Lattice study of an electroweak phase transition at m_h ~ 126 GeV

TL;DR

The study investigates whether a strong first-order electroweak phase transition can persist for a Higgs mass around 126 GeV in a MSSM-like scenario with a light right-handed stop, using a dimensionally reduced 3d effective theory and nonperturbative lattice simulations. It finds a nonperturbatively stronger transition than 2-loop perturbation theory, with Tc* ≈ 79 GeV, Higgs discontinuity v(Tc*)/Tc* ≈ 1.12, latent heat L/(Tc*)^4 ≈ 0.443, and surface tension σ/(Tc*)^3 ≈ 0.035; these results point to a window for electroweak baryogenesis and suggest a physical right-handed stop mass around 155 GeV, within uncertainties. The analysis depends on the accuracy of the 2-loop dimensional reduction and vacuum renormalization, which remain to be improved. The work also compares lattice and perturbative predictions, highlighting nonperturbative strengthening of the transition and possible implications for LHC constraints on stop-like particles.

Abstract

We carry out lattice simulations of a cosmological electroweak phase transition for a Higgs mass m_h ~ 126 GeV. The analysis is based on a dimensionally reduced effective theory for an MSSM-like scenario including a relatively light coloured SU(2)-singlet scalar, referred to as a right-handed stop. The non-perturbative transition is stronger than in 2-loop perturbation theory, and may offer a window for electroweak baryogenesis. The main remaining uncertainties concern the physical value of the right-handed stop mass which according to our analysis could be as high as m_tR ~ 155 GeV; a more precise effective theory derivation and vacuum renormalization than available at present are needed for confirming this value.

Figures (8)

• Figure 1: Slices of the perturbative phase diagram of the effective theory considered, in terms of the MSSM-like parameters defined in the text. The upper boundary corresponds to parameters at which $v(T_{\rm c}^*) /T_{\rm c}^*$ equals 0.9 in the Landau gauge; the lower boundary to values below which the theory is driven to a colour-broken minimum according to the 2-loop effective potential.
• Figure 2: Left panel: the expectation values of $\langle H_2^\dagger H^{ }_2\rangle$ and $\langle U^\dagger U\rangle$ as functions of the temperature $T^*$ in the continuum limit. The vertical dashed line shows the phase transition temperature. Right panel: continuum extrapolation of $\langle H_2^\dagger H^{ }_2\rangle$ at four chosen temperatures.
• Figure 3: The volume-averaged probability distribution of $H_2^\dagger H^{ }_2$ at three different volumes with $\beta_w=16$ and at $T_{{{\hbox{\scriptsize c}}},\beta_w=16}^*$. As the volume increases, the probability density between the two peaks decreases exponentially.
• Figure 4: The critical temperature as a function of the lattice spacing $1/\beta_w$. With the volumes shown in table \ref{['table:volumes']} no systematic volume dependence is seen, and all volumes are included in the plot. The interpolating curve is a second-order polynomial in $a$, fit to the points $\beta_w \ge 14$.
• Figure 5: Contour plot of the joint probability distribution of the volume-averaged $H_2^\dagger H^{ }_2$ and $U^\dagger U$ at $T_{\rm c}^*$. The measurement is for $\beta_w=20$, volume $=32^2\times 64$. The ${\overline{\hbox{\rm MS}}}$ scheme value of $\langle U^\dagger U \rangle$ is slightly negative in the low-temperature phase (cf. the text).