Finite-volume effects due to spatially nonlocal operators

Journal Article · 26 July 2018 · Physical Review D

DOI: https://doi.org/10.1103/PhysRevD.98.014511 · OSTI ID:1461723

Briceno, Raul A. ^[1]; Guerrero, Juan V. ^[2]; Hansen, Maxwell T. ^[3]; Monahan, Christopher J. ^[4]

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1. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Old Dominion Univ., Norfolk, VA (United States)
2. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Hampton Univ., Hampton, VA (United States)
3. European Organization for Nuclear Research (CERN), Geneva (Switzerland)
4. Univ. of Washington, Seattle, WA (United States)

Spatially non-local matrix elements are useful lattice-QCD observables in a variety of contexts, for example in determining hadron structure. In order 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 these effects by considering a simple toy model in which the non-local operator is 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 $$m$$ 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 $$L^a/|L - \xi|^b$$ that can lead to enhanced volume effects. As a result, these observations {might be relevant} for 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.

• Research Organization: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Nuclear Physics (NP)
• Grant/Contract Number: AC05-06OR23177; SC0008791; FG02-00ER41132
• OSTI ID: 1461723
• Alternate ID(s): OSTI ID: 1462022
• Report Number(s): JLAB-THY-18-2697; DOE/OR/23177-4429; arXiv:1805.01034; CERN-TH-2018-109; INT-PUB-18-019; PRVDAQ; TRN: US1902092
• Journal Information: Physical Review D, Vol. 98, Issue 1; ISSN 2470-0010
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English