A general study on the volume dependence of spectral weights in lattice field theory

TL;DR

This paper investigates how the volume dependence of spectral weights in lattice field theory can distinguish particle states, finding it applicable mainly to stable particles and narrow resonances, and explores extracting resonance parameters.

Contribution

It extends the analysis of spectral weight volume dependence to general quantum field theories using L"uscher's formalism, clarifying its applicability to broad resonances.

Findings

Volume dependence distinguishes stable and narrow resonances

The criterion is not valid for broad resonances

Spectral weights can help extract resonance parameters

Abstract

It has been suggested that the volume dependence of the spectral weight could be utilized to distinguish single and multi-particle states in Monte Carlo simulations. In a recent study using a solvable model, the Lee model, we found that this criteria is applicable only for stable particles and narrow resonances, not for the broad resonances. In this paper, the same question is addressed within the finite size formalism outlined by L\"uscher. Using a quantum mechanical scattering model, the conclusion that was found in previous Lee model study is recovered. Then, following similar arguments as in L\"uscher's, it is argued that the result is valid for a general massive quantum field theory under the same conditions as the L\"uscher's formulae. Using the spectral weight function, a possibility of extracting resonance parameters is also pointed out.