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Nonperturbative Renormalization of Nonlocal Quark Bilinears for Parton Quasidistribution Functions on the Lattice Using an Auxiliary Field

Jeremy Green, Karl Jansen, and Fernanda Steffens
Phys. Rev. Lett. 121, 022004 – Published 13 July 2018

Abstract

Parton quasidistribution functions provide a path toward an ab initio calculation of parton distribution functions (PDFs) using lattice QCD. One of the problems faced in calculations of quasi-PDFs is the renormalization of a nonlocal operator. By introducing an auxiliary field, we can replace the nonlocal operator with a pair of local operators in an extended theory. On the lattice, this is closely related to the static quark theory. In this approach, we show how to understand the pattern of mixing that is allowed by chiral symmetry breaking and obtain a master formula for renormalizing the nonlocal operator that depends on three parameters. We present an approach for nonperturbatively determining these parameters and use perturbation theory to convert to the modified minimal subtraction (MS¯) scheme. Renormalization parameters are obtained for two lattice spacings using Wilson twisted mass fermions and for different discretizations of the Wilson line in the nonlocal operator. Using these parameters, we show the effect of renormalization on nucleon matrix elements with a pion mass of approximately 370 MeV and compare renormalized results for the two lattice spacings. The renormalized matrix elements are consistent among the different Wilson line discretizations and lattice spacings.

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  • Received 2 August 2017
  • Revised 22 January 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.022004

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

  1. Physical Systems
Particles & Fields

Authors & Affiliations

Jeremy Green*, Karl Jansen, and Fernanda Steffens

  • NIC, Deutsches Elektronen-Synchrotron, 15738 Zeuthen, Germany

  • *jeremy.green@desy.de

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Issue

Vol. 121, Iss. 2 — 13 July 2018

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