams (e) and (f), which have UV divergences removed by Z χ , are in agreement with those presented in [44] The complete one-loop smeared matrix element is therefore (22) and…”

“…Several approaches have been proposed: inspired by heavy quark effective theory, the authors of [20,21] suggested an exponentiated mass renormalisation to remove the powerdivergence and, more recently, RI/MOM [22,23] and RI [24] schemes have been introduced. In [25], we presented an alternative approach, the smeared quasi distribution, that avoids some of the challenges of the power divergence by taking advantage of the properties of the gradient flow [26][27][28].…”

Perturbative matching of continuum and lattice quasi-distributions

“…Recently, the nonperturbative renormalization of this operator using RI/MOM scheme has been demonstrated in Refs. [17][18][19][20]. Lattice QCD formulation respects not all the symmetries possessed in the continuum theory.…”

Matching the Quasi Parton Distribution in a Momentum Subtraction Scheme

“…Efforts have been made to use this proposal to calculate the iso-vector quark distributions f u−d , including unpolarized, polarized, and transversity distributions, as well as pion distribution amplitude, from lattice QCD [17,18,19,20,21,22,23,24]. For this channel the mixing is not important and so the indicies i and j are dropped.…”

“…[26,18]. The nucleon-mass corrections of O(M 2 /P 2 z ) have already been included in the lattice calculations [17,18,19,20,21,23,24], and the O(Λ 2 QCD /P 2 z ) correction was numerically fitted in Ref. [19].…”