Locally smeared operator product expansions in scalar field theory
We propose a new locally smeared operator product expansion to decompose nonlocal operators in terms of a basis of smeared operators. The smeared operator product expansion formally connects nonperturbative matrix elements determined numerically using lattice field theory to matrix elements of nonlocal operators in the continuum. These nonperturbative matrix elements do not suffer from powerdivergent mixing on the lattice, which significantly complicates calculations of quantities such as the moments of parton distribution functions, provided the smearing scale is kept fixed in the continuum limit. The presence of this smearing scale complicates the connection to the Wilson coefficients of the standard operator product expansion and requires the construction of a suitable formalism. We demonstrate the feasibility of our approach with examples in real scalar field theory.
 Authors:

^{[1]};
^{[2]}
 College of William and Mary, Williamsburg, VA (United States)
 College of William and Mary, Williamsburg, VA (United States); Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
 Publication Date:
 Report Number(s):
 JLAB/THY152008; DOE/OR231773290
Journal ID: ISSN 15507998; PRVDAQ; ArticleNumber: 074513
 Grant/Contract Number:
 FG0204ER41302; AC0506OR23177; NSFPHY10034278
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review. D, Particles, Fields, Gravitation and Cosmology
 Additional Journal Information:
 Journal Volume: 91; Journal Issue: 7; Journal ID: ISSN 15507998
 Publisher:
 American Physical Society (APS)
 Research Org:
 Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Nuclear Physics (NP) (SC26)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; quantum chromodynamics (QCD); euclidean lattices; scalar field theory; operator product expansion (OPE)
 OSTI Identifier:
 1178567
 Alternate Identifier(s):
 OSTI ID: 1178585
Monahan, Christopher, and Orginos, Kostas. Locally smeared operator product expansions in scalar field theory. United States: N. p.,
Web. doi:10.1103/PhysRevD.91.074513.
Monahan, Christopher, & Orginos, Kostas. Locally smeared operator product expansions in scalar field theory. United States. doi:10.1103/PhysRevD.91.074513.
Monahan, Christopher, and Orginos, Kostas. 2015.
"Locally smeared operator product expansions in scalar field theory". United States.
doi:10.1103/PhysRevD.91.074513. https://www.osti.gov/servlets/purl/1178567.
@article{osti_1178567,
title = {Locally smeared operator product expansions in scalar field theory},
author = {Monahan, Christopher and Orginos, Kostas},
abstractNote = {We propose a new locally smeared operator product expansion to decompose nonlocal operators in terms of a basis of smeared operators. The smeared operator product expansion formally connects nonperturbative matrix elements determined numerically using lattice field theory to matrix elements of nonlocal operators in the continuum. These nonperturbative matrix elements do not suffer from powerdivergent mixing on the lattice, which significantly complicates calculations of quantities such as the moments of parton distribution functions, provided the smearing scale is kept fixed in the continuum limit. The presence of this smearing scale complicates the connection to the Wilson coefficients of the standard operator product expansion and requires the construction of a suitable formalism. We demonstrate the feasibility of our approach with examples in real scalar field theory.},
doi = {10.1103/PhysRevD.91.074513},
journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},
number = 7,
volume = 91,
place = {United States},
year = {2015},
month = {4}
}