Divergences in the Effective Interaction between Chern–Simons Bosons and SM Fermions in Non-Unitary Gauge

A vector extension of the Standard Model (SM) involving an interaction of the Chern–Simons type is analyzed. The model introduces a new massive vector field, referred to as the Chern–Simons (CS) boson, which does not couple directly to the fermionic sector of the SM. The study focuses on the structure and renormalizability of the effective loop-induced interactions between the CS boson and SM fermions in an arbitrary gauge. It is demonstrated that the ultraviolet divergences arising in the loop calculations cannot be consistently removed for interactions involving fermions of identical flavor, while the corresponding loop-induced couplings between fermions of distinct flavors remain finite. The specific interaction operators associated with divergent coefficients are identified, and their treatment within the framework of effective field theory is proposed.