Where the electroweak phase transition ends

TL;DR

The paper determines where the electroweak phase transition ends in the 3d SU(2)-Higgs effective theory by combining latent-heat analysis and Lee–Yang zeroes. Using lattice simulations at $eta_G=12$ and $16$ for $M_H^*$ in the 70–80 GeV range and reweighting techniques, it locates the endpoint through two complementary routes: vanishing condensate discontinuity and the movement of complex-plane zeros. The study finds a critical coupling ratio $rac{ ext{3}}{g_3^2}_{ ext{crit}} = 0.102(2)$ with an associated endpoint at $M_H^* oughly 72.2(6)$ GeV, and an upper bound $rac{ ext{3}}{g_3^2}_{ ext{crit}} < 0.107(2)$ from latent-heat extrapolations. These results, consistent with prior work, help delineate the region where the electroweak transition ceases to be first order and provide insight into the connection to the corresponding 4d theory.

Abstract

We give a more precise characterisation of the end of the electroweak phase transition in the framework of the effective 3d SU(2)--Higgs lattice model than has been given before. The model has now been simulated at gauge couplings beta_G=12 and 16 for Higgs masses M_H^*=70, 74, 76 and 80 GeV up to lattices 96^3 and the data have been used for reweighting. The breakdown of finite volume scaling of the Lee-Yang zeroes indicates the change from a first order transition to a crossover at lambda_3/g_3^2=0.102(2) in rough agreement with results of Karsch et al (hep-lat/9608087) at β_G=9 and smaller lattices. The infinite volume extrapolation of the discontinuity Delta < phi^+ phi > /g_3^2 turns out to be zero at lambda_3/g_3^2=0.107(2) being an upper limit. We comment on the limitations of the second method.

Figures (11)

• Figure 1: Histograms of $\rho^2$ for different $M_H^*$ at the respective pseudo--critical $\beta_H$ (defined by the minimum of the Binder cumulant) for a $80^3$ lattice, $\beta_G=12$
• Figure 2: Quadratic Higgs condensate jump $\Delta \langle \phi^+ \phi \rangle/g_3^2$ as function of inverse physical length squared, upper data correspond to $M_H^*=70$ GeV, lower to $M_H^*=76$ GeV
• Figure 3: Quadratic Higgs condensate jump $\Delta \langle \phi^+ \phi \rangle/g_3^2$ as function of inverse physical length squared at $M_H^*=74$ GeV
• Figure 4: Infinite volume discontinuity $\Delta \langle \phi^+\phi \rangle/g_3^2$ shown vs. $\lambda_3/g_3^2$. Filled symbols mark the Higgs masses $M_H^*=70$, $74$ and $76$ GeV where data have been taken, open symbols denote results from FS interpolation. The isolated lower data point at $M_H^*=74$ GeV refers to an infinite volume extrapolation including only $80^3$ and $96^3$ lattices as described in the text.
• Figure 5: $3d$ view of $\left|Z_{\mathrm{norm}}\right|$ near to the first zeroes at $\beta_G=12$, $80^3$ and $M_H^*=70$ GeV