Charged hadrons in local finite-volume QED+QCD with C* boundary conditions

TL;DR

This paper analyzes how C* boundary conditions enable consistent description of charged states in finite-volume lattice QED+QCD simulations, reducing finite-volume effects and facilitating QED corrections calculations.

Contribution

It provides a detailed analysis of QED with C* boundary conditions, demonstrating the construction of charged states without gauge fixing and assessing finite-volume corrections.

Findings

Charged states can be constructed consistently with C* boundary conditions.

Finite-volume corrections to charged particle masses are significantly reduced.

C* boundary conditions are suitable for numerical QED+QCD simulations.

Abstract

In order to calculate QED corrections to hadronic physical quantities by means of lattice simulations, a coherent description of electrically-charged states in finite volume is needed. In the usual periodic setup, Gauss's law and large gauge transformations forbid the propagation of electrically-charged states. A possible solution to this problem, which does not violate the axioms of local quantum field theory, has been proposed by Wiese and Polley, and is based on the use of C* boundary conditions. We present a thorough analysis of the properties and symmetries of QED in isolation and QED coupled to QCD, with C* boundary conditions. In particular we learn that a certain class of electrically-charged states can be constructed in this setup in a fully consistent fashion, without relying on gauge fixing. We argue that this class of states covers most of the interesting phenomenological applications in the framework of numerical simulations. We also calculate finite-volume corrections to the mass of stable charged particles and show that these are much smaller than in non-local formulations of QED.