Locally smeared operator product expansions in scalar field theory

TL;DR

This paper introduces a new locally smeared operator product expansion that simplifies lattice calculations of nonperturbative matrix elements by avoiding power-divergent mixing, demonstrated in scalar field theory.

Contribution

It presents a novel smeared operator product expansion formalism that connects lattice nonperturbative matrix elements to continuum operators, overcoming power-divergent mixing issues.

Findings

The formalism effectively relates lattice and continuum matrix elements.

It avoids power-divergent mixing in lattice calculations.

Feasibility demonstrated with scalar field theory examples.

Abstract

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.