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.
Highlights
State-of-the-art simulations of quantum chromodynamics (QCD) reliably predict a number of spectral quantities and hadronic matrix elements with a precision below the percent level; see for instance the review by the Flavour Lattice Averaging Group (FLAG) [1]
Most of the results listed by FLAG have been obtained within an isospin-symmetric QCD, i.e., with equal light quark masses and ignoring electromagnetic interactions
A logical step in the continuous improvement of calculations of spectra, matrix elements and scattering amplitudes is the inclusion of isospin breaking effects, which by naive power counting are expected to contribute at the percent level and are becoming significant
Summary
State-of-the-art simulations of QCD reliably predict a number of spectral quantities and hadronic matrix elements with a precision below the percent level; see for instance the review by the Flavour Lattice Averaging Group (FLAG) [1]. In a number of cases, the leading coefficients of the power expansion are universal In such cases, the large-distance limit of the finite-volume effects are equivalent to those of point particles and can be computed and corrected for analytically, for instance by means of perturbative calculations in scalar/fermionic QED or in effective field theories; see e.g, Refs. Some general remarks on QEDTL and QEDL are provided, and it is shown how each of these theories are quantized in the path-integral formalism This is followed by the core part of this paper, namely a proposal for a systematic computation of QED finite-volume effects in terms of a large-volume expansion. New local operators with volume-dependent coefficients are introduced into the effective theories without the need to include the antiparticle modes
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