Gauge invariant determination of charged hadron masses

Abstract

In this paper we show, for the first time, that charged-hadron masses can be calculated on the lattice without relying on gauge fixing at any stage of the calculations. In our simulations we follow a recent proposal and formulate full QCD+QED on a finite volume, without spoiling locality, by imposing C-periodic boundary conditions in the spatial directions. Electrically charged states are interpolated with a class of operators, originally suggested by Dirac and built as functionals of the photon field, that are invariant under local gauge transformations. We show that the quality of the numerical signal of charged-hadron masses is the same as in the neutral sector and that charged-neutral mass splittings can be calculated with satisfactory accuracy in this setup. We also discuss how to describe states of charged hadrons with real photons in a fully gauge-invariant way by providing a first evidence that the proposed strategy can be numerically viable.

arXiv comment17 pages, 3 figures, 1 table, accepted for publication in JHEP

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• FLAG Review 2019
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• FLAG Review 2024
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• Theoretical aspects of quantum electrodynamics in a finite volume with periodic boundary conditions
• Electromagnetic finite-size effects to the hadronic vacuum polarization
• Isospin-breaking corrections to light-meson leptonic decays from lattice simulations at physical quark masses
• openQ*D code: a versatile tool for QCD+QED simulations
• Notes on QED Corrections in Weak Decays
• Lattice calculation of the pion mass difference $M_{{\pi }^{+}}-M_{{\pi }^0}$ at order $\mathcal{O}({\alpha }_{em})$
• Resolving Charged Hadrons in QED -- Gauge Invariant Interpolating Operators