The Lee-Wick Standard Model at Finite Temperature

TL;DR

This paper investigates the thermodynamics and electroweak phase transition in the Lee-Wick Standard Model at finite temperature, revealing a crossover transition similar to the Standard Model but with modified high-temperature behavior due to negative-norm states.

Contribution

It explores two approaches to formulating Lee-Wick theories at finite temperature and calculates the thermodynamic variables and effective potential within these frameworks.

Findings

Electroweak phase transition is a continuous crossover in the Lee-Wick Standard Model.

High-temperature behavior is altered by cancellations between negative- and positive-norm states.

The study provides a foundation for understanding finite-temperature effects in Lee-Wick theories.

Abstract

The Lee-Wick Standard Model at temperatures near electroweak scale is considered, with the aim of studying the electroweak phase transition. While Lee-Wick theories possess states of negative norm, they are not pathological but instead are treated by imposing particular boundary conditions and using particular integration contours in the calculation of S-matrix elements. It is not immediately clear how to extend this prescription to formulate the theory at finite temperature; we explore two different pictures of finite-temperature LW theories, and calculate the thermodynamic variables and the (one-loop) thermal effective potential. We apply these results to study the Lee-Wick Standard Model and find that the electroweak phase transition is a continuous crossover, much like in the Standard Model. However, the high-temperature behavior is modified due to cancellations between thermal corrections arising from the negative- and positive-norm states.