Parton Physics on a Euclidean Lattice

Abstract

I show that the parton physics related to correlations of quarks and gluons on the light-cone can be studied through the matrix elements of frame-dependent, equal-time correlators in the large momentum limit. This observation allows practical calculations of parton properties on an Euclidean lattice. As an example, I demonstrate how to recover the leading-twist quark distribution by boosting an equal-time correlator to a large momentum.

Quasi-parton distribution functions, momentum distributions, and pseudo-parton distribution functions

“…A possible way to find the Ioffe-time distributions on the lattice (suggested by K. Orginos) is to calculate M(P z 3 , z 2 3 ) for several values of P , and then to fit the results by a function of ν and z 2 3 . Recalling our discussion of two apparently independent sources of obtaining k 3 for a moving hadron, one may hope that M(ν, z 2 3 ) factorizes, i.e., M(ν,…”

“…Since one cannot have light-like separations on the lattice, it was proposed [2] to consider spacelike separations z = (0, 0, 0, z 3 ) [or, for brevity, z = z 3 ]. Then, in the p = (E, 0 ⊥ , P ) frame, one introduces the quasi-PDF Q(y, P ) through a parametrization…”

“…The usual way out is to calculate their moments. However, recently, X. Ji [2] suggested a method allowing to calculate PDFs as functions of x. To this end, he proposes to use purely space-like separations z = (0, 0, 0, z 3 ).…”

Round table: Nucleon tomography. What can we do better today than Rutherford 100 years ago?

“…The systematic error results from the difference between using one-and two-levels of stout smearing. Having obtained both the quark and the gluon momentum fractions, we can check the momentum sum q x q + x g = 1.01 (10) A new approach that could allow us to obtain the parton distribution functions directly from lattice QCD has been proposed by Ji [89]. One considers the matrix element…”

“…The above correlator includes a Wilson line W(0 → z) extending from the location of the quark field at 0 to ∞ along the z direction [89]. First results have been obtained for N f = 2 + 1 + 1 (two degenerate u and d quarks, plus a strange and a charm quark) clover fermions on a HISQ sea [90,91], and for N f = 2 + 1 + 1 twisted-mass fermions [92,93] using simulations with a pion mass of about 310 MeV and 370 MeV, respectively.…”