Locally-smeared operator product expansions

TL;DR

This paper introduces a locally-smeared operator product expansion (sOPE) that uses smearing techniques to connect nonperturbative lattice matrix elements with continuum non-local operators, avoiding power-divergent mixing.

Contribution

The paper proposes a novel sOPE framework utilizing smearing to improve nonperturbative lattice computations and demonstrates its feasibility in scalar field theory.

Findings

sOPE avoids power-divergent mixing on the lattice

Feasibility shown in scalar field theory example

Introduces a two-scale formalism for connection to standard OPE

Abstract

We propose a "locally-smeared Operator Product Expansion" (sOPE) to decompose non-local operators in terms of a basis of locally-smeared operators. The sOPE formally connects nonperturbative matrix elements of smeared degrees of freedom, determined numerically using the gradient flow, to non-local operators in the continuum. The nonperturbative matrix elements do not suffer from power-divergent mixing on the lattice, provided the smearing scale is kept fixed in the continuum limit. The presence of this smearing scale prevents a simple connection to the standard operator product expansion and therefore requires the construction of a two-scale formalism. We demonstrate the feasibility of our approach using the example of real scalar field theory.