2025/11/06 by Spanoudes, Gregoris, Costa, Marios, Mitsidi, Kyproulla +1
#FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Phenomenology (hep-ph)
paper · doi:10.48550/arxiv.2511.04305
In this paper we study a complete set of scalar and pseudoscalar four-quark operators, with a particular emphasis on their renormalization within a Gauge-Invariant Renormalization Scheme (GIRS). We focus on operators that do not mix with lower-dimensional operators by virtue of their transformation properties under the flavor-symmetry group. This class includes all ΔF = 2 operators, as well as their partners that transform under the same irreducible representations of the flavor group. These encompass a substantial subset of ΔF = 1 and ΔF = 0 operators. The present analysis provides a detailed classification of all four-quark operators, exploring their Fierz identities, symmetry properties, and mixing patterns. Different variants of GIRS are explored, including a democratic version that treats all mixing operators uniformly. For selected variants, which exhibit smaller mixing effects, we present the conversion matrices from GIRS to the MS scheme at next-to-leading order.