CP-Odd Tadpole Renormalization of Higgs Scalar-Pseudoscalar Mixing

TL;DR

This work examines an Abelian two-Higgs model with a CP-invariant tree-level potential that accommodates soft-CP-violating Yukawa interactions. Using the non-renormalization theorem, it derives consistency conditions under which a CP-odd counterterm can exist and ensures that one-loop HA (Higgs–pseudoscalar) mixing is UV finite, with CP-odd tadpole renormalization determined from Higgs potential minimization. Loop analyses with charged scalars show that including the CP-odd tadpole renormalization cancels UV divergences in G^0h and hA self-energies and reveals non-decoupling effects that can enhance EDMs via Barr-Zee-type mechanisms. The results connect the theoretical structure of CP-violating scalar-pseudoscalar mixing to EDM phenomenology of neutron, electron, and muon, and offer a framework that can inform MSSM-like extensions and future experimental tests.

Abstract

We consider an Abelian model with a CP-conserving Higgs potential spanned by two complex Higgs fields. The CP invariance of the Higgs potential is then broken explicitly beyond the Born approximation by introducing soft-CP-violating Yukawa interactions. Based on the non-renormalization theorem, we derive the consistency conditions under which a CP-odd counterterm exists and, at the same time, renders the one-loop-induced mixing of a CP-even Higgs boson with a CP-odd Higgs scalar ultra-violet finite. The novel CP-odd tadpole renormalization may then be determined from the minimization constraints on the Higgs potential. Finally, we discuss the phenomenological consequences of the so-generated CP-violating scalar-pseudoscalar mixing for the electric dipole moments of neutron, electron and muon.