Electric dipole moment constraints on minimal electroweak baryogenesis

TL;DR

The paper analyzes a minimal effective-field-theory extension of the Standard Model for electroweak baryogenesis via CP-odd dimension-six Higgs operators, quantifying the induced CP violation and its compatibility with electric dipole moment constraints. It computes the full set of two-loop Barr–Zee-type EDM contributions, mapping the CP-odd sources to Tl, neutron, and Hg EDMs, and explores the parameter space of the new physics scales Λ and Λ_CP in both single- and decoupled-threshold scenarios. The results show that current EDM bounds, especially the neutron EDM, strongly constrain but do not exclude the scenario, with partial cancellations under minimal flavor violation able to relax some limits; a light Higgs region remains particularly favored. The study finds that next-generation EDM experiments will provide a decisive test of this EWBG realization, potentially probing CP-odd scales up to multi-TeV, and highlights the predictive link between Higgs-sector operators and low-energy CP-violating observables.

Abstract

We study the simplest generic extension of the Standard Model which allows for conventional electroweak baryogenesis, through the addition of dimension six operators in the Higgs sector. At least one such operator is required to be CP-odd, and we study the constraints on such a minimal setup, and related scenarios with minimal flavor violation, from the null results of searches for electric dipole moments (EDMs), utilizing the full set of two-loop contributions to the EDMs. The results indicate that the current bounds are stringent, particularly that of the recently updated neutron EDM, but fall short of ruling out these scenarios. The next generation of EDM experiments should be sufficiently sensitive to provide a conclusive test.

Figures (5)

• Figure 1: The solid lines indicate the strength of the phase transition, with $\xi=1.1,~2,~3$ (from above), with $\xi\sim 3$ delineating metastability of the symmetric minimum, while below the fourth (lowest) solid line the electroweak minimum is no longer the global one. The dashed lines indicate constant wall thickness $L_w=3T_c^{-1},~6T_c^{-1},~12T_c^{-1}$ (from below).
• Figure 2: The two-loop contribution to $d_f$ and $\tilde{d}_f$ mediated by an induced pseudoscalar $hF\tilde{F}$ coupling generated by the top-loop.
• Figure 3: The two-loop contributions to $d_f$ and $\tilde{d}_f$ mediated by an induced scalar $hFF$ coupling, generated either by quark (top) loops or various vector boson and/or Goldstone loops.
• Figure 4: Contours of $\eta_b$ -- labelled as $\eta_x$ where $\eta_b/\eta_{\rm exp}=x$ -- and the EDMs over the $\Lambda$ vs $m_h$ plane, with correlated thresholds, $\Lambda_{\rm CP}=\Lambda$. The shaded region is excluded by the EDMs, primarily the neutron EDM bound in this case. On the left, we retain only a single $CP$-odd phase in the top-Higgs vertex, while on the right the full set required to retain the Standard Model flavor structure is introduced, which allows the $d_n$ and $d_{Hg}$ bounds to be weakened (the $d_{Hg}$ contour actually lies below the 300 GeV ctuoff imposed on $\Lambda$ and so does not appear on the right-hand plot).
• Figure 5: Fixing several values of $\Lambda$ -- labelled as $\Lambda_x$ where $\Lambda=x$ [GeV] -- $d_n$ is plotted against $m_h$, with $\Lambda_{\rm CP}$ fixed to ensure that $\eta_b$ matches its observed value. Note that the EDMs are only logarithmically dependent on $m_h$, and thus the primary dependence arises implicitly via $\eta_b$. The shaded upper region is excluded by the neutron EDM bound, while the shaded lower region is excluded by metastability of the symmetric vacuum.