Stepping Into Electroweak Symmetry Breaking: Phase Transitions and Higgs Phenomenology

TL;DR

This paper analyzes electroweak baryogenesis in a minimal SM extension with a real SU(2)$_L$ triplet ${\Sigma}$ stabilized by a $(Z_2)_{\Sigma}$ symmetry. It demonstrates a novel two-step electroweak phase transition, with the first step $O\to\Sigma$ potentially generating the baryon asymmetry and the second step $\Sigma\to H$ yielding the SM Higgs phase while leaving a dark matter candidate ${\Sigma}^0$; the authors compute the finite-temperature effective potential in a gauge-independent framework, examine monopole- and sphaleron-mediated B+L washout to formulate BNPC constraints, and explore regions of parameter space compatible with both a strong first-order transition and collider constraints from $H\to\gamma\gamma$. The study shows that the two-step pattern arises for plausible values of the Higgs-portal coupling $a_2$ and triplet mass $m_{\Sigma}$, with entropy production tightly controlled and observable implications for Higgs diphoton decays. The results motivate generalizations to higher-dimensional scalar multiplets, offering a realistic template for baryogenesis and dark matter in extended scalar sectors testable at the LHC and future colliders.

Abstract

We study the dynamics of electroweak symmetry-breaking in an extension of the Standard Model where the Higgs sector is augmented by the addition of a real (Y = 0) isospin triplet. We show that this scenario exhibits a novel, two-step electroweak phase transition, wherein the first step provides the strongly first order transition as required for electroweak baryogenesis followed by a second step to the Standard Model Higgs phase that also admits a cold dark matter candidate. We analyze the constraints on this scenario from recent results obtained at the Large Hadron Collider for the Higgs diphoton decay channel. We argue that this two-step scenario can be generalized to extensions of the Standard Model with additional higher-dimensional scalar multiplets that may yield realistic baryogenesis dynamics.

Figures (8)

• Figure 1: Field phase space indicating critical (extremal) points in the tree-level potential at zero temperature, and the expected two-step pattern of symmetry breaking at finite temperature. Red points are related to black points via $(Z_2)_H$ and $(Z_2)_\Sigma$ symmetries.
• Figure 2: Regions A (yellow striped) plus B (solid blue) indicate where tree-level electroweak vacuum stability condition of (\ref{['eq:explicitVacStab']}) is satisfied. Left panel: the $m_\Sigma$-$b_4$ plane for fixed $(m_H=125\text{ GeV},\,a_2=1.07)$; right panel: the $a_2$-$b_4$ plane for fixed $(m_H=150\text{ GeV},\,m_\Sigma=150\text{ GeV})$. Regions B indicate where (\ref{['eq:metastableSigma']}) is also satisfied and the tree-level potential exhibits a metastable minimum along neutral $\Sigma$ direction. Illustrative representations of the scalar potential for regions A and B are indicated in the left and right panels of Fig. \ref{['fig:potentials']}, respectively.
• Figure 3: Qualitative picture of the potential $V(h,\,\sigma)$ of (\ref{['eq:treePotential']}) in the two different regions of parameter space as indicated in Fig. \ref{['fig:vacuumStab']}. Potential A (corresponding to regions A of Fig. \ref{['fig:vacuumStab']}) displays no critical point along the $\sigma$ direction, whereas Potential B (corresponding to regions B of Fig. \ref{['fig:vacuumStab']}) exhibits a metastable minimum along the $\sigma$-direction.
• Figure 4: Extremum points of the potential as a function of temperature for two choices of model parameters. Curves are labeled according to phases defined in Fig. \ref{['fig:vacuumSketch']}. Upper panel: the there is only one critical point, corresponding to a SM-like phase transition ($O\rightarrow H$); lower panel: the system exhibits two critical temperatures, favorable for baryogenesis, corresponding to transitions at critical temperatures $T_\sigma$: $O\rightarrow\Sigma$ and $T_h$: $\Sigma\rightarrow H$.
• Figure 5: Phase transition order parameters: Red contours indicate constant $\bar{x}(T_\sigma)/T_\sigma$ for first step. For the second step, dashed blue contours correspond to $\bar{v}(T_h)/T_h$ with values {1.2, 1.6, 2.0, 2.4, 2.8, 3.2, 3.6, 4.0}, read right to left. Outside the contoured region, the EWPT proceeds in a single SM-like step ($O\rightarrow H$) and is unfavorable for baryogenesis.