Perturbative Corrections for Staggered Four-fermion Operators

We present results for one-loop matching coefficients between continuum fourfermion operators, defined in the Naive Dimensional Regularization scheme, and staggered fermion operators of various types. We calculate diagrams involving gluon exchange between quark lines, and “penguin” diagrams containing quark loops. For the former we use Landau gauge operators, with and without O(a) improvement, and including the tadpole improvement suggested by Lepage and Mackenzie. For the latter we use gauge-invariant operators. Combined with existing results for two-loop anomalous dimension matrices and one-loop matching coefficients, our results allow a lattice calculation of the amplitudes for KK mixing and K → ππ decays with all corrections of O(g) included. We also discuss the mixing of ∆S = 1 operators with lower dimension operators, and show that, with staggered fermions, only a single lower dimension operator need be removed by non-perturbative subtraction. October 1993 Email: [email protected] Email: [email protected]