Electroweak Baryogenesis and Colored Scalars

TL;DR

This work analyzes electroweak baryogenesis in models with a Standard Model–like Higgs that couples to new scalars, focusing on two-loop finite-temperature effects. It compares colored and colorless scalars, showing that color-bearing states generate large 2-loop gluon diagrams that can significantly strengthen the phase transition, with $\phi_C/T_C$ enhanced up to about 3.5 for $m_h=115$ GeV. The study maps the viable parameter space for a colored scalar (and contrasts it with singlets), highlighting a substantial baryogenesis-friendly region when the scalar is colored and noting experimental constraints from colliders. It further argues that light colored scalars yield promising LHC signatures in jets plus missing energy or dijet resonances, thereby linking detailed finite-temperature dynamics to concrete collider searches.

Abstract

We consider the 2-loop finite temperature effective potential for a Standard Model-like Higgs boson, allowing Higgs boson couplings to additional scalars. If the scalars transform under color, they contribute 2-loop diagrams to the effective potential that include gluons. These 2-loop effects are perhaps stronger than previously appreciated. For a Higgs boson mass of 115 GeV, they can increase the strength of the phase transition by as much as a factor of 3.5. It is the analogue of this effect that is responsible for the survival of the tenuous electroweak baryogenesis window of the Minimal Supersymmetric Standard Model. We further illuminate the importance of these 2-loop diagrams by contrasting models with colored scalars to models with singlet scalars. We conclude that baryogenesis favors models with light colored scalars. This motivates searches for pair-produced di-jet resonances or jet(s) + missing energy.

Figures (5)

• Figure 1: The dominant 2-loop diagrams involving a new scalar state, $X$, which couples to the Higgs boson. Dashed lines are scalars and curly lines are gluons. $h$ is the Higgs boson, and $\chi$ is the Goldstone boson. Note that if $X$ is a singlet the diagrams involving $X$ and gluons do not exist.
• Figure 2: Contours of $\phi_C/T_C$ [black, solid] and the physical $X$ mass [purple, dashed] in the $\sqrt{-M_X^2}$ vs. $Q$ plane in the model with an additional colored scalar, $X_c$. The Higgs mass is fixed to be 115 GeV and $K=1.6$. The thickest solid contour marks $\phi_C/T_C = 0.9$ and the contours to the right (left) of it mark successive values of $+$ ($-$) 0.2. The dashed contours are for $X$ masses of 140 GeV, 180 GeV, 220 GeV, and 260 GeV from left to right. First orderness is maximized for larger values of $Q$ and more negative values of $M_X^2$. In the yellow region there would be a phase transition to a vacuum with $\langle X_c \rangle\neq 0$. The maximum value of $Q$ plotted corresponds to where the high temperature expansion begins to break down.
• Figure 3: The 2-loop and 1-loop values of $\phi_C/T_C$ as a function of $M_X^2$ for $Q = 0.75$ [green, solid] and $Q = 1.75$ [blue, dashed]. The other parameters are fixed to be $K = 1.6$ and $m_h = 115 \hbox{GeV}$. The minimum value of $M_X^2$ plotted corresponds to the boundary where the $\langle X_c \rangle\neq 0$ phase transition would occur before the Higgs phase transition.
• Figure 4: We show various contributions to the 2-loop finite temperature potential for the respective 2-loop value of $T_C$ as a function of $\phi$. Specifically the curves are the total 2-loop contribution [black, solid]; the contribution from the $X_c$-$g$ loop [green, dot-dashed]; the contribution from the $X_c$-$X_c$-$g$ loop [red, dashed]; and the contribution from the $X_c$-$X_c$-$h$, $X_c$-$h$, $X_c$-$\chi$, $X_c$-$X_c$ and pure Standard Model diagrams summed together [blue, dotted]. The gray vertical line marks $\phi_C$. $M_X^2 = 0$ for the left figure and $M_X^2 = -(98 \hbox{GeV})^2$ for right figure. The other parameters are taken to be $Q = 0.7$, $K = 1.6$, and $m_h = 115$ GeV. The 2-loop analysis yields $\phi_C = 45.1 \hbox{GeV}$ and $T_C = 130.9 \hbox{GeV}$ for $M_X^2 = 0$, and $\phi_C = 122.8 \hbox{GeV}$ and $T_C = 115.9 \hbox{GeV}$ for $M_X^2 = -(98 \hbox{GeV})^2$.
• Figure 5: Contours of $\phi_C/T_C$ [black, solid] and the physical $X$ mass [purple, dashed] in the $\sqrt{-M_X^2}$ vs. $Q$ plane in the model with six additional real singlet scalars, $X_0$. The Higgs mass is fixed to be 115 GeV and $K=1.6$. The thickest solid contour marks $\phi_C/T_C = 0.9$ and the contours to the right (left) of it mark successive values of $+$ ($-$) 0.2. The dashed contours are for $X$ masses of 140 GeV, 180 GeV, and 220 GeV from left to right. In the yellow region there would be a phase transition to a vacuum with $\langle X_0 \rangle\neq 0$ before the electroweak phase transition would occur. The maximum value of $Q$ plotted corresponds to where the high temperature expansion begins to break down.