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 nonlo...

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Bibliographic Details
Published in:Physical review. D, Particles, fields, gravitation, and cosmology Particles, fields, gravitation, and cosmology, 2015-04, Vol.91 (7), Article 074513
Main Authors: Monahan, Christopher, Orginos, Kostas
Format: Article
Language:English
Subjects:
Continuums
Cosmology
euclidean lattices
Field theory
Formalism
Galling
Lattices
NUCLEAR PHYSICS AND RADIATION PHYSICS
operator product expansion (OPE)
Operators
quantum chromodynamics (QCD)
scalar field theory
Scalars
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Summary: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 power-divergent 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.
ISSN:1550-7998
1550-2368
DOI:10.1103/PhysRevD.91.074513