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

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.

26 pages, 13 eps figures, LaTeX2e file

References in corpus (6)

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• Sine-Gordon form factors in finite volume
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Cited by in corpus (8)

• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Diagonal multi-soliton matrix elements in finite volume
• Comments on World-Sheet Form Factors in AdS/CFT
• Sine-Gordon multi-soliton form factors in finite volume
• Form factor approach to diagonal finite volume matrix elements in Integrable QFT
• Exact finite volume expectation values of local operators in excited states
• One-point functions in finite volume/temperature: a case study
• Finite volume form factors in the presence of integrable defects