Bound state spectrum in the finite volume

TL;DR

This paper investigates how bound states can be identified in finite volume lattice simulations by analyzing energy spectra and volume dependence, using positronium in a U(1) gauge theory as a case study.

Contribution

It applies Luscher's finite size method to distinguish bound states from scattering states in lattice simulations with massive photons.

Findings

Bound states show specific volume dependence in energy spectra.

Positronium in the Higgs phase exhibits identifiable bound state signatures.

Finite volume effects are crucial for interpreting lattice bound state signals.

Abstract

The signature of bound state formation on the lattice is of particular interest in this talk. In the finite volume, where all states have discrete energies, it is rather hard to distinguish between a bound state and a scattering state if the bound state were close to threshold, i.e., like a "loosely bound state". To study bound states in the finite volume, we calculate the positronium spectroscopy in the Higgs phase of U(1) gauge dynamics, where the photon is massive and then massive photons give rise to the short-ranged interparticle force. We try to identify bound state formation on the basis of the Luscher's finite size method, which suggests specific volume dependences of the energy gap/shift from the threshold energy for either bound states or scattering states.