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Title: Theoretical aspects of quantum electrodynamics in a finite volume with periodic boundary conditions

Abstract

First-principles studies of strongly interacting hadronic systems using lattice quantum chromodynamics (QCD) have been complemented in recent years with the inclusion of quantum electrodynamics (QED). The aim is to confront experimental results with more precise theoretical determinations, e.g. for the anomalous magnetic moment of the muon and the C P -violating parameters in the decay of mesons. Quantifying the effects arising from enclosing QED in a finite volume remains a primary target of investigations. To this end, finite-volume corrections to hadron masses in the presence of QED have been carefully studied in recent years. This paper extends such studies to the self-energy of moving charged hadrons, both on and away from their mass shell. In particular, we present analytical results for leading finite-volume corrections to the self-energy of spin-0 and spin-$$1\over{2}$$ particles in the presence of QED on a periodic hypercubic lattice, once the spatial zero mode of the photon is removed, a framework that is called QEDL. By altering modes beyond the zero mode, an improvement scheme is introduced to eliminate the leading finite-volume corrections to masses, with potential applications to other hadronic quantities. Our analytical results are verified by a dedicated numerical study of a lattice scalar field theory coupled to QEDL. Further, this paper offers new perspectives on the subtleties involved in applying low-energy effective field theories in the presence of QEDL, a theory that is rendered nonlocal with the exclusion of the spatial zero mode of the photon, clarifying recent discussions on this matter.

Authors:
; ; ; ;
Publication Date:
Research Org.:
Univ. of Washington, Seattle, WA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1497247
Alternate Identifier(s):
OSTI ID: 1609321
Grant/Contract Number:  
FG02-00ER41132
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 99 Journal Issue: 3; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Astronomy & Astrophysics; Physics

Citation Formats

Davoudi, Z., Harrison, J., Jüttner, A., Portelli, A., and Savage, M. J. Theoretical aspects of quantum electrodynamics in a finite volume with periodic boundary conditions. United States: N. p., 2019. Web. doi:10.1103/PhysRevD.99.034510.
Davoudi, Z., Harrison, J., Jüttner, A., Portelli, A., & Savage, M. J. Theoretical aspects of quantum electrodynamics in a finite volume with periodic boundary conditions. United States. doi:10.1103/PhysRevD.99.034510.
Davoudi, Z., Harrison, J., Jüttner, A., Portelli, A., and Savage, M. J. Thu . "Theoretical aspects of quantum electrodynamics in a finite volume with periodic boundary conditions". United States. doi:10.1103/PhysRevD.99.034510.
@article{osti_1497247,
title = {Theoretical aspects of quantum electrodynamics in a finite volume with periodic boundary conditions},
author = {Davoudi, Z. and Harrison, J. and Jüttner, A. and Portelli, A. and Savage, M. J.},
abstractNote = {First-principles studies of strongly interacting hadronic systems using lattice quantum chromodynamics (QCD) have been complemented in recent years with the inclusion of quantum electrodynamics (QED). The aim is to confront experimental results with more precise theoretical determinations, e.g. for the anomalous magnetic moment of the muon and the C P -violating parameters in the decay of mesons. Quantifying the effects arising from enclosing QED in a finite volume remains a primary target of investigations. To this end, finite-volume corrections to hadron masses in the presence of QED have been carefully studied in recent years. This paper extends such studies to the self-energy of moving charged hadrons, both on and away from their mass shell. In particular, we present analytical results for leading finite-volume corrections to the self-energy of spin-0 and spin-$1\over{2}$ particles in the presence of QED on a periodic hypercubic lattice, once the spatial zero mode of the photon is removed, a framework that is called QEDL. By altering modes beyond the zero mode, an improvement scheme is introduced to eliminate the leading finite-volume corrections to masses, with potential applications to other hadronic quantities. Our analytical results are verified by a dedicated numerical study of a lattice scalar field theory coupled to QEDL. Further, this paper offers new perspectives on the subtleties involved in applying low-energy effective field theories in the presence of QEDL, a theory that is rendered nonlocal with the exclusion of the spatial zero mode of the photon, clarifying recent discussions on this matter.},
doi = {10.1103/PhysRevD.99.034510},
journal = {Physical Review D},
number = 3,
volume = 99,
place = {United States},
year = {2019},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.99.034510

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Cited by: 4 works
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Works referenced in this record:

Finite volume corrections to the electromagnetic mass of composite particles
journal, February 2016


Heavy-quark bound states in lattice QCD
journal, January 1991


Uncertainty quantification in lattice QCD calculations for nuclear physics
journal, February 2015

  • Beane, Silas R.; Detmold, William; Orginos, Kostas
  • Journal of Physics G: Nuclear and Particle Physics, Vol. 42, Issue 3
  • DOI: 10.1088/0954-3899/42/3/034022

Heavy-quark symmetry
journal, September 1994


Calculation of the Hadronic Vacuum Polarization Contribution to the Muon Anomalous Magnetic Moment
journal, July 2018


Electromagnetic Splittings and Light Quark Masses in Lattice QCD
journal, May 1996


Baryon chiral perturbation theory using a heavy fermion lagrangian
journal, February 1991


Strange and charm HVP contributions to the muon (g − 2) including QED corrections with twisted-mass fermions
journal, October 2017

  • Giusti, D.; Lubicz, V.; Martinelli, G.
  • Journal of High Energy Physics, Vol. 2017, Issue 10
  • DOI: 10.1007/JHEP10(2017)157

Locally smeared operator product expansions in scalar field theory
journal, April 2015


Improving the volume dependence of two-body binding energies calculated with lattice QCD
journal, December 2011


SU(N) gauge theories with C-periodic boundary conditions (I). Topological structure
journal, July 1991


Finite-volume electromagnetic corrections to the masses of mesons, baryons, and nuclei
journal, September 2014


Electromagnetic structure of light baryons in lattice QCD
journal, September 1997


Double exponential formulas for numerical integration
journal, January 1973

  • Takahasi, Hidetosi; Mori, Masatake
  • Publications of the Research Institute for Mathematical Sciences, Vol. 9, Issue 3
  • DOI: 10.2977/prims/1195192451

Isospin breaking corrections to meson masses and the hadronic vacuum polarization: a comparative study
journal, September 2017

  • Boyle, P.; Gülpers, V.; Harrison, J.
  • Journal of High Energy Physics, Vol. 2017, Issue 9
  • DOI: 10.1007/JHEP09(2017)153

Finite-volume QED corrections to decay amplitudes in lattice QCD
journal, February 2017


Leading isospin breaking effects on the lattice
journal, June 2013


Two-particle elastic scattering in a finite volume including QED
journal, October 2014


An effective field theory for heavy quarks at low energies
journal, April 1990


Full QED + QCD Low-Energy Constants through Reweighting
journal, August 2012


Gauge invariant determination of charged hadron masses
journal, May 2018

  • Hansen, M.; Lucini, B.; Patella, A.
  • Journal of High Energy Physics, Vol. 2018, Issue 5
  • DOI: 10.1007/JHEP05(2018)146

Finite-volume corrections to electromagnetic masses for larger-than-physical electric charges
journal, May 2017


Two-baryon systems with twisted boundary conditions
journal, April 2014


1 + 1 + 1 flavor QCD + QED simulation at the physical point
journal, August 2012


Ab initio calculation of the neutron-proton mass difference
journal, March 2015


Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states
journal, June 1986

  • Lüscher, M.
  • Communications in Mathematical Physics, Vol. 105, Issue 2
  • DOI: 10.1007/BF01211097

Quantum electrodynamics in finite volume and nonrelativistic effective field theories
journal, April 2016


openQ*D simulation code for QCD+QED
journal, January 2018


The strategy for computing the hadronic mass spectrum
journal, January 1984


Effective Field Theories of the Standard Model: Proceedings of the Workshop
conference, November 2014


Using infinite-volume, continuum QED and lattice QCD for the hadronic light-by-light contribution to the muon anomalous magnetic moment
journal, August 2017


On the calculation of lattice sums
journal, January 1957


Simulations of QCD and QED with C * boundary conditions
journal, January 2018


Heavy quark effective theory and nonrelativistic QCD Lagrangian to order α s / m 3
journal, July 1997


C- and G-periodic QCD at finite temperature
journal, May 1992


NRQED Lagrangian at order 1 / M 4
journal, March 2013


Charged hadrons in local finite-volume QED+QCD with C⋆ boundary conditions
journal, February 2016

  • Lucini, B.; Patella, A.; Ramos, A.
  • Journal of High Energy Physics, Vol. 2016, Issue 2
  • DOI: 10.1007/JHEP02(2016)076

High statistics analysis using anisotropic clover lattices. II. Three-baryon systems
journal, October 2009


Feynman diagrams for the Yang-Mills field
journal, July 1967


Deep-inelastic scattering and the operator product expansion in lattice QCD
journal, January 2006


Power corrections at short distances
journal, January 1980


Restoration of rotational symmetry in the continuum limit of lattice field theories
journal, September 2012


QED in Finite Volume and Finite Size Scaling Effect on Electromagnetic Properties of Hadrons
journal, September 2008

  • Uno, S.; Hayakawa, M.
  • Progress of Theoretical Physics, Vol. 120, Issue 3
  • DOI: 10.1143/PTP.120.413

Review of lattice results concerning low-energy particle physics: Flavour Lattice Averaging Group (FLAG)
journal, February 2017


SU suN) gauge theories with C-periodic boundary conditions (II). Small-volume dynamics
journal, July 1993


Effective field theory approach to processes involving both light and heavy fields
journal, July 1988


Boundaries forSU(3) c xU(1)el lattice gauge theory with a chemical potential
journal, March 1993

  • Polley, L.
  • Zeitschrift f�r Physik C: Particles and Fields, Vol. 59, Issue 1
  • DOI: 10.1007/BF01555844

Up and Down Quark Masses and Corrections to Dashen’s Theorem from Lattice QCD and Quenched QED
journal, August 2016


Electromagnetic mass splittings of the low lying hadrons and quark masses from 2 + 1 flavor lattice QCD + QED
journal, November 2010


High statistics analysis using anisotropic clover lattices: Single hadron correlation functions
journal, June 2009


Isospin splittings of meson and baryon masses from three-flavor lattice QCD + QED
journal, September 2016


Leading isospin-breaking corrections to pion, kaon, and charmed-meson masses with twisted-mass fermions
journal, June 2017


Effective lagrangians for simulating of heavy quark systems
journal, April 1988


Electromagnetic corrections to the hadronic vacuum polarization of the photon within QED L and QED M
journal, January 2018


Two-nucleon systems in a finite volume. II. S 1 3 D 1 3 coupled channels and the deuteron
journal, December 2013


Massive Photons: An Infrared Regularization Scheme for Lattice QCD + QED
journal, August 2016


Isospin Splittings in the Light-Baryon Octet from Lattice QCD and QED
journal, December 2013


First Lattice Calculation of the QED Corrections to Leptonic Decay Rates
journal, February 2018


QED corrections to hadronic processes in lattice QCD
journal, April 2015


QED effects in the pseudoscalar meson sector
journal, April 2016

  • Horsley, R.; Nakamura, Y.; Perlt, H.
  • Journal of High Energy Physics, Vol. 2016, Issue 4
  • DOI: 10.1007/JHEP04(2016)093

Including electromagnetism in K → ππ decay calculations
journal, January 2018