New order parameter for the Higgs transition in SU(2) -Higgs theory

Abstract

We investigate the Higgs transition within the four-dimensional $SU(2)$-Higgs model in search for an order parameter as a function of the Higgs field hopping parameter, $\ensuremath{\kappa}$, 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 ${N}_{\ensuremath{\tau}}=2$. The computation is carried out with gauge coupling, ${\ensuremath{\beta}}_{g}=8$, for a range of scalar self-coupling, $\ensuremath{\lambda}={0.00010,0.00350}$, with an emphasis near the critical end point. Finite size scaling analysis of the gauge fixed condensate and its cumulants agree with the standard 3D Ising values $\ensuremath{\nu}=0.62997$, $\ensuremath{\beta}/\ensuremath{\nu}=0.518$, $\ensuremath{\gamma}/\ensuremath{\nu}=1.964$ at $\ensuremath{\lambda}=0.00150$. These results are in agreement with previous studies suggesting 3D Ising universality class. The numerical results also indicate that, at the transition point, the gauge fixed condensate vanishes in the infinite volume limit.