Critical Higgs Mass Research Articles

The Ising model universality of the electroweak theory

Lattice simulations have shown that the first order electroweak phase transition turns into a regular cross-over at a critical Higgs mass m H,c . We have developed a method which enables us to make a detailed investigation of the critical properties of the electroweak theory at m H,c . We find that the transition falls into the 3d Ising universality class. The continuum limit extrapolation of the critical Higgs mass is m H,c = 72(2) GeV, which implies that there is no electroweak phase transition in the Standard Model.

Embedded topological defects in hot electroweak theory: a lattice study

We study the properties of Nambu monopoles and Z-vortices in the 3 D lattice SU(2) Higgs theory which represents the Standard Model at high temperature. We show that the densities of the Nambu monopoles and the Z-vortices are O(1) in the symmetric phase and generically small in the Higgs phase. Near to the critical Higgs mass and in the vicinity of the phase transition the densities are no more negligible in the broken phase. The percolation probability of the Z-vortex lines is found as a new disorder parameter for this phase transition. We conclude that the transition to the symmetric phase is accompanied by Z-vortex condensation. Simulations comparing elementary and extended vortices and monopoles at different β G values, aiming to show that the density of vortices and monopoles of fixed physical size might have a well-defined continuum limit, gives encouraging but so far inconclusive results.

The endpoint of the electroweak phase transition

The 3 d SU(2)-Higgs model is used to find the critical Higgs mass above which the first order phase transition ends. One method is focused on the disappearance of the two-state signal of the scalar condensate (vanishing of the latent heat). Another method is based on the analysis of Lee-Yang zeroes of the partition function which allows to characterise the change from first order transition into an analytical crossover.

Critical Higgs mass and temperature dependence of gauge Boson masses in the SU(2) gauge-higgs model

We study the effective 3-D SU(2) Gauge-Higgs model at finite temperature for Higgs-masses in the range from 60 GeV up to 100 GeV. The first order electroweak phase transition weakens with increasing Higgs-mass and terminates at a critical end-point. For Higgs-mass values larger than about m H,c = 75.4(6) GeV the thermodynamic signature of the transition is described by a crossover. Close to this Higgs-mass value we investigate the vector boson propagator in Landau gauge. The calculated W-boson screening masses are compared with predictions based on gap equations.

Phase structure and phase transition of the SU(2) Higgs model in three dimensions

We derive a set of gauge independent gap equations for Higgs boson and vector boson masses for the SU(2) Higgs model in three dimensions. The solutions can be associated with the Higgs phase and the symmetric phase, respectively. In the Higgs phase the calculated masses are in agreement with results from perturbation theory. In the symmetric phase a non-perturbative vector boson mass is generated by the non-abelian gauge interactions, whose value is rather independent of the scalar self-coupling λ. For small values of λ the phase transition is first-order. Its strength decreases with increasing λ, and at a critical value λ c the first-order transition changes to a crossover. Based on a perturbative matching the three-dimensional theory is related to the four-dimensional theory at high temperatures. The critical Higgs mass m H c , corresponding to the critical coupling λ c , is estimated to be below 100 GeV. The “symmetric phase” of the theory can be interpreted as a Higgs phase whose parameters are determined non-perturbatively. The obtained Higgs boson and vector boson masses are compared with recent results from lattice Monte Carlo simulations.

Electroweak baryon number violation at finite temperature

We consider baryon and lepton number violating processes in the electroweak theory induced by gauge and Higgs fields passing the sphaleron solution at finite temperature. We show that for temperatures larger than 19 GeV the anomalous baryon and lepton number violating processes are suppressed by the Boltzmann factor exp (−βE sp), whereE sp is the sphaleron energy, rather than by the instanton tunneling factor exp (−8π2/g 2). We caculate the rate of baryon and lepton number violating processes at finite temperature and determine the freezing temperature of the anomalous processes in the early universe as a function of the Higgs mass. We compare the freezing temperature with the critical temperature of the electroweak phase transition infered from the one-loop finite-temperature effective potential. We obtain a critical Higgs mass of the order of 100 GeV, slightly depending on the top mass and the magnitude of the pre-exponential factor in the rate of theB non-conservation, above which the anomalous processes are certainly in equilibrium after the electroweak phase transition. Assuming that the temperature-dependence of the sphaleron energy is given by that found from the one-loop finitetemperature effective potential, this critical Higgs mass is lowered to a value of the order of 50 GeV.

Tree-level unitarity violation for large Higgs mass in a supersymmetric extension of the standard model

In a minimal supersymmetric extension of the standard model we calculate the critical Higgs mass for violation of tree-level unitarity in scattering processes involving intermediate vector bosons and Higgs and their supersymmetric partners. We also calculate the critical energy for violation of tree-level unitary in the limit of very large Higgs mass. We find, within this minimal model, that both bosonic and fermionic processes in certain definite channels simultaneously violate, at large s, tree-level unitarity beyond a critical value of the Higgs mass of the order of 770 GeV, rather lower than the corresponding critical mass, 1 TeV, for which violation is expected in the standard model. Also, when taking the large Higgs mass limit and going to large s, we find that tree-level unitarity gets violated at a critical energy s c of the order of 1 TeV, again lower than the corresponding value for the standard model (∼1.7 TeV).

Critical Higgs mass for the (2 + 1) dimensional Georgi-Glashow model

The ground state of a (2+1) dimensional Georgi-Glashow model is discussed in a dilute monopole gas approximation. In addition to the Coulomb interaction of the latter, we include a Higgs force which is attractive irrespective of the sign of monopole charges. For (Higgs masses) −1 comparable to the mean free distance of monopoles we find a phase transition which is presumably of first order. Strings of monopoles dominate the clustering behaviour near the critical Higgs mass.