Abstract
Spatially non-local matrix elements are useful lattice-QCD observables in a variety of contexts, for example in determining hadron structure. To quote credible estimates of the systematic uncertainties in these calculations, one must understand, among other things, the size of the finite-volume effects when such matrix elements are extracted from numerical lattice calculations. In this work, we estimate finite-volume effects for matrix elements of non-local operators, composed of two currents displaced in a spatial direction by a distance $\xi$. We find that the finite-volume corrections depend on the details of the matrix element. If the external state is the lightest degree of freedom in the theory, e.g.~the pion in QCD, then the volume corrections scale as $ e^{-m_\pi (L- \xi)} $, where $m_\pi$ is the mass of the light state. For heavier external states the usual $e^{- m_\pi L}$ form is recovered, but with a polynomial prefactor of the form $L^m/|L - \xi|^n$ that can lead to enhanced volume effects. These observations are potentially relevant to a wide variety of observables being studied using lattice QCD, including parton distribution functions, double-beta-decay and Compton-scattering matrix elements, and long-range weak matrix elements.
Highlights
One of the fundamental goals in theoretical nuclear physics is the prediction of hadron structure from firstprinciples calculations based on the underlying gauge theory of the strong nuclear force, QCD
For matrix elements of composite currents, we show that finite-volume effects take the form hMjJ ð0; ξÞJ ð0ÞjMiL − hMjJ ð0; ξÞJ ð0ÞjMi∞
We focus on two terms, one scaling with the mass of the external state and the other with the mass of the lightest d.o.f
Summary
One of the fundamental goals in theoretical nuclear physics is the prediction of hadron structure from firstprinciples calculations based on the underlying gauge theory of the strong nuclear force, QCD. (corresponding to the pion in QCD) and one heavy (corresponding to a nucleon or heavy meson) d.o.f. Proposals to extract hadronic structure observables from lattice-QCD calculations using these types of operators, in place of those defined with a Wilson line, appeared in Refs. Proposals to extract hadronic structure observables from lattice-QCD calculations using these types of operators, in place of those defined with a Wilson line, appeared in Refs. This additional factor may lead to matrix elements of this operator being closer to their infinite-volume counterparts than in the case of products of currents that satisfy ξ-periodicity. Technical details of certain functions used in the analysis are discussed in the Appendix
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