Electroweak Baryogenesis in Top-Philic Type-III Two-Higgs-Doublet Model motivated by the $t\bar{t}$ Excess at the LHC

Abstract: Recently, the CMS and ATLAS Collaborations reported an enhancement near the production threshold in the invariant-mass distribution of top-antitop pairs. Possible interpretations include a pseudoscalar toponium quasi-bound state and an additional elementary pseudoscalar that coexists or mixes with toponium. Motivated by the latter interpretation, we identify the additional pseudoscalar with the CP-odd Higgs boson of a top-philic Type-III two-Higgs-doublet model (2HDM). This possibility is also interesting from the viewpoint of electroweak baryogenesis: the extended scalar sector can support a strong first-order electroweak phase transition, while the additional top-quark Yukawa interaction can provide a CP-violating source through the bubble-wall background. We therefore investigate whether the same parameter region motivated by the $t\bar{t}$ threshold enhancement can also account for the observed baryon asymmetry of the Universe (BAU). We compare two scenarios with different origins of CP violation. In the explicit CP violation scenario, a complex phase is introduced into the additional top-quark Yukawa coupling $ρ_{tt}$. In the transitional CP violation (TCPV) scenario, a CP-odd field configuration is generated dynamically inside the bubble wall through finite-temperature effects. Within the present one-loop treatment, explicit CP violation remains a scheme-dependent possibility, whereas no viable transitional CP violation branch is identified. In addition, we discuss the physical differences and viability of these two scenarios.

• The paper examines a top-philic Type-III two-Higgs-doublet model (2HDM) as an explanation for both the LHC $tar{t}$ threshold excess and electroweak baryogenesis.
• Of two CP-violating mechanisms, only explicit CPV (under Parwani resummation) achieves baryon asymmetry within given constraints, significantly enhancing arbitrary high-parameter restraining.
• Current gravitational-wave detectors are unable to detect the signal produced by the viable electroweak phase transitions and further refinement and updated methods are needed for future research.

Motivation and scope

The CMS and ATLAS Collaborations have reported an enhancement near the $t\bar{t}$ production threshold in the invariant-mass spectrum, with candidate interpretations including a pseudoscalar toponium quasi-bound state or an additional elementary pseudoscalar coexisting with toponium. The paper under discussion adopts the latter interpretation and identifies the additional pseudoscalar with the CP-odd Higgs boson of a top-philic Type-III two-Higgs-doublet model (2HDM), then asks whether the same parameter region can also realize electroweak baryogenesis (EWBG) and reproduce the observed baryon asymmetry of the Universe, $Y_B^{\rm obs}\simeq 8.7\times10^{-11}$. The analysis is organized around three questions: whether the model supports a strong first-order electroweak phase transition near the pseudoscalar mass suggested by the excess ($m_A\simeq345$ GeV); whether either of two CP-violation mechanisms yields the observed BAU; and whether the surviving points satisfy collider and dipole-moment constraints while producing an observable gravitational-wave signal.

Model setup

The framework is the most general renormalizable scalar potential in the Higgs basis, with the simplifying assumptions $m_{12}^2=\lambda_6=0$ at a reference scale and real $\lambda_{1,\dots,5,7}$. The Type-III structure allows both doublets to couple to the same fermions; to suppress tree-level flavor-changing neutral currents, the analysis works in the top-philic limit in which only the nonstandard Yukawa coupling $\rho_{tt}=\rho_{ttR}+i\rho_{ttI}$ connecting $H_2$ to the top quark is sizable. The finite-temperature effective potential is evaluated with unexpanded thermal functions $J_B$ and $J_F$, since the high-temperature expansion is not uniformly valid for the field-dependent masses encountered along the bounce trajectory. Both the Arnold–Espinosa and Parwani daisy-resummation prescriptions are implemented, and the paper explicitly requires that viable solutions be found in both prescriptions before being regarded as robust.

Explicit CP violation: successful only in one resummation scheme

In the explicit CPV scenario, $\operatorname{Im}\rho_{tt}\neq0$ generates a spatially varying complex phase in the top-quark mass across the bubble wall, feeding the CP-odd source moments into a finite-wall-velocity two-moment transport system for the species $Y_B^{\rm obs}\simeq 8.7\times10^{-11}$0. Bubble profiles are obtained from the three-field $Y_B^{\rm obs}\simeq 8.7\times10^{-11}$1 bounce via CosmoTransitions, with nucleation imposed through $Y_B^{\rm obs}\simeq 8.7\times10^{-11}$2 and the strong-transition criterion $Y_B^{\rm obs}\simeq 8.7\times10^{-11}$3.

The central result is starkly scheme-dependent. Under the Parwani prescription, parameter points exist that satisfy nucleation, the strong first-order transition, vacuum stability, oblique parameters within $Y_B^{\rm obs}\simeq 8.7\times10^{-11}$4, the $Y_B^{\rm obs}\simeq 8.7\times10^{-11}$5 constraint, and EDM limits near $Y_B^{\rm obs}\simeq 8.7\times10^{-11}$6 GeV; these points yield a baryon asymmetry consistent with observation. The corresponding coupling ranges are $Y_B^{\rm obs}\simeq 8.7\times10^{-11}$7 up to roughly unity, $Y_B^{\rm obs}\simeq 8.7\times10^{-11}$8 (nonzero), $Y_B^{\rm obs}\simeq 8.7\times10^{-11}$9, $m_A\simeq345$0, and nucleation temperatures in the range $m_A\simeq345$1 GeV. By contrast, no Arnold–Espinosa point simultaneously satisfies nucleation and the strong-transition condition, even though a critical temperature $m_A\simeq345$2 GeV exists in that scheme.

The paper identifies a plausible physical origin of this discrepancy: the successful Parwani points require a large quartic coupling $m_A\simeq345$3, which enhances higher-order corrections and amplifies sensitivity to the resummation treatment. Consequently, the explicit-CPV scenario cannot presently be regarded as established in a scheme-independent way — a limitation the author states plainly rather than obscuring. A definitive verdict would require higher-order finite-temperature corrections and a systematic resummation treatment.

Transitional CP violation: no viable branch

The second scenario, transitional CP violation (TCPV), posits a CP-symmetric Lagrangian and CP-symmetric vacua, with CP broken only dynamically inside the bubble wall. The diagnostic is well defined: perturb the CP-even wall by the CP-odd field $m_A\simeq345$4, form the fluctuation operator $m_A\simeq345$5, and require a negative lowest eigenvalue $m_A\simeq345$6, followed by verification that the full three-field bounce dominates over the two-field CP-even bounce. Under exact CP symmetry the two branches are degenerate and the ensemble-averaged asymmetry vanishes, so any controlled prediction also requires a branch-selection bias.

Within the mass window motivated by the $m_A\simeq345$7 excess, $m_A\simeq345$8 GeV, no parameter point develops the required negative mode while maintaining a viable first-order transition. Realizing $m_A\simeq345$9 generally demands large $m_{12}^2=\lambda_6=0$0 together with moderately large $m_{12}^2=\lambda_6=0$1, but the scalar-mass relations and phenomenological constraints at this mass significantly restrict both couplings. In lower-mass regions, $m_{12}^2=\lambda_6=0$2 GeV, $m_{12}^2=\lambda_6=0$3 can be brought numerically closer to zero but remains positive throughout the scan. The conclusion — that TCPV is difficult to realize in this model within the one-loop treatment — is stated as conditional on the loop order, since higher-order corrections could modify the CP-odd fluctuation operator. Within the present analysis, EWBG in this setup therefore appears to require an explicit source of CP violation.

Gravitational-wave prospects

For a representative Parwani point, the stochastic gravitational-wave spectrum from sound waves plus MHD turbulence (with bubble-wall collisions neglected, appropriate for non-runaway transitions) is computed using $m_{12}^2=\lambda_6=0$4, $m_{12}^2=\lambda_6=0$5, and $m_{12}^2=\lambda_6=0$6. The transition parameters are $m_{12}^2=\lambda_6=0$7 and $m_{12}^2=\lambda_6=0$8. The large inverse duration strongly suppresses the amplitude through the factor $m_{12}^2=\lambda_6=0$9 and shifts the peak upward in frequency; the resulting spectrum lies several orders of magnitude below the projected sensitivities of LISA, DECIGO, and BBO. Observation would require substantial improvement in the decihertz-to-few-hertz band, and even then would constitute evidence for the phase transition rather than for baryogenesis itself.

Dipole moments

The appendices develop the EDM machinery coherently: the one-loop top CEDM is controlled by the rephasing-invariant combination $\lambda_{1,\dots,5,7}$0 and vanishes identically when $\lambda_{1,\dots,5,7}$1 due to exact $\lambda_{1,\dots,5,7}$2 degeneracy cancellation, while the leading two-loop contribution is governed by $\lambda_{1,\dots,5,7}$3 via a $\lambda_{1,\dots,5,7}$4-induced off-diagonal scalar self-energy insertion. Electron, neutron, and proton EDMs are derived through RG running and threshold matching, with current bounds $\lambda_{1,\dots,5,7}$5cm, $\lambda_{1,\dots,5,7}$6cm, and $\lambda_{1,\dots,5,7}$7cm imposed on the viable points. Notably, the Barr–Zee channel is absent in the top-philic limit ($\lambda_{1,\dots,5,7}$8).

Limitations and open questions

Several caveats bear directly on the results. First, the scheme dependence of the explicit-CPV outcome is severe: success in Parwani but failure in Arnold–Espinosa means the viability claim rests on a single resummation treatment, likely aggravated by $\lambda_{1,\dots,5,7}$9. Second, the radiative regeneration of $\rho_{tt}=\rho_{ttR}+i\rho_{ttI}$0 and $\rho_{tt}=\rho_{ttR}+i\rho_{ttI}$1 is neglected after imposing them at a reference scale. Third, the effective Higgs-fluid statistical weight is fixed at its relativistic value $\rho_{tt}=\rho_{ttR}+i\rho_{ttI}$2, although thermal masses with $\rho_{tt}=\rho_{ttR}+i\rho_{ttI}$3 should shift it. Fourth, the large quartics may drive a Landau pole below the Planck scale; without a dedicated RG study, the model may be interpretable only as an EFT requiring UV completion. Finally, the TCPV null result is strictly one-loop and confined to the scanned parameter regions.

Conclusion

This work connects the LHC $\rho_{tt}=\rho_{ttR}+i\rho_{ttI}$4 threshold excess to early-Universe baryogenesis in a concrete and computationally complete manner. Its principal findings are twofold: explicit CP violation via $\rho_{tt}=\rho_{ttR}+i\rho_{ttI}$5 can yield the observed BAU, but only within the Parwani resummation prescription, leaving the result scheme-dependent; and transitional CP violation fails to materialize anywhere in the explored parameter space. The gravitational-wave signal accompanying the viable transitions is too weak for baseline space-based detectors. The paper's value lies as much in its negative results and its quantified theoretical uncertainties as in the successful parameter points it identifies.