Electroweak Baryogenesis with a Pseudo-Goldstone Higgs

TL;DR

The paper demonstrates that a pseudo-Goldstone Higgs, described by an SU(2)-custodial invariant Higgs effective field theory with parametrically enhanced dimension-6 operators, can yield a strongly first-order electroweak phase transition and enhanced CP violation necessary for electroweak baryogenesis. By performing a ring-improved one-loop finite-temperature analysis and introducing a thermal mass eigenstate basis for SM gauge bosons, the authors show that regions with $f oughly 500 ext{ GeV} ext{--} 1 ext{ TeV}$ and $m_h$ up to about 160 GeV can satisfy the washout condition and generate the observed baryon asymmetry. The framework relies on NP effects that significantly modify the Higgs self-coupling and CP-violating operators without conflicting with EWPD, making the scenario testable via Higgs pair production and EDM measurements. Collectively, the work provides a concrete, falsifiable path for PGH-related baryogenesis and highlights distinctive signatures in Higgs phenomenology and CP-violating observables.

Abstract

We examine the nature of electroweak Baryogenesis when the Higgs boson's properties are modified by the effects of new physics. We utilize the effective potential to one loop (ring improving the finite temperature perturbative expansion) while retaining parametrically enhanced dimension six operators of O(v^2/f^2) in the Higgs sector. These parametrically enhanced operators would be present if the Higgs is a pseudo-goldstone boson of a new physics sector with a characteristic mass scale Lambda ~ TeV, a coupling constant (4 pi) > g > 1 and a strong decay constant scale f = Lambda/g. We find that generically the effect of new physics of this form allows a sufficiently first order electro-weak phase transition so that the produced Baryon number can avoid washing out, and has enhanced effects due to new sources CP violation. We also improve the description of the electroweak phase transition in perturbation theory by determining the thermal mass eigenstate basis of the standard model gauge boson fields. This improves the calculation of the finite temperature effects through incorporating mixing in the determination of the vector boson thermal masses of the standard model. These effects are essential to determining the nature of the phase transition in the standard model and are of interest in our Pseudo-Goldstone Baryogenesis scenario.

Figures (12)

• Figure 1: One loop diagrams that contribute to the effective potential.
• Figure 2: The $n$ tadpole loop contribution to the diasy diagram of the Higgs propagator.
• Figure 3: The $n$ tadpole loop contribution to the sunset diagram of the Higgs propagator.
• Figure 4: Case $1$ where $\lambda_2$ and $\lambda_1$ are treated as independent. The green ($0 < \overline{\lambda_1}(f,T) < 5.6 \times 10^{-2}$) and light blue ($-0.2 < \lambda_1 < 0$) regions satisfy the first order phase transition (and small $\lambda_1$) conditions for Higgs masses of $115 {\rm \, GeV}$ (top) and $130 {\rm \, GeV}$ (bottom). Also plotted is the condition that $2 v^2 C_\phi/f^2 < 1$ which is the region between the horizontal dashed lines, Eqn. (\ref{['firstrec']}) which is satisfied below the short dashed line and the ascending solid line above which $T_b^2$ is positive. For each Higgs mass we plot the region of allowed Wilson coefficients for a strong decay constant of $f = 500 \, , 750 \, ,1000 \, ,1250 \, {\rm GeV}$ (left to right). The region that our calculation is self consistent, with a perturbative loop expansion that is under control, and has the signs of $\lambda_1$ and $m^2$ the same as in the SM is the small region in the green band bounded between the ascending solid and short dashed lines. For almost all of the viable parameter space the nature of the EW phase transition is different than in the SM. For the blue region the potential must be stabilized by the $\lambda_2$ operator.
• Figure 5: Case $2$ where we plot $\tilde{\lambda_2}=\lambda_2/\lambda_1$. As in Fig. 4, the green ($0 < \overline{\lambda_1}(f,T) < 5.6 \times 10^{-2}$) and light blue ($-0.2 < \lambda_1 < 0$) regions satisfy the first order phase transition (and small $\lambda_1$) conditions for Higgs masses of $115 {\rm \, GeV}$ (top) and $130 {\rm \, GeV}$ (bottom).The lines are the same as in Fig. 4. For almost all of the parameter space, $\lambda_1$ is positive, however the nature of the EW phase transition is still quite different than in the SM as we discuss in Section \ref{['washout']}.