The endpoint of the first-order phase transition of the SU(2) gauge-Higgs model on a 4-dimensional isotropic lattice

TL;DR

This study investigates the endpoint of the first-order finite-temperature electroweak phase transition in the 4D SU(2) gauge-Higgs theory on isotropic lattices with Nt=2. The authors combine finite-size scaling of Lee-Yang zeros, susceptibility analyses, Binder cumulants, and zero-temperature mass measurements to locate the endpoint and translate it into a physical Higgs mass. They find an endpoint at λ_c = 0.00116(16) corresponding to M_{H,c} = 73.3 ± 6.4 GeV (for M_W = 80 GeV), with the transition turning into a crossover beyond this point. The results are consistent with 3D effective theory and anisotropic 4D studies, and suggest that incorporating fermions and U(1) would shift the physical bound upward, reinforcing that SM electroweak baryogenesis is not viable.

Abstract

We study the first-order finite-temperature electroweak phase transition of the SU(2) gauge-Higgs model defined on a 4-dimensional isotropic lattice with temporal extension N_t=2. Finite-size scaling study of Lee-Yang zeros yields the value of the Higgs self coupling of the endpoint at lambda_c=0.00116(16). An independent analysis of Binder cumulant gives a consistent value for the endpoint. Combined with our zero-temperature measurement of Higgs and W boson masses, this leads to M_{H,c}=73.3 +- 6.4 GeV for the critical Higgs boson mass beyond which the electroweak transition turns into a crossover.

Figures (9)

• Figure 1: Peak height of susceptibility of $\rho^2$ against inverse volume normalized by critical temperature $VT_c^3=N_s^3/N_t^3$. Dotted lines are guides for eyes.
• Figure 2: Absolute value of normalized partition function as a function of complex $\kappa$ for $\lambda=0.00075$ and $N_s=60$.
• Figure 3: Contour plot of Fig. \ref{['fig:abs_z_f60d']}.
• Figure 4: Imaginary part of first Lee-Yang zero as a function of inverse volume normalized by the critical temperature. Solid lines are least $\chi^2$ fits with ${\rm Im}\kappa_0(V) = \kappa_0^c + C V^{-\nu}$.
• Figure 5: Imaginary part of first Lee-Yang zero at infinite-volume limit as a function of Higgs self coupling. Filled symbols are calculated without $\lambda$-reweighting, while open symbols with $\lambda$-reweighting from the filled symbol with same shape. Solid line is a linear fit to $\lambda=0.00135, 0.00145$ and $0.0017235$ (filled symbols).