On the Implementation of General Background Electromagnetic Fields on a Periodic Hypercubic Lattice

Abstract

Nonuniform background electromagnetic fields, once implemented in lattice quantum chromodynamics calculations of hadronic systems, provide a means to constrain a large class of electromagnetic properties of hadrons and nuclei, from their higher electromagnetic moments and charge radii to their electromagnetic form factors. We show how nonuniform fields can be constructed on a periodic hypercubic lattice under certain conditions and determine the precise form of the background U(1) gauge links that must be imposed on the quantum chromodynamics gauge-field configurations to maintain periodicity. Once supplemented by a set of quantization conditions on the background-field parameters, this construction guarantees that no nonuniformity occurs in the hadronic correlation functions across the boundary of the lattice. The special cases of uniform electric and magnetic fields, a nonuniform electric field that varies linearly in one spatial coordinate (relevant to the determination of quadruple moment and charge radii), nonuniform electric and magnetic fields with given temporal and spatial dependences (relevant to the determination of nucleon spin polarizabilities) and plane-wave electromagnetic fields (relevant to the determination of electromagnetic form factors) are discussed explicitly.

27 pages, 4 figures

References in corpus (11)

• Ab initio calculation of the neutron-proton mass difference
• Hadronic light-by-light scattering contribution to the muon anomalous magnetic moment from lattice QCD
• Electromagnetic mass splittings of the low lying hadrons and quark masses from 2+1 flavor lattice QCD+QED
• Determination of light quark masses from the electromagnetic splitting of pseudoscalar meson masses computed with two flavors of domain wall fermions
• Ab initio calculation of the $np\to d\gamma$ radiative capture process
• Magnetic moments of light nuclei from lattice quantum chromodynamics
• The NRQED lagrangian at order 1/M^4
• Extracting Nucleon Magnetic Moments and Electric Polarizabilities from Lattice QCD in Background Electric Fields
• Electromagnetic and spin polarisabilities in lattice QCD
• Hadronic vacuum polarization and muon g-2 from magnetic susceptibilities on the lattice
• Reconciling the lattice background field method with nonrelativistic QED: Spinor case

Cited by in corpus (15)

• Proton-proton fusion and tritium $\beta$-decay from lattice quantum chromodynamics
• Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes
• Electromagnetic form factors at large momenta from lattice QCD
• Double-$\beta$ Decay Matrix Elements from Lattice Quantum Chromodynamics
• Lattice QCD evaluation of the Compton amplitude employing the Feynman-Hellmann theorem
• Octet Baryon Magnetic Moments from Lattice QCD: Approaching Experiment from a Three-Flavor Symmetric Point
• Pion magnetic polarisability using the background field method
• Finite volume effects on the electric polarizability of neutral hadrons in lattice QCD
• Towards charged hadron polarizabilities from four-point functions in lattice QCD
• Nucleon in a periodic magnetic field
• Charged pion electric polarizability from four-point functions in lattice QCD
• Composite Vector Particles in External Electromagnetic Fields
• Charged pion electric polarizability from lattice QCD
• Nucleon in a periodic magnetic field: Finite-volume aspects
• Finite volume corrections to forward Compton scattering off the nucleon