Determining matrix elements and resonance widths from finite volume: the dangerous mu-terms

TL;DR

This paper reveals that exponential finite size effects, specifically mu-terms from bound state poles, can significantly impact the accuracy of matrix element and resonance width calculations in finite volume methods, challenging previous assumptions.

Contribution

It demonstrates that mu-term finite size corrections can be larger than expected and affect the determination of physical quantities, with implications for lattice QCD and related models.

Findings

Mu-terms can cause large finite size effects in sine-Gordon model.

Explicit evaluation of mu-terms explains discrepancies in matrix element calculations.

Finite size effects depend on general field theoretic features, not just two-dimensional models.

Abstract

The standard numerical approach to determining matrix elements of local operators and width of resonances uses the finite volume dependence of energy levels and matrix elements. Finite size corrections that decay exponentially in the volume are usually neglected or taken into account using perturbation expansion in effective field theory. Using two-dimensional sine-Gordon field theory as "toy model" it is shown that some exponential finite size effects could be much larger than previously thought, potentially spoiling the determination of matrix elements in frameworks such as lattice QCD. The particular class of finite size corrections considered here are mu-terms arising from bound state poles in the scattering amplitudes. In sine-Gordon model, these can be explicitly evaluated and shown to explain the observed discrepancies to high precision. It is argued that the effects observed are not special to the two-dimensional setting, but rather depend on general field theoretic features that are common with models relevant for particle physics. It is important to understand these finite size corrections as they present a potentially dangerous source of systematic errors for the determination of matrix elements and resonance widths.