Speaker
Description
We study the renormalization of $\Delta F=1$ four-quark operators in a gauge-invariant renormalization scheme (GIRS). We begin by classifying a complete basis of scalar and pseudoscalar four-quark operators into irreducible representations of the flavor symmetry group and analysing their symmetry properties and mixing patterns. We then consider all classes of $\Delta F=1$ operators, including those that can mix with lower-dimensional operators. To determine the full operator mixing set in the latter case, we further investigate relevant spurionic symmetries on the lattice. Our calculations are performed in both continuum and lattice perturbation theory, employing Osterwalder-Seiler fermions in the lattice regularization. We formulate and explore a wide range of GIRS variants and identify those with reduced mixing effects. For selected promising variants, we present next-to-leading order results for the conversion matrices to the $\overline{\rm MS}$ scheme.