[Paper Review] Baryogenesis at the electroweak phase transition

Nicholas Petropoulos|ArXiv.org|Apr 29, 2003

Neutrino Physics Research3 citations

TL;DR

This paper investigates electroweak baryogenesis in the Standard Model, proposing that a first-order electroweak phase transition driven by a nontrivial effective potential at finite temperature can generate the observed baryon asymmetry. Using one-loop finite-temperature effective potential calculations, it finds that the transition is first-order only for specific Higgs and top quark masses, with the strength depending on these unknown parameters, thus identifying a critical window for baryogenesis in the minimal model.

ABSTRACT

A possible solution to the observed baryon asymmetry in the universe is described, based on the physics of the standard model of electroweak interactions. At temperatures high enough electroweak physics provides violation of baryon number, while C and CP symmetries are not exactly conserved, although in the context of the minimal electroweak model with one Higgs doublet the rate of CP violation is not sufficient enough to generate the observed asymmetry. The condition that the universe must be out of thermal equilibrium requires the electroweak phase transition (EWPT) to be first order. The dynamics of the phase transition in the minimal model is investigated through the effective potential, which is calculated at the one loop order. Finite temperature effects on the effective potential are treated numerically and within the high temperature approximation, which is found to be in good agreement with the exact calculation. At the one loop level the phase transition was found to be of the first order, while the strength of the transition depends on the unknown parameters of the theory which are the Higgs boson and top quark masses.

Motivation & Objective

• To assess whether the Standard Model of electroweak interactions can generate the observed baryon asymmetry in the universe.
• To determine whether the electroweak phase transition is first-order under finite-temperature conditions, a necessary condition for baryogenesis.
• To analyze the role of the finite-temperature effective potential in driving the phase transition and enabling baryon number violation.
• To evaluate the viability of electroweak baryogenesis in the minimal model with one Higgs doublet, given constraints on CP violation and thermal equilibrium.

Proposed method

• Calculates the finite-temperature effective potential at one-loop order using the path integral formalism and high-temperature expansion.
• Treats finite-temperature corrections to scalar, fermion, and gauge boson loops using thermal field theory techniques.
• Applies the high-temperature approximation to the effective potential and compares it with exact numerical results.
• Investigates the dynamics of the phase transition via bubble nucleation, requiring the transition to be first-order.
• Evaluates the baryon asymmetry generation via sphaleron processes during the transition, contingent on CP violation and out-of-equilibrium conditions.
• Uses the one-loop effective potential to determine the critical temperature and vacuum expectation value evolution during the transition.

Experimental results

Research questions

• RQ1 Can the Standard Model generate a sufficient baryon asymmetry via electroweak baryogenesis?
• RQ2 Is the electroweak phase transition in the minimal Standard Model first-order at finite temperature?
• RQ3 How do the Higgs and top quark masses influence the strength and order of the electroweak phase transition?
• RQ4 To what extent does the high-temperature approximation accurately describe the finite-temperature effective potential?
• RQ5 What are the implications of a first-order transition for bubble nucleation and baryon number violation?

Key findings

• The one-loop finite-temperature effective potential calculation shows that the electroweak phase transition in the minimal Standard Model is first-order under certain conditions.
• The strength of the phase transition depends critically on the unknown values of the Higgs and top quark masses, which determine the barrier height between vacua.
• The high-temperature approximation of the effective potential is found to be in good agreement with the exact numerical calculation.
• The transition is consistent with the necessary condition for baryogenesis—being out of thermal equilibrium—provided it is first-order.
• The paper confirms that the minimal Standard Model can, in principle, support electroweak baryogenesis, but only if the Higgs and top masses lie within a narrow window.
• The work highlights the importance of the phase transition dynamics and bubble nucleation for sustaining a net baryon asymmetry.