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 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.
- Authors:
-
- 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)
- 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)
- OSTI Identifier:
- 1371541
- Alternate Identifier(s):
- OSTI ID: 1369328
- Report Number(s):
- JLAB-THY-17-2434; DOE/OR/23177-4188; arXiv:1703.06072
Journal ID: ISSN 2470-0010; PRVDAQ
- Grant/Contract Number:
- AC05-06OR23177
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Physical Review D
- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 1; Journal ID: ISSN 2470-0010
- 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. https://doi.org/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. https://doi.org/10.1103/PhysRevD.96.014502. https://www.osti.gov/servlets/purl/1371541.
@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 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.},
doi = {10.1103/PhysRevD.96.014502},
url = {https://www.osti.gov/biblio/1371541},
journal = {Physical Review D},
issn = {2470-0010},
number = 1,
volume = 96,
place = {United States},
year = {Tue Jul 11 00:00:00 EDT 2017},
month = {Tue Jul 11 00:00:00 EDT 2017}
}
Web of Science
Works referenced in this record:
Lattice calculation of the nucleon’s spin-dependent structure function reexamined
journal, March 2001
- Göckeler, M.; Horsley, R.; Kürzinger, W.
- Physical Review D, Vol. 63, Issue 7
Lattice calculation of parton distributions
journal, July 2015
- Alexandrou, Constantia; Cichy, Krzysztof; Drach, Vincent
- Physical Review D, Vol. 92, Issue 1
Volume dependence of the energy spectrum in massive quantum field theories: I. Stable particle states
journal, June 1986
- Lüscher, M.
- Communications in Mathematical Physics, Vol. 104, Issue 2
Extraction of Parton Distributions from Lattice qcd
journal, December 2003
- Detmold, W.; Melnitchouk, W.; Thomas, A. W.
- Modern Physics Letters A, Vol. 18, Issue 38
Matrix elements of unstable states
journal, September 2012
- Bernard, V.; Hoja, D.; Meißner, U. -G.
- Journal of High Energy Physics, Vol. 2012, Issue 9
Relating the finite-volume spectrum and the two-and-three-particle matrix for relativistic systems of identical scalar particles
journal, April 2017
- Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
- Physical Review D, Vol. 95, Issue 7
Nonperturbative evolution of parton quasi-distributions
journal, April 2017
- Radyushkin, A. V.
- Physics Letters B, Vol. 767
Effects of finite volume on the mass difference
journal, June 2015
- Christ, N. H.; Feng, X.; Martinelli, G.
- Physical Review D, Vol. 91, Issue 11
Leptonic widths of heavy quarkonia: -wave QCD/NRQCD matching coefficients for the electromagnetic vector annihilation current at
journal, January 2007
- Hart, A.; von Hippel, G. M.; Horgan, R. R.
- Physical Review D, Vol. 75, Issue 1
Improved quasi parton distribution through Wilson line renormalization
journal, February 2017
- Chen, Jiunn-Wei; Ji, Xiangdong; Zhang, Jian-Hui
- Nuclear Physics B, Vol. 915
Lattice corrections to the quark quasidistribution at one loop
journal, May 2017
- Carlson, Carl E.; Freid, Michael
- Physical Review D, Vol. 95, Issue 9
A framework for the calculation of the <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>N</mml:mi><mml:msup><mml:mrow><mml:mi>γ</mml:mi></mml:mrow><mml:mrow><mml:mo>⁎</mml:mo></mml:mrow></mml:msup></mml:math> transition form factors on the lattice
journal, September 2014
- Agadjanov, Andria; Bernard, Véronique; Meißner, Ulf-G.
- Nuclear Physics B, Vol. 886
Parton physics from large-momentum effective field theory
journal, May 2014
- Ji, XiangDong
- Science China Physics, Mechanics & Astronomy, Vol. 57, Issue 7
Relativistic, model-independent, multichannel transition amplitudes in a finite volume
journal, July 2016
- Briceño, Raúl A.; Hansen, Maxwell T.
- Physical Review D, Vol. 94, Issue 1
One-loop matching for generalized parton distributions
journal, July 2015
- Ji, Xiangdong; Schäfer, Andreas; Xiong, Xiaonu
- Physical Review D, Vol. 92, Issue 1
Investigation of the second moment of the nucleon’s and structure functions in two-flavor lattice QCD
journal, September 2005
- Göckeler, M.; Horsley, R.; Pleiter, D.
- Physical Review D, Vol. 72, Issue 5
Quasi parton distributions and the gradient flow
journal, March 2017
- Monahan, Christopher; Orginos, Kostas
- Journal of High Energy Physics, Vol. 2017, Issue 3
Moments of nucleon light cone quark distributions calculated in full lattice QCD
journal, August 2002
- Dolgov, D.; Brower, R.; Capitani, S.
- Physical Review D, Vol. 66, Issue 3
Parton Physics on a Euclidean Lattice
journal, June 2013
- Ji, Xiangdong
- Physical Review Letters, Vol. 110, Issue 26
One-loop matching for parton distributions: Nonsinglet case
journal, July 2014
- Xiong, Xiaonu; Ji, Xiangdong; Zhang, Jian-Hui
- Physical Review D, Vol. 90, Issue 1
Pion structure functions from lattice QCD
journal, October 1987
- Martinelli, G.; Sachrajda, C. T.
- Physics Letters B, Vol. 196, Issue 2
Nucleon helicity and transversity parton distributions from lattice QCD
journal, October 2016
- Chen, Jiunn-Wei; Cohen, Saul D.; Ji, Xiangdong
- Nuclear Physics B, Vol. 911
Nucleon generalized parton distributions from full lattice QCD
journal, May 2008
- Hägler, Ph.; Schroers, W.; Bratt, J.
- Physical Review D, Vol. 77, Issue 9
Pion distribution amplitude from lattice QCD
journal, May 2017
- Zhang, Jian-Hui; Chen, Jiunn-Wei; Ji, Xiangdong
- Physical Review D, Vol. 95, Issue 9
Multichannel transition amplitudes in a finite volume
journal, February 2015
- Briceño, Raúl A.; Hansen, Maxwell T.; Walker-Loud, André
- Physical Review D, Vol. 91, Issue 3
Multichannel and transition amplitudes for arbitrary spin particles in a finite volume
journal, October 2015
- Briceño, Raúl A.; Hansen, Maxwell T.
- Physical Review D, Vol. 92, Issue 7
Parton distributions from lattice QCD
journal, August 2001
- Detmold, W.; Melnitchouk, W.; Thomas, A. W.
- EPJ direct, Vol. 3, Issue 1
Pion Distribution Amplitude from Lattice QCD
journal, August 2013
- Cloët, I. C.; Chang, L.; Roberts, C. D.
- Physical Review Letters, Vol. 111, Issue 9
Nucleon helicity and transversity parton distributions from lattice QCD
text, January 2016
- Chen, Jiunn-Wei; Cohen, Saul D.; Ji, Xiangdong
- Universität Regensburg
Pion distribution amplitude from lattice QCD
text, January 2017
- Zhang, Jian-Hui; Chen, Jiunn-Wei; Ji, Xiangdong
- Universität Regensburg
Nucleon Generalized Parton Distributions from Full Lattice QCD
text, January 2007
- Hägler, Ph.; Schroers, W.; Bratt, J.
- arXiv
Parton Physics from Large-Momentum Effective Field Theory
preprint, January 2014
- Ji, Xiangdong
- arXiv
Nucleon Helicity and Transversity Parton Distributions from Lattice QCD
text, January 2016
- Chen, Jiunn-Wei; Cohen, Saul D.; Ji, Xiangdong
- arXiv
Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles
text, January 2017
- Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
- arXiv
Pion Distribution Amplitude from Lattice QCD
text, January 2017
- Zhang, Jian-Hui; Chen, Jiunn-Wei; Ji, Xiangdong
- arXiv
Lattice corrections to the quark quasidistribution at one-loop
text, January 2017
- Carlson, Carl E.; Freid, Michael
- arXiv
Parton distributions from lattice QCD
text, January 2001
- Detmold, W.; Melnitchouk, W.; Thomas, A. W.
- arXiv
Moments of Nucleon Light Cone Quark Distributions Calculated in Full Lattice QCD
text, January 2002
- Collaboration, Lhpc; Collaboration, Sesam; Dolgov, D.
- arXiv
Extraction of parton distributions from lattice QCD
text, January 2003
- Detmold, W.; Melnitchouk, W.; Thomas, A. W.
- arXiv
Improved quasi parton distribution through Wilson line renormalization
text, January 2016
- Chen, Jiunn-Wei; Ji, Xiangdong; Zhang, Jian-Hui
- Universität Regensburg
Works referencing / citing this record:
Gluon quasidistribution function at one loop
journal, February 2018
- Wang, Wei; Zhao, Shuai; Zhu, Ruilin
- The European Physical Journal C, Vol. 78, Issue 2
A Guide to Light-Cone PDFs from Lattice QCD: An Overview of Approaches, Techniques, and Results
journal, June 2019
- Cichy, Krzysztof; Constantinou, Martha
- Advances in High Energy Physics, Vol. 2019
Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point
text, January 2019
- Alexandrou, Constantia; Cichy, Krzysztof; Constantinou, Martha
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Parton distribution functions from reduced Ioffe-time distributions
text, January 2018
- Zhang, Jian-Hui; Chen, Jiunn-Wei; Monahan, Christopher
- Universität Regensburg
Parton distribution function with nonperturbative renormalization from lattice QCD
text, January 2018
- Chen, Jiunn-Wei; Ishikawa, Tomomi; Jin, Luchang
- Universität Regensburg
Unpolarized isovector quark distribution function from lattice QCD: A systematic analysis of renormalization and matching
text, January 2020
- Liu, Yu-Sheng; Chen, Jiunn-Wei; Huo, Yi-Kai
- Universität Regensburg
Matching the Quasi Parton Distribution in a Momentum Subtraction Scheme
conference, March 2018
- Zhao, Yong; Stewart, Iain W.
- Proceedings of QCD Evolution 2017 — PoS(QCDEV2017)
Gluon quasidistribution function at one loop
text, January 2017
- Wang, Wei; Zhao, Shuai; Zhu, Ruilin
- arXiv
Matching the Quasi Parton Distribution in a Momentum Subtraction Scheme
text, January 2017
- Stewart, Iain W.; Zhao, Yong
- arXiv
Parton distribution functions from reduced Ioffe-time distributions
text, January 2018
- Zhang, Jian-Hui; Chen, Jiunn-Wei; Monahan, Christopher
- arXiv
Finite-volume effects due to spatially non-local operators
text, January 2018
- Briceño, Raúl A.; Guerrero, Juan V.; Hansen, Maxwell T.
- arXiv
Renormalization of Wilson-line operators in the presence of nonzero quark masses
text, January 2018
- Spanoudes, G.; Panagopoulos, H.
- arXiv
Unpolarized isovector quark distribution function from Lattice QCD: A systematic analysis of renormalization and matching
text, January 2018
- Liu, Yu-Sheng; Chen, Jiunn-Wei; Huo, Yi-Kai
- arXiv
A guide to light-cone PDFs from Lattice QCD: an overview of approaches, techniques and results
text, January 2018
- Cichy, Krzysztof; Constantinou, Martha
- arXiv
General Methods for Digital Quantum Simulation of Gauge Theories
text, January 2019
- Lamm, Henry; Lawrence, Scott; Yamauchi, Yukari
- arXiv
Transverse momentum dependent parton quasidistributions
text, January 2019
- Ji, Xiangdong; Jin, Lu-Chang; Yuan, Feng
- Universität Regensburg