Locally smeared operator product expansions in scalar field theory

Understand

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.