Locally-smeared operator product expansions

Understand

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.