Role of the Euclidean signature in lattice calculations of quasidistributions and other nonlocal matrix elements
Abstract
Lattice quantum chromodynamics (QCD) provides the only known systematic, nonperturbative method for firstprinciples calculations of nucleon structure. However, for quantities such as lightfront 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, zerotime operators, referred to as quasidistributions. Still, even for these timeindependent 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 LehmannSymanzikZimmermann 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.
 Authors:
 Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
 Johannes GutenbergUniv. Mainz, Mainz (Germany)
 The State Univ. of New Jersey, Piscataway, NJ (United States)
 Publication Date:
 Research Org.:
 Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Nuclear Physics (NP) (SC26)
 OSTI Identifier:
 1371541
 Report Number(s):
 JLABTHY172434; DOE/OR/231774188; arXiv:1703.06072
Journal ID: ISSN 24700010; PRVDAQ
 Grant/Contract Number:
 AC0506OR23177
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 96; Journal Issue: 1; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Briceno, Raul A., Hansen, Maxwell T., and Monahan, Christopher J. Role of the Euclidean signature in lattice calculations of quasidistributions and other nonlocal matrix elements. United States: N. p., 2017.
Web. doi:10.1103/PhysRevD.96.014502.
Briceno, Raul A., Hansen, Maxwell T., & Monahan, Christopher J. Role of the Euclidean signature in lattice calculations of quasidistributions and other nonlocal matrix elements. United States. doi:10.1103/PhysRevD.96.014502.
Briceno, Raul A., Hansen, Maxwell T., and Monahan, Christopher J. 2017.
"Role of the Euclidean signature in lattice calculations of quasidistributions and other nonlocal matrix elements". United States.
doi:10.1103/PhysRevD.96.014502.
@article{osti_1371541,
title = {Role of the Euclidean signature in lattice calculations of quasidistributions and other nonlocal matrix elements},
author = {Briceno, Raul A. and Hansen, Maxwell T. and Monahan, Christopher J.},
abstractNote = {Lattice quantum chromodynamics (QCD) provides the only known systematic, nonperturbative method for firstprinciples calculations of nucleon structure. However, for quantities such as lightfront 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, zerotime operators, referred to as quasidistributions. Still, even for these timeindependent 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 LehmannSymanzikZimmermann 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.},
doi = {10.1103/PhysRevD.96.014502},
journal = {Physical Review D},
number = 1,
volume = 96,
place = {United States},
year = 2017,
month = 7
}

Four Euclidean conformal group in atomic calculations: Exact analytical expressions for the boundbound twophoton transition matrix elements in the H atom
By combining SturmianCoulomb techniques with a local representation of the four Euclidean conformal group SU* (4) approx. =Spin(1,5), a compact analytical form, suitable for any analytic continuation on the energy variable, is obtained for the following boundbound twophoton transition matrix element in the H atom: I/sub NNprime/(E) =,where G(E) is the Coulomb Green's function.