Broken electroweak phase at high temperature in the Littlest Higgs model with T-parity

TL;DR

This paper investigates the behavior of electroweak symmetry at high temperatures in the Littlest Higgs model, revealing that T-parity enables symmetry nonrestoration and a strong first-order phase transition, unlike the model without T-parity.

Contribution

It demonstrates that T-parity in the Littlest Higgs model allows for symmetry nonrestoration at high temperature, unlike the T-parity absent case, with implications for early universe baryogenesis.

Findings

Symmetry nonrestoration occurs only with T-parity.

The model with T-parity shows a strong first-order phase transition.

Without T-parity, the effective potential always increases with temperature.

Abstract

We have examined in detail the nonrestoration of symmetry at high temperature in a finite-temperature Littlest Higgs model, without and with T-parity, by evaluating the one-loop-order finite-temperature integrals of the effective potential numerically, without the high-temperature approximation, We observe that in the model without T-parity it is not possible to find a transition temperature within the allowed temperature range of the model (0<T<4f) if the UV completion factors are those which give the Standard Model electroweak minimum, as the effective potential always increases with temperature in the positive direction. However, in the case of the model with T-parity, it is possible to find a transition temperature with the same set of UV completion factors, as, with the increase of temperature, the effective potential decreases in magnitude in the positive side, becomes negative, and increases in magnitude in the negative side, indicating symmetry breaking at high temperature. This type of symmetry nonrestoration at high temperature has been observed earlier in some models involving pseudo Nambu-Goldstone bosons. The behaviour of the global structure of the effective potential with T-parity in the theory indicates a strong first order electroweak phase transition, conducive to baryogenesis in the early universe.