Four Generations, the Electroweak Phase Transition, and Supersymmetry

TL;DR

This work investigates electroweak baryogenesis within a four-generation supersymmetric model (4MSSM), showing that heavy fourth-generation quarks and their scalar partners can strengthen the electroweak phase transition to a strong first-order regime ($φ_c/T_c \gtrsim 1$) while also yielding a Higgs mass above LEP bounds. The analysis combines a controlled tanβ=1 setup, one-loop Coleman-Weinberg potentials, and finite-temperature corrections, highlighting the delicate balance between heavy-fermion and squark contributions to both zero- and finite-temperature potentials. A key finding is that achieving the desired phase-transition strength requires a small squark-to-quark mass ratio near unity (roughly $1 \lesssim m_{\tilde{q}'}/m_{q'} \lesssim 1.1$) with $m_{q'} \gtrsim 300$ GeV, situating the relevant parameter region just beyond current Tevatron limits and within reach of the LHC. The results point to a viable, testable scenario for electroweak baryogenesis in low-energy SUSY with a fourth generation and motivate collider searches for both fourth-generation quarks and their superpartners.

Abstract

We calculate the strength of the electroweak phase transition in a supersymmetric model with four chiral generations. The additional chiral fermions (and scalar partners) lower the critical temperature and thus strengthen the first-order phase transition. The scalar partners stabilize the potential, leading to an effective theory that is bounded from below. We identify the ensemble of parameters where phi_c/T_c \gsim 1 simultaneous with obtaining a large enough Higgs mass. Our calculations focus on a subset of the full four generational supersymmetric parameter space: We take the pseudoscalar heavy, tan(beta)=1, and neglect all subleading contributions to the effective potential. We find that the region of parameter space with a strong first-order phase transition requires m_tilde{q}'/m_q' \lsim 1.1 while the constraint on the lightest Higgs mass requires m_tilde{q}'/m_q' /gsim 1 with m_q' \gsim 300 GeV. We are led to an intriguing prediction of quarks and squarks just beyond the current Tevatron direct search limits that are poised to be discovered quickly at the LHC.

Figures (7)

• Figure 1: An estimate of the cutoff scale of the 4MSSM as a function of the fourth generation fermion mass by running the one-loop RGEs of the quark Yukawas up to where they encounter a Landau pole ($y_{f'} \sim 4\pi$).
• Figure 2: An illustration of the effect of adding one additional heavy fermion that obtains a mass of 400 GeV entirely from electroweak symmetry breaking. The figure (a) on the left shows the effective potential at the critical temperature $T_c$ (solid line) in the 4MSSM with $m_{t'} = m_{b'} = 400$ GeV and $m_{\tilde{q}'}/m_{q'} = 1.05$. Adding an additional heavy fermion (with $n = -1$) to the effective potential is shown (dashed-line), except that only the finite-temperature contribution, $V_{T1}$, is included in (a). Figure (b) on the right shows the the effect of including just the finite-temperature contribution (dashed-line), identical to Figure (a), and then the effect of including both the finite-temperature as well as the zero-temperature contribution $V_1$ (solid-line). The net effect shown in Figure (b) solid-line is that the global minimum at $\phi \simeq \phi_c$ decreases and thus $T_c$ increases.
• Figure 3: This plot shows that the electroweak phase transition order parameter decreases if an additional heavy chiral quark is added to the theory without its corresponding superpartner.
• Figure 4: Contour plot with the ratio $m_{\tilde{q}'}/m_{q'}$ fixed, from top to bottom, as $1.05, 1.1, 1.15, 1.2$. The masses of the fourth generation quarks are taken to be equal.
• Figure 5: Contour plot of the lightest Higgs mass as a function of the fourth generation quark mass. Each contour corresponds to a fixed ratio $m_{\tilde{q}'}/m_{q'}$, from top to bottom, 1.2, 1.1, 1.0, 0.95 with $m_{t'} = m_{b'}$ and $m_{\tilde{t}} = m_{\tilde{q}'}$.