Finite-volume effects due to spatially nonlocal operators

Briceño, Raúl A.; Guerrero, Juan V.; Hansen, Maxwell T.; Monahan, Christopher J.

doi:10.1103/PhysRevD.98.014511

Title: Finite-volume effects due to spatially nonlocal operators

Journal Article · Thu Jul 26 00:00:00 EDT 2018 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.98.014511· OSTI ID:1461723

Briceño, Raúl A.; Guerrero, Juan V.; Hansen, Maxwell T.; Monahan, Christopher J.

Spatially non-local matrix elements are useful lattice-QCD observables in a variety of contexts, for example in determining hadron structure. In order to quote credible estimates of the systematic uncertainties in these calculations, one must understand, among other things, the size of the finite-volume effects when such matrix elements are extracted from numerical lattice calculations. In this work we estimate these effects by considering a simple toy model in which the non-local operator is composed of two currents displaced in a spatial direction by a distance $$\xi$$. We find that the finite-volume corrections depend on the details of the matrix element. If the external state is the lightest degree of freedom in the theory, e.g.~the pion in QCD, then the volume corrections scale as $$ e^{-m_\pi (L- \xi)} $$, where $$m$$ is the mass of the light state. For heavier external states the usual $$e^{- m_\pi L}$$ form is recovered, but with a polynomial prefactor of the form $$L^a/|L - \xi|^b$$ that can lead to enhanced volume effects. As a result, these observations {might be relevant} for a wide variety of observables being studied using lattice QCD, including parton distribution functions, double-beta decay and Compton scattering matrix elements, and long-range weak matrix elements.

View Journal Article

Cite

Export

Save

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; SC0008791; FG02-00ER41132

OSTI ID:: 1461723

Alternate ID(s):: OSTI ID: 1462022

Report Number(s):: JLAB-THY-18-2697; DOE/OR/23177-4429; arXiv:1805.01034; CERN-TH-2018-109; INT-PUB-18-019; PRVDAQ; 014511

Journal Information:: Physical Review D, Journal Name: Physical Review D Vol. 98 Journal Issue: 1; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 38 works

Citation information provided by
Web of Science

References (54)

Physics opportunities with the 12 GeV upgrade at Jefferson Lab Dudek, Jozef; Ent, Rolf; Essig, Rouven The European Physical Journal A, Vol. 48, Issue 12 https://doi.org/10.1140/epja/i2012-12187-1	journal	December 2012
Exclusive processes in position space and the pion distribution amplitude Braun, V. M.; Müller, D. The European Physical Journal C, Vol. 55, Issue 3 https://doi.org/10.1140/epjc/s10052-008-0608-4	journal	May 2008
Generalized parton distributions for the pion in chiral perturbation theory Diehl, M.; Manashov, A.; Schäfer, A. Physics Letters B, Vol. 622, Issue 1-2 https://doi.org/10.1016/j.physletb.2005.06.079	journal	August 2005
Baryon axial charge in a finite volume Beane, S. R.; Savage, M. J. Physical Review D, Vol. 70, Issue 7 https://doi.org/10.1103/PhysRevD.70.074029	journal	October 2004
Volume dependence of the energy spectrum in massive quantum field theories: I. Stable particle states Lüscher, M. Communications in Mathematical Physics, Vol. 104, Issue 2 https://doi.org/10.1007/BF01211589	journal	June 1986
The pion mass in finite volume Colangelo, G.; Dürr, S. The European Physical Journal C, Vol. 33, Issue 4 https://doi.org/10.1140/epjc/s2004-01593-y	journal	March 2004
Parton distributions and lattice QCD calculations: A community white paper Lin, Huey-Wen; Nocera, Emanuele R.; Olness, Fred Progress in Particle and Nuclear Physics, Vol. 100 https://doi.org/10.1016/j.ppnp.2018.01.007	journal	May 2018
Novel quark smearing for hadrons with high momenta in lattice QCD Bali, Gunnar S.; Lang, Bernhard; Musch, Bernhard U. Physical Review D, Vol. 93, Issue 9 https://doi.org/10.1103/PhysRevD.93.094515	journal	May 2016
Finite size effects onMπ in QCD from chiral perturbation theory Colangelo, G.; Du¨rr, S.; Sommer, R. Nuclear Physics B - Proceedings Supplements, Vol. 119 https://doi.org/10.1016/S0920-5632(03)80450-4	journal	May 2003
Exploring Partonic Structure of Hadrons Using ab initio Lattice QCD Calculations Ma, Yan-Qing; Qiu, Jian-Wei Physical Review Letters, Vol. 120, Issue 2 https://doi.org/10.1103/PhysRevLett.120.022003	journal	January 2018
The Resolving Power of Gross Earth Data Backus, George; Gilbert, Freeman Geophysical Journal International, Vol. 16, Issue 2 https://doi.org/10.1111/j.1365-246X.1968.tb00216.x	journal	October 1968
Exponential reduction of finite volume effects with twisted boundary conditions Cherman, Aleksey; Sen, Srimoyee; Wagman, Michael L. Physical Review D, Vol. 95, Issue 7 https://doi.org/10.1103/PhysRevD.95.074512	journal	April 2017
Weak Transition Matrix Elements¶from Finite-Volume Correlation Functions Lellouch, Laurent; Lüscher, Martin Communications in Mathematical Physics, Vol. 219, Issue 1 https://doi.org/10.1007/s002200100410	journal	May 2001
Perturbative renormalization of quasi-parton distribution functions Constantinou, Martha; Panagopoulos, Haralambos Physical Review D, Vol. 96, Issue 5 https://doi.org/10.1103/PhysRevD.96.054506	journal	September 2017
Constructing Parton Convolution in Effective Field Theory Chen, Jiunn-Wei; Ji, Xiangdong Physical Review Letters, Vol. 87, Issue 15 https://doi.org/10.1103/PhysRevLett.87.152002	journal	September 2001
Progress in computing parton distribution functions from the quasi-PDF approach Alexandrou, Constantia; Cichy, Krzysztof; Constantinou, Martha EPJ Web of Conferences, Vol. 175 https://doi.org/10.1051/epjconf/201817506021	journal	January 2018
Two-loop sunset integrals at finite volume Bijnens, Johan; Boström, Emil; Lähde, Timo A. Journal of High Energy Physics, Vol. 2014, Issue 1 https://doi.org/10.1007/JHEP01(2014)019	journal	January 2014
Theoretical Considerations Concerning Quantized Magnetic Flux in Superconducting Cylinders Byers, N.; Yang, C. N. Physical Review Letters, Vol. 7, Issue 2 https://doi.org/10.1103/PhysRevLett.7.46	journal	July 1961
Parton Physics on a Euclidean Lattice Ji, Xiangdong Physical Review Letters, Vol. 110, Issue 26 https://doi.org/10.1103/PhysRevLett.110.262002	journal	June 2013
Nucleon Structure Functions from Operator Product Expansion on the Lattice Chambers, A. J.; Horsley, R.; Nakamura, Y. Physical Review Letters, Vol. 118, Issue 24 https://doi.org/10.1103/PhysRevLett.118.242001	journal	June 2017
Model independent determination of the light-cone wave functions for exclusive processes Aglietti, U.; Ciuchini, M.; Corbò, G. Physics Letters B, Vol. 441, Issue 1-4 https://doi.org/10.1016/S0370-2693(98)01138-1	journal	November 1998
Renormalizability of quasiparton distribution functions Ishikawa, Tomomi; Ma, Yan-Qing; Qiu, Jian-Wei Physical Review D, Vol. 96, Issue 9 https://doi.org/10.1103/PhysRevD.96.094019	journal	November 2017
Effective chiral lagrangians for nucleon-pion interactions and nuclear forces Weinberg, Steven Nuclear Physics B, Vol. 363, Issue 1 https://doi.org/10.1016/0550-3213(91)90231-L	journal	September 1991
Two-baryon systems with twisted boundary conditions Briceño, Raúl A.; Davoudi, Zohreh; Luu, Thomas C. Physical Review D, Vol. 89, Issue 7 https://doi.org/10.1103/PhysRevD.89.074509	journal	April 2014
Lattice calculation of parton distributions Alexandrou, Constantia; Cichy, Krzysztof; Drach, Vincent Physical Review D, Vol. 92, Issue 1 https://doi.org/10.1103/PhysRevD.92.014502	journal	July 2015
An asymptotic formula for the pion decay constant in a large volume Colangelo, Gilberto; Haefeli, Christoph Physics Letters B, Vol. 590, Issue 3-4 https://doi.org/10.1016/j.physletb.2004.03.080	journal	June 2004
Aharonov–Bohm effect and nucleon–nucleon phase shifts on the lattice Bedaque, Paulo F. Physics Letters B, Vol. 593, Issue 1-4 https://doi.org/10.1016/j.physletb.2004.04.045	journal	July 2004
Nuclear forces from chiral lagrangians Weinberg, Steven Physics Letters B, Vol. 251, Issue 2 https://doi.org/10.1016/0370-2693(90)90938-3	journal	November 1990
Pion distribution amplitude from Euclidean correlation functions Bali, Gunnar S.; Braun, Vladimir M.; Gläßle, Benjamin The European Physical Journal C, Vol. 78, Issue 3 https://doi.org/10.1140/epjc/s10052-018-5700-9	journal	March 2018
On the chiral expansion for parton distributions at small <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"><mml:mi>x</mml:mi><mml:mo>∼</mml:mo><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mi>m</mml:mi><mml:mi>π</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo stretchy="false">)</mml:mo></mml:math> Kivel, N.; Polyakov, M. V. Physics Letters B, Vol. 664, Issue 1-2 https://doi.org/10.1016/j.physletb.2008.04.048	journal	June 2008
Nucleon masses and magnetic moments in a finite volume Beane, Silas R. Physical Review D, Vol. 70, Issue 3 https://doi.org/10.1103/PhysRevD.70.034507	journal	August 2004
Nonperturbative evolution of parton quasi-distributions Radyushkin, A. V. Physics Letters B, Vol. 767 https://doi.org/10.1016/j.physletb.2017.02.019	journal	April 2017
Effects of finite volume on the $K_{L} - K_{S}$ mass difference Christ, N. H.; Feng, X.; Martinelli, G. Physical Review D, Vol. 91, Issue 11 https://doi.org/10.1103/PhysRevD.91.114510	journal	June 2015
Erratum: Constructing Parton Convolution in Effective Field Theory [Phys. Rev. Lett. 87, 152002 (2001)] Chen, Jiunn-Wei; Ji, Xiangdong Physical Review Letters, Vol. 88, Issue 24 https://doi.org/10.1103/PhysRevLett.88.249901	journal	May 2002
Chiral perturbation theory for hadrons containing a heavy quark Wise, Mark B. Physical Review D, Vol. 45, Issue 7 https://doi.org/10.1103/PhysRevD.45.R2188	journal	April 1992
Deep-inelastic scattering and the operator product expansion in lattice QCD Detmold, William; Lin, C. -J. David Physical Review D, Vol. 73, Issue 1 https://doi.org/10.1103/PhysRevD.73.014501	journal	January 2006
Lattice QCD exploration of parton pseudo-distribution functions Orginos, Kostas; Radyushkin, Anatoly; Karpie, Joseph Physical Review D, Vol. 96, Issue 9 https://doi.org/10.1103/PhysRevD.96.094503	journal	November 2017
Role of the Euclidean signature in lattice calculations of quasidistributions and other nonlocal matrix elements Briceño, Raúl A.; Hansen, Maxwell T.; Monahan, Christopher J. Physical Review D, Vol. 96, Issue 1 https://doi.org/10.1103/PhysRevD.96.014502	journal	July 2017
Parton distribution function with nonperturbative renormalization from lattice QCD Chen, Jiunn-Wei; Ishikawa, Tomomi; Jin, Luchang Physical Review D, Vol. 97, Issue 1 https://doi.org/10.1103/PhysRevD.97.014505	journal	January 2018
A complete non-perturbative renormalization prescription for quasi-PDFs Alexandrou, Constantia; Cichy, Krzysztof; Constantinou, Martha Nuclear Physics B, Vol. 923 https://doi.org/10.1016/j.nuclphysb.2017.08.012	journal	October 2017
Uniqueness in the Inversion of Inaccurate Gross Earth Data Backus, G.; Gilbert, F. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 266, Issue 1173 https://doi.org/10.1098/rsta.1970.0005	journal	March 1970
Quasi-parton distribution functions, momentum distributions, and pseudo-parton distribution functions Radyushkin, A. V. Physical Review D, Vol. 96, Issue 3 https://doi.org/10.1103/PhysRevD.96.034025	journal	August 2017
Quasi parton distributions and the gradient flow Monahan, Christopher; Orginos, Kostas Journal of High Energy Physics, Vol. 2017, Issue 3 https://doi.org/10.1007/JHEP03(2017)116	journal	March 2017
Applying twisted boundary conditions for few-body nuclear systems Körber, Christopher; Luu, Thomas Physical Review C, Vol. 93, Issue 5 https://doi.org/10.1103/PhysRevC.93.054002	journal	May 2016
Electron-Ion Collider: The next QCD frontier: Understanding the glue that binds us all Accardi, A.; Albacete, J. L.; Anselmino, M. The European Physical Journal A, Vol. 52, Issue 9 https://doi.org/10.1140/epja/i2016-16268-9	journal	September 2016
From deep inelastic scattering to heavy-flavor semileptonic decays: Total rates into multihadron final states from lattice QCD Hansen, Maxwell T.; Meyer, Harvey B.; Robaina, Daniel Physical Review D, Vol. 96, Issue 9 https://doi.org/10.1103/PhysRevD.96.094513	journal	November 2017
Parton distribution functions from reduced Ioffe-time distributions Zhang, Jian-Hui; Chen, Jiunn-Wei; Monahan, Christopher Physical Review D, Vol. 97, Issue 7 https://doi.org/10.1103/PhysRevD.97.074508	journal	April 2018
Flavor structure of the nucleon sea from lattice QCD Lin, Huey-Wen; Chen, Jiunn-Wei; Cohen, Saul D. Physical Review D, Vol. 91, Issue 5 https://doi.org/10.1103/PhysRevD.91.054510	journal	March 2015
Nucleon helicity and transversity parton distributions from lattice QCD Chen, Jiunn-Wei; Cohen, Saul D.; Ji, Xiangdong Nuclear Physics B, Vol. 911 https://doi.org/10.1016/j.nuclphysb.2016.07.033	journal	October 2016
Renormalization in Large Momentum Effective Theory of Parton Physics Ji, Xiangdong; Zhang, Jian-Hui; Zhao, Yong Physical Review Letters, Vol. 120, Issue 11 https://doi.org/10.1103/PhysRevLett.120.112001	journal	March 2018
Target mass effects in parton quasi-distributions Radyushkin, A. V. Physics Letters B, Vol. 770 https://doi.org/10.1016/j.physletb.2017.05.024	journal	July 2017
Preliminaries on a lattice analysis of the pion light-cone wave function: A partonic signal? Abada, A.; Boucaud, Ph.; Herdoiza, G. Physical Review D, Vol. 64, Issue 7 https://doi.org/10.1103/PhysRevD.64.074511	journal	September 2001
Updated lattice results for parton distributions Alexandrou, Constantia; Cichy, Krzysztof; Constantinou, Martha Physical Review D, Vol. 96, Issue 1 https://doi.org/10.1103/PhysRevD.96.014513	journal	July 2017
Updated lattice results for parton distributions Alexandrou, Constantia; Cichy, Krzysztof; Constantinou, Martha Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-09401	text	January 2017

Cited By (5)

Light-Cone Parton Distribution Functions from Lattice QCD Alexandrou, Constantia; Cichy, Krzysztof; Constantinou, Martha Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2018-03714	text	January 2018
Hadrons and nuclei Detmold, William; Edwards, Robert G.; Dudek, Jozef J. The European Physical Journal A, Vol. 55, Issue 11 https://doi.org/10.1140/epja/i2019-12902-4	journal	November 2019
Lattice QCD and neutrino-nucleus scattering Kronfeld, Andreas S.; Richards, David G.; Detmold, William The European Physical Journal A, Vol. 55, Issue 11 https://doi.org/10.1140/epja/i2019-12916-x	journal	November 2019
A Guide to Light-Cone PDFs from Lattice QCD: An Overview of Approaches, Techniques, and Results Cichy, Krzysztof; Constantinou, Martha Advances in High Energy Physics, Vol. 2019 https://doi.org/10.1155/2019/3036904	journal	June 2019
Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point Alexandrou, Constantia; Cichy, Krzysztof; Constantinou, Martha Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2019-02720	text	January 2019

Similar Records

PDFs in small boxes

Conference · Thu Nov 01 00:00:00 EDT 2018 · Proceedings of Science (PoS) · OSTI ID:1461723

Briceno, Raul; Guerrero, Juan V.; Hansen, Maxwell T.; +1 more

Lattice QCD study of mixed systems of pions and kaons

Journal Article · Fri Jul 01 00:00:00 EDT 2011 · Phys.Rev.D · OSTI ID:1461723

William Detmold, Brian Smigielski

High Statistics Analysis using Anisotropic Clover Lattices: (IV) The Volume Dependence of the Light Hadron Masses

Journal Article · Fri Jul 01 00:00:00 EDT 2011 · Physical Review. D, Particles, Fields, Gravitation and Cosmology · OSTI ID:1461723

Beane, S R; Detmold, W; Lin, H W; +6 more

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Title: Finite-volume effects due to spatially nonlocal operators

Citation Formats

References (54)

Cited By (5)

Similar Records

Related Subjects