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Finite volume corrections to the electromagnetic mass of composite particles

Jong-Wan Lee1,* and Brian C. Tiburzi1,2,3,†

  • 1Department of Physics, The City College of New York, New York, New York 10031, USA
  • 2Graduate School and University Center, The City University of New York, New York, New York 10016, USA
  • 3RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973, USA

  • *Present address: Department of Physics, College of Science, Swansea University, Swansea SA2 8PP, United Kingdom. jwlee2@ccny.cuny.edu
  • †btiburzi@ccny.cuny.edu
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Phys. Rev. D 93, 034012 – Published 8 February, 2016

DOI: https://doi.org/10.1103/PhysRevD.93.034012

Abstract

The long-range electromagnetic interaction presents a challenge for numerical computations in QCD+QED. In addition to power-law finite volume effects, the standard lattice gauge theory approach introduces nonlocality through removal of photon zero-momentum modes. The resulting finite volume effects must be quantitatively understood; and, to this end, nonrelativistic effective field theories are an efficient tool, especially in the case of composite particles. Recently an oddity related to nonlocality of the standard lattice approach was uncovered by the Budapest-Marseille-Wuppertal collaboration. Explicit contributions from antiparticles appear to be required so that finite volume QED results for a pointlike fermion can be reproduced in the effective field theory description. We provide transparency for this argument by considering pointlike scalars and spinors in finite volume QED using the method of regions. For the more germane case of composite particles, we determine that antiparticle modes contribute to the finite volume electromagnetic mass of composite spinors through terms proportional to the squares of timelike form factors evaluated at threshold. We extend existing finite volume calculations to one order higher, which is particularly relevant for the electromagnetic mass of light nuclei. Additionally, we verify that the analogous finite volume contributions to the nucleon mass in chiral perturbation theory vanish in accordance with locality.

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Phys. Rev. D 93, 034012– Published 8 February, 2016
  • Received 1 September 2015
Article part of CHORUS

© 2016 American Physical Society

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