Role of the Euclidean signature in lattice calculations of quasidistributions and other nonlocal matrix elements

Briceno, Raul A.; Hansen, Maxwell T.; Monahan, Christopher J.

doi:10.1103/PhysRevD.96.014502

Title: Role of the Euclidean signature in lattice calculations of quasidistributions and other nonlocal matrix elements

Journal Article · Tue Jul 11 00:00:00 EDT 2017 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.96.014502· OSTI ID:1371541

Briceno, Raul A. ^[1]; Hansen, Maxwell T. ^[2]; Monahan, Christopher J. ^[3]

Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Johannes Gutenberg-Univ. Mainz, Mainz (Germany)
The State Univ. of New Jersey, Piscataway, NJ (United States)

Lattice quantum chromodynamics (QCD) provides the only known systematic, nonperturbative method for first-principles calculations of nucleon structure. However, for quantities such as light-front parton distribution functions (PDFs) and generalized parton distributions (GPDs), the restriction to Euclidean time prevents direct calculation of the desired observable. Recently, progress has been made in relating these quantities to matrix elements of spatially nonlocal, zero-time operators, referred to as quasidistributions. Still, even for these time-independent matrix elements, potential subtleties have been identified in the role of the Euclidean signature. In this work, we investigate the analytic behavior of spatially nonlocal correlation functions and demonstrate that the matrix elements obtained from Euclidean lattice QCD are identical to those obtained using the Lehmann-Symanzik-Zimmermann reduction formula in Minkowski space. After arguing the equivalence on general grounds, we also show that it holds in a perturbative calculation, where special care is needed to identify the lattice prediction. Lastly, we present a proof of the uniqueness of the matrix elements obtained from Minkowski and Euclidean correlation functions to all order in perturbation theory.

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Research Organization:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: AC05-06OR23177

OSTI ID:: 1371541

Alternate ID(s):: OSTI ID: 1369328

Report Number(s):: JLAB-THY-17-2434; DOE/OR/23177-4188; arXiv:1703.06072; PRVDAQ

Journal Information:: Physical Review D, Vol. 96, Issue 1; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 44 works

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Matching the Quasi Parton Distribution in a Momentum Subtraction Scheme Stewart, Iain W.; Zhao, Yong arXiv https://doi.org/10.48550/arxiv.1709.04933	text	January 2017
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A guide to light-cone PDFs from Lattice QCD: an overview of approaches, techniques and results Cichy, Krzysztof; Constantinou, Martha arXiv https://doi.org/10.48550/arxiv.1811.07248	text	January 2018
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