### Electroweak Baryogenesis

In a recent post, I discussed the puzzle posed for cosmologists and particle physicists by the observation of the baryon asymmetry of the universe (BAU) - the fact that the universe is composed almost entirely of matter, with a negligible amount of antimatter. There was quite a bit of interest in this topic expressed in the comments for that post, and I thought it would be fun to go into a little more detail about one popular idea about how the BAU might be generated. Obviously, all my posts won't be as technical as this one, but it seemed like there would be some audience for such a description. If people are interested in even more (some might say excessive) detail, they could read this review article, or this one.

The precise question that concern us is; as the universe cooled from early times, at which one would expect equal amounts of matter and antimatter, to today, what processes, both particle physics and cosmological, were responsible for the generation of the BAU? In 1967, Andrei Sakharov established that any scenario for achieving this must satisfy the following three criteria;

At zero temperature, baryon number violating events are exponentially suppressed (this is most certainly a good thing, since we would like the protons making up our bodies to remain stable). However, at temperatures above or comparable to the critical temperature of the electroweak phase transition, B-violating vacuum transitions may occur frequently due to thermal activation.

Fermions in the electroweak theory are chirally coupled to the gauge fields. In terms of the discrete symmetries of the theory, these chiral couplings result in the electroweak theory being maximally C-violating.

However, the issue of CP-violation is more complex. CP is known not to be an exact symmetry of the weak interactions (this is observed experimentally in the neutral Kaon system). However, the relevant effects are parametrized by a dimensionless constant which is no larger than 10

The question of the order of the electroweak phase transition is central to electroweak baryogenesis. Since the equilibrium description of particle phenomena is extremely accurate at electroweak temperatures, baryogenesis cannot typically occur at such low scales without the aid of phase transitions. For a continuous transition, the associated departure from equilibrium is insufficient to lead to relevant baryon number production. For a first order transition, quantum tunneling occurs around a critical temperature, and nucleation of bubbles of the true vacuum in the sea of false begins. At a particular temperature below this, bubbles just large enough to grow nucleate. These are termed critical bubbles, and they expand, eventually filling all of space and completing the transition. As the bubble walls pass each point in space there is a significant departure from thermal equilibrium so that, if the phase transition is strongly enough first order, it is possible to satisfy the third Sakharov criterion.

There is a further criterion to be satisfied. As the wall passes a point in space, the Higgs fields evolve rapidly and both CP violation and the departure from equilibrium occur. Afterwards, the point is in the true vacuum, baryogenesis has ended, and baryon number violation is suppressed. Since baryogenesis is now over, it is imperative that baryon number violation be small enough at this temperature in the broken phase, otherwise any baryonic excess generated will be equilibrated to zero. Such an effect is known as washout of the asymmetry and the criterion for this not to happen translates into, among other things, a bound on the mass of the lightest Higgs particle in the theory. In the minimal standard model, current experimental bounds on the Higgs mass imply that this criterion is not satisfied. This is therefore a second reason to turn to extensions of the minimal model.

One important example of a theory beyond the standard model, in which these requirements can be met, is the MSSM. In addition, there are also light stops (the superpartners of the top quark) in the theory, which can help to achieve a strongly first order phase transition. For those of you who care about the numbers, according to recent calculations, baryogenesis is possible if the lightest Higgs particle has a mass less than 120 GeV, and the lightest stop has a mass less than the top quark mass.

What would it take to have confidence that electroweak baryogenesis within a particular SUSY model actually occurred? First, there are some general predictions: if the Higgs is found, the next test will come from the search for the lightest stop, and important supporting evidence will come from CP-violating effects which may be observable in experiments involving B-mesons.

However, to establish a complete model, what are really necessary are precision measurements of the spectrum, masses, couplings and branching ratios to compare with theoretical requirements for a sufficient BAU. Such a convincing case would require both the Large Hadron Collider (LHC) and, ultimately, the International Linear Collider (ILC), in order to establish that this is truly how nature works.

The precise question that concern us is; as the universe cooled from early times, at which one would expect equal amounts of matter and antimatter, to today, what processes, both particle physics and cosmological, were responsible for the generation of the BAU? In 1967, Andrei Sakharov established that any scenario for achieving this must satisfy the following three criteria;

- Violation of the baryon number (B) symmetry
- Violation of the discrete symmetries C (charge conjugation) and CP (the composition of parity and C)
- A departure from thermal equilibrium.

At zero temperature, baryon number violating events are exponentially suppressed (this is most certainly a good thing, since we would like the protons making up our bodies to remain stable). However, at temperatures above or comparable to the critical temperature of the electroweak phase transition, B-violating vacuum transitions may occur frequently due to thermal activation.

Fermions in the electroweak theory are chirally coupled to the gauge fields. In terms of the discrete symmetries of the theory, these chiral couplings result in the electroweak theory being maximally C-violating.

However, the issue of CP-violation is more complex. CP is known not to be an exact symmetry of the weak interactions (this is observed experimentally in the neutral Kaon system). However, the relevant effects are parametrized by a dimensionless constant which is no larger than 10

^{-20}. This appears to be much too small to account for the observed BAU and so it is usual to turn to extensions of the minimal theory. In particular the minimal supersymmetric standard model (MSSM).The question of the order of the electroweak phase transition is central to electroweak baryogenesis. Since the equilibrium description of particle phenomena is extremely accurate at electroweak temperatures, baryogenesis cannot typically occur at such low scales without the aid of phase transitions. For a continuous transition, the associated departure from equilibrium is insufficient to lead to relevant baryon number production. For a first order transition, quantum tunneling occurs around a critical temperature, and nucleation of bubbles of the true vacuum in the sea of false begins. At a particular temperature below this, bubbles just large enough to grow nucleate. These are termed critical bubbles, and they expand, eventually filling all of space and completing the transition. As the bubble walls pass each point in space there is a significant departure from thermal equilibrium so that, if the phase transition is strongly enough first order, it is possible to satisfy the third Sakharov criterion.

There is a further criterion to be satisfied. As the wall passes a point in space, the Higgs fields evolve rapidly and both CP violation and the departure from equilibrium occur. Afterwards, the point is in the true vacuum, baryogenesis has ended, and baryon number violation is suppressed. Since baryogenesis is now over, it is imperative that baryon number violation be small enough at this temperature in the broken phase, otherwise any baryonic excess generated will be equilibrated to zero. Such an effect is known as washout of the asymmetry and the criterion for this not to happen translates into, among other things, a bound on the mass of the lightest Higgs particle in the theory. In the minimal standard model, current experimental bounds on the Higgs mass imply that this criterion is not satisfied. This is therefore a second reason to turn to extensions of the minimal model.

One important example of a theory beyond the standard model, in which these requirements can be met, is the MSSM. In addition, there are also light stops (the superpartners of the top quark) in the theory, which can help to achieve a strongly first order phase transition. For those of you who care about the numbers, according to recent calculations, baryogenesis is possible if the lightest Higgs particle has a mass less than 120 GeV, and the lightest stop has a mass less than the top quark mass.

What would it take to have confidence that electroweak baryogenesis within a particular SUSY model actually occurred? First, there are some general predictions: if the Higgs is found, the next test will come from the search for the lightest stop, and important supporting evidence will come from CP-violating effects which may be observable in experiments involving B-mesons.

However, to establish a complete model, what are really necessary are precision measurements of the spectrum, masses, couplings and branching ratios to compare with theoretical requirements for a sufficient BAU. Such a convincing case would require both the Large Hadron Collider (LHC) and, ultimately, the International Linear Collider (ILC), in order to establish that this is truly how nature works.

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