A New Order Parameter for the Higgs Transition in $SU(2)$-Higgs Theory

TL;DR

This study identifies a new order parameter for the Higgs transition in the $SU(2)$-Higgs model using lattice techniques, confirming its critical behavior aligns with the 3D Ising universality class.

Contribution

The paper introduces a gauge-fixed Higgs condensate as a novel order parameter and analyzes its critical behavior near the transition point using finite size scaling.

Findings

Gauge fixed condensate vanishes at the transition in the infinite volume limit.

Critical exponents match 3D Ising universality class values.

Results support previous findings of Ising-like critical behavior.

Abstract

We investigate the Higgs transition within the four dimensional $SU(2)-$ gauge-Higgs model in search for an order parameter as a function of the Higgs field hopping parameter, $\kappa$, using Lattice technique. We measure the Higgs condensate after applying Landau Gauge Fixing and study the corresponding susceptibility, magnetization and fourth order Binder cumulant using four different spatial volumes with $N_\tau =2$. The computation is carried out with gauge coupling, $\beta_g = 8$, for a range of scalar self-coupling, $\lambda = \{0.00010, 0.00350\}$, with emphasis near the critical end-point. Finite size scaling analysis of the gauge fixed condensate and its cumulants agree with the standard $3$d Ising values $\nu=0.62997$, $\beta/\nu=0.518$, $\gamma/\nu=1.964$ at $\lambda = 0.00150$. These results are in agreement with previous studies suggesting $3$d Ising universality class. The numerical results also indicate that, at the transition point, the gauge fixed condensate vanishes in the infinite volume limit.