Operator product expansion on the lattice: analytic Wilson coefficients

Abstract

We present first results for Wilson coefficients of operators up to first order in the covariant derivatives for the case of Wilson fermions. They are derived from the off-shell Compton scattering amplitude $\mathcal{W}_{μν}(a,p,q)$ of massless quarks with momentum $p$. The Wilson coefficients are classified according to the transformation of the corresponding operators under the hypercubic group H(4). We give selected examples for a special choice of the momentum transfer $q$. All Wilson coefficients are given in closed analytic form and in an expansion in powers of $a$ up to first corrections.