  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.
