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

Theoretical aspects of quantum electrodynamics in a finite volume with periodic boundary conditions
Theoretical aspects of quantum electrodynamics in a finite volume with periodic boundary conditions
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 CP-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-$\frac{1}{2}$ 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 $\mathrm{QED}_{\mathrm{L}}$. 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 $\mathrm{QED}_{\mathrm{L}}$. Further, this paper offers new perspectives on the subtleties involved in applying low-energy effective field theories in the presence of $\mathrm{QED}_{\mathrm{L}}$, a theory that is rendered non-local with the exclusion of the spatial zero mode of the photon, clarifying recent discussions on this matter.
hep-lat, hep-th
1550-7998
Davoudi, Zohreh
4b1e5421-637e-4bd8-b929-411cc608cb2f
Harrison, James
59274288-5351-4f0b-a7df-0a9042b71e49
Jüttner, Andreas
a90ff7c5-ae8f-4c8e-9679-b5a95b2a6247
Portelli, Antonin
a2526d4a-144e-4095-802a-229cddb10f0f
Savage, Martin J.
b56b632c-bda2-4bd6-89f2-e1fbd721c7e4
Davoudi, Zohreh
4b1e5421-637e-4bd8-b929-411cc608cb2f
Harrison, James
59274288-5351-4f0b-a7df-0a9042b71e49
Jüttner, Andreas
a90ff7c5-ae8f-4c8e-9679-b5a95b2a6247
Portelli, Antonin
a2526d4a-144e-4095-802a-229cddb10f0f
Savage, Martin J.
b56b632c-bda2-4bd6-89f2-e1fbd721c7e4

Davoudi, Zohreh, Harrison, James, Jüttner, Andreas, Portelli, Antonin and Savage, Martin J. (2019) Theoretical aspects of quantum electrodynamics in a finite volume with periodic boundary conditions. Physical Review D, 99. (doi:10.1103/PhysRevD.99.034510).

Record type: Article

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 CP-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-$\frac{1}{2}$ 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 $\mathrm{QED}_{\mathrm{L}}$. 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 $\mathrm{QED}_{\mathrm{L}}$. Further, this paper offers new perspectives on the subtleties involved in applying low-energy effective field theories in the presence of $\mathrm{QED}_{\mathrm{L}}$, a theory that is rendered non-local with the exclusion of the spatial zero mode of the photon, clarifying recent discussions on this matter.

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Published date: 28 February 2019
Additional Information: 57 pages, 10 figures
Keywords: hep-lat, hep-th

Identifiers

Local EPrints ID: 429062
URI: https://eprints.soton.ac.uk/id/eprint/429062
ISSN: 1550-7998
PURE UUID: 5148a588-1a72-49ca-a771-f09a702b80ed

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Date deposited: 20 Mar 2019 17:30
Last modified: 19 Apr 2019 16:30

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