Hadronic CP Violation in the 2HDM

TL;DR

We address hadronic CP violation in the unconstrained two-Higgs doublet model by computing light-quark EDMs, chromo-EDMs, the Weinberg operator, and CP-violating lepton-quark interactions at two-loop order. The approach matches the 2HDM onto a five-flavor effective field theory at the weak scale and employs renormalization-group evolution to sum leading logarithms down to the hadronic scale, using a comprehensive operator basis that includes dipoles, four-quark, semileptonic, and the Weinberg operator. The authors provide complete analytic weak-scale matching conditions, threshold corrections, and both fermionic and bosonic contributions, validating gauge-independence and scheme consistency. The results form a broadly applicable framework beyond the 2HDM for models without light degrees of freedom and are complemented by a public Python implementation for numerical studies.

Abstract

We present the first complete two-loop calculation of the electric and chromo-electric dipole moments of the light quarks and the gluon, as well as contributions to CP-violating lepton-quark interactions, in the unconstrained two-Higgs doublet model. We include the most general Yukawa interactions of the Higgs doublets with the Standard Model fermions up to quadratic order, and allow for generic phases in the Higgs potential. We pay particular attention to a consistent treatment of all fermionic contributions in the low-energy effective theory, including a consistent renormalization-group summation of all leading-logarithmic effects. This latter part of the work is independent of the specific UV model and can generally be applied to a large class of models that do not introduce new light degrees of freedom. A python implementation of our results is provided via a public git repository.

Figures (8)

• Figure 1: Representative Feynman diagrams for the one-loop contributions to the EDM (left panel) and chromo-EDM (center panel) of the up quark, and to the EDM of the down quark (right panel). Solid lines denote quarks, and dashed lines denote Higgs bosons (labelled by $h_k$ and $H^\pm$).
• Figure 2: Representative two-loop diagrams contributing to the light-quark EDM.
• Figure 3: Integrating out the neutral Higgs bosons at tree level generates scalar four-fermion operators. They mix into tensor operators via one-loop photon exchange, and the tensor operators mix into the electric dipole operators. This generates the leading quadratic logarithms in Eq. \ref{['eq:edm:leptons']}. QCD RG evolution then sums the leading logarithms to all orders in $\alpha_s$.
• Figure 4: Integrating out the Higgs, $W$, and $Z$ bosons at one-loop generates tensor four-fermion operators. They mix into the electric dipole operators. This generates the leading linear logarithms in Eq. \ref{['eq:edm:leptons']}. QCD RG evolution then sums the leading logarithms to all orders in $\alpha_s$.
• Figure 5: Representative non-Barr-Zee two-loop diagrams with $W$ exchange contributing to the light-quark EDM. The external photon can be attached to any internal charged line. The four diagrams represented by the left panel have no correspondence in the electron EDM case; they turn out to be zero.