Matter v Antimatter II: Electroweak Baryogenesis

By Mark Trodden | July 29, 2008 7:35 am

In my last 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. In this post I’ll to go into a little more detail about one popular idea about how the BAU might be generated. Although I’ll be a little more technical here than usual, if people are interested in even more detail, they could read this review article, or this one.

The precise question that concerns 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.

In recent years, perhaps the most widely studied scenario for generating the BAU has been electroweak baryogenesis. In the standard electroweak theory baryon number is an exact global symmetry. However, baryon number is violated at the quantum level through nonperturbative processes – it is an anomalous symmetry. This feature is closely related to the nontrivial vacuum structure of the electroweak theory, as I explained here some time ago. 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 – the temperature at which the expectation value of the Higgs field becomes nonzero as the universe cools – 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.

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 still insufficient to lead to relevant baryon number production. However, for a first order transition, at a critical temperature the nucleation of bubbles of the true vacuum in the sea of false begins, and 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 thing that I find fascinating about the baryon asymmetry problem is that it alone is evidence, from cosmology, of physics beyond the standard model. An important example of such physics, in which these requirements can be met, is the Minimal Supersymmetric Standard Model (MSSM). In addition to allowing a light enough Higgs particle, this theory can also contain light stops (the superpartners of the top quark), which can help to achieve a strongly first order phase transition. For those of you who care about the numbers, according to relatively current 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 perhaps ultimately an International Linear Collider (ILC), in order to establish that this is truly how nature works.

We certainly wouldn’t build a collider just for the chance of illuminating the problem of the baryon asymmetry. But it is a wonderful thing that, along with probing the origin of electroweak symmetry breaking, mapping the fundamental symmetries of nature, and showing us what lies around the corner for particle physics, the imminent turn-on of the LHC may hold the key to some of the problems that our telescopes have revealed.

  • Yoo

    Would there always be the same excess of matter over antimatter at the critical temperature? Or is there some mechanism which forces the excess to converge around some fixed amount? I’m wondering how the entire universe seemed to have managed to result in similar excesses of matter over antimatter.

    Or am I wrong about the excesses being relatively uniform, and there’s only a randomly fluctuating excess across the universe, the only thing being constant is that only matter is left over (perhaps due to CP-asymmetry)?

  • Mark

    Hi Yoo. The excess needs to be remarkably uniform over the observable universe (and, presumably, significantly beyond this).

    When you ask about whether there is “some mechanism which forces the excess to converge around some fixed amount” – this is precisely what successful baryogenesis scenarios have to explain. The observed baryon asymmetry isn’t just rough and qualitative (more of one than the other); it is very precisely quantified (magnitude and sign), and baryogenesis must explain this.

    In the case of electroweak baryogenesis, it happens because the phase transition takes place at the same temperature and the bubble walls sweep through all of space before the transition is complete. Therefore, other than minute fluctuations at a level much below the measured asymmetry, the same number is obtained everywhere.

  • Sunny

    What are the chances that the Baryon asymmetry issue and the arrow of Time problem are related? I’d say there is 60% chance that the underlying mechanisms are either the same or are very closely related.

    What are the chances that the Baryon asymmetry issue and the Dark matter puzzles are related? I’d say about 10% probability that these two problems explained by the same physics.

    Look forward to reading rest of the articles.

  • Mark

    Hi Sunny. I’ve no idea how to assign a probability to this. Of course, at a rather basic level they are related because the universe needs to be out of equilibrium and evolving in order to have a chance of generating an asymmetry, but other than that I know of no other connection.

  • Paul Stankus

    Hi Mark —

    Expanding on Sunny’s question (#3), and roping in Sean’s favorite topic, I can suggest another potentially deep connection between baryon asymmetry and the arrow of time: a non-zero net density of a massive species is necessary to enable gravitational entropy creation. In a universe where there is no net density (or, if you prefer, no non-zero chemical potential) of a stable, massive species of particle then there will be no gravitational clumping or binding — no clusters, no galaxies, no stars, no black holes — since all particles will either be relativistic (and hence unbound), or relic massive particles which will meet their antiparticles as soon as they start to bind gravitationally. The evolution of such a radiation-dominated universe is (very close to) being reversible, and hence isentropic in a co-moving volume; effectively it has no real arrow of time.

    In our present universe, of course, the non-zero net density of baryons (and leptons) does allow for gravitational generation of entropy and all the associated, irreversible structure formation that gives this universe an arrow of time and makes it so interesting to observe. In that sense, a universe with a non-zero net density of a massive species has a much higher ultimate entropy than does a radiation-dominated universe of the same total energy. So there seems to be an important connection, though I can’t attach it to any particular property of baryons, leptons or electroweak fields specifically. What do you think?



  • Sili

    If the stop is lighter than the top why haven’t it been found yet? I mean, we have seen tops, right?

    Do I understand you correctly if I think that the asymmetry is fixed? In the sense that with the laws as we know them (and hypothesise them) we would always find an excess of matter as we know it? That is Matter is unique, and not just an accident of it being what we have? I guess it’s easier to explain what I mean by referring to aminoacids: all the naturally occuring AAs are L and not D, but this is in all likelihood just a frozen coïncidence – the first aminoacids to form replicators just happened to be L, but there’s nothing in Nature that hinders life from forming from D-AAs. (I know that life may well have originated in RNA-world, but then we have the same deal for D-sugars vs. L-sugars.)

  • Mark

    Sorry Paul, I don’t know how to construct an argument along these lines. The baryon asymmetry is a very specifically quantified number – it is certainly possible to ague that structure might not exist in the same way if there was a lot of matter and antimatter around, but I know of no way to connect the particular observed asymmetry to an argument like this.

    Sili – the asymmetry is observed to be a fixed number through observations of the abundances of the lightest elements and through the details of the peaks in the CMB power spectrum. The issue isn’t that we have matter and not anti-matter, but the actual amount that we can measure. The challenge is to explain from the laws of physics (and, particularly, those waiting to be discovered, since the standard model can’t do the job), how this happened.

  • stas

    Hi Mark,
    Could you explain why the lightest stop has to be so light? Would it still be possible to find a mechanism to generate BAU if all the scalars turn out to be heavy like in split SUSY?

  • Sam Cox

    Mark noted that…

    “One thing I find fascinating about the baryon asymmetry problem is that it alone is evidence, from cosmology, of physics beyond the standard model”.

    This statement, it seems to me is conceptually very profound.

    I have really enjoyed reading your detailed discussion of this topic and its ramifications!

  • Mark

    stas. For electroweak baryogenesis, when one calculates the finite temperature effective potential, it is the presence of light scalars that makes the barrier between the false and true vacuum higher, thus making the phase transition more strongly first order and allowing a large departure from equilibrium and little washout. In the MSSM, the lightest Higgs and the lightest right handed stop turn out to be the light scalars that play this role.

    If all the light scalars are heavy, as in split SUSY, then I don’t think conventional electroweak baryogenesis can work. There are, however, many other ways to generate the asymmetry in that case – leptogenesis, Affleck-Dine baryogenesis, GUT baryogenesis, baryogenesis through preheating, defect-mediated baryogenesis, … I may get to discuss some of these in the future.

    Sam – thanks.

  • Matt

    This is an unrelated question, but I can’t seem to find the answer anywhere. I was hoping you could help clear it up.

    There’s a familiar theorem that unbroken global SUSY requires a vanishing vacuum energy, going along the lines of:

    Q|0>=0 together with [Q,Q*]=H and positive-definiteness of the Hilbert space implies =0.

    Where does this theorem break down to allow theories with unbroken *local* SUSY to have negative vacuum energy, giving rise to AdS space, but not positive vacuum energy, as in dS space? Is the loophole that the SUSY algebra itself is modified in the case of curved spacetime, or is the loophole that in any covariantly quantized gauge for local SUSY, the Hilbert space contains negative-norm states (such as for certain polarizations of the gravitino) that violate the assumption of positive-definiteness? And why does negative vacuum energy make it through the loophole but not positive vacuum energy?

    Most arguments on these issues that I’ve found involve looking directly at the scalar part of the superpotential of supergravity theories, and are thus somewhat less than enlightening, because they don’t explain where is the loophole in the theorem above.


  • Matt

    That “=0” should read “expectation value of H in |0> is zero”.

  • Matt

    Another part to my question: The existence of unbroken supersymmetry in a maximally symmetric supergravity solution, from what I understand, requires that the gravitino and all tensor fields vanish, and that the supersymmetry variation of the gravitino must also vanish. Being that the supersymmetry variation of the gravitino is the covariant derivative of the local spinor parameterizing the supersymmetry transformation, this would seem to always imply that the condition for supersymmetry is that there must exist a covariantly constant spinor field.

    But then you take the commutator of two covariant derivatives acting on this spinor field and get a relation involving the Riemann tensor. If you continue to assume maximal symmetry for the spacetime, then this would seem to imply that only Minkowski space is allowed, not AdS or dS, since they have nonvanishing Ricci scalar. Where’s the loophole to this that allows AdS space, but not dS?

  • http://deleted Simon DeDeo

    Hello Mark! Just stopping by. The Baryon Asymmetry is, I totally agree, a very deep deep thing and, I agree again, the best evidence we have for non-SM physics. Inflation doesn’t even come close.

    So I ask myself why isn’t is a bigger thing for people to work on in departments (like mine was as a grad student) where grad students are all like “oh man I am going to do this thing on inflation, it’s going to be deep.” What’s odd is that except for a few “Physics Today”-level articles, I have very little folk understanding of the issues whereas I’m pretty good at this point of judging the side-effects and observables of a random inflation model.

    Perhaps there’s a need for yet another BA review paper? It almost seems to me that if the problem were slightly rephrased, or somehow repictured, it could capture the energy of a much wider community (perhaps a bit like how many parts of inflation, e.g., the extent to which it’s a phase transition, or how it’s vital to solve GUT defect problems, were dumped and in the end — for better or for worse, ask Sean — “chaotic” inflation and slow-roll came to the fore.)

    Anyway, I’m curious to hear what you think (you can also drop me a line if you like.)

  • Dr. Pablito

    I happened to browse by because I was looking for material on the web. I’m writing a lecture about permanent electric dipole moments, which as everyone knows, are a probe of CP (well, PT) violation, and have a lot to say about Beyond Std. Model physics and the baryogenesis problem. And I get testy when people speak about LHC as having a lock on searches for BSM physics. And your next-to-last paragraph emphasizes the significance of LHC or ILC type searches, while ignoring to mention input from low-energy, high precision tests. Wouldn’t want your readers to miss out on the low-energy fun.

  • Mark

    Who says they’re going to miss out – I have a lot of time to post. I actually agree with the spirit of your comment, but if electroweak baryogenesis (which this particular post was about) is correct in some extension of the standard model, then colliders will be more critical to confirming the main structure than anything else, although I certainly agree other types of measurements may have an important role to play.

    I don’t think one can read my post as saying that LHC/ILC have a lock on searches for BSM physics.

  • Lawrence B. Crowell

    Mark wrote: However, baryon number is violated at the quantum level through nonperturbative processes – it is an anomalous symmetry.

    By this I presume you mean that the vacuum state does not have the symmetry of the Lagrangian. If I infer what you are saying correctly then the probability for a process such as

    B~=~(b,~{bar u})~rightarrow~W~rightarrow~tau~+~{barnu}_tau

    will deviate from a standard prediction, as will other lepton generating B decays.

    It would be interesting if this data can be teased out of the LHC, which is not primarily a “B-machine.”

    Lawrence B. Crowell

  • Mark

    That isn’t what I meant Lawrence. That type of breaking is what is meant by a symmetry being spontaneously broken. Anomalies are different and nonperturbative. Anomalous symmetries (must be global) are exact classically and at the perturbative quantum level. As a result there will be no processes at collider experiments due to them.

  • Lawrence B. Crowell

    Ok, so this symmetry breaking is the standard Higgsian “phi 2 the 4th” type of thing.

    L. C.

  • Mark

    No – it isn’t! That type of breaking is spontaneous symmetry breaking – not anomalous breaking.

  • Lawrence B. Crowell

    It looks as if I have never familiarized myself with this idea. I started to look at your paper

    It looks at first blush that the BAU is due to a cocycle with the Chern-Simon Lagrangian. Though I might be writing out of line right now. The CS is # is not gauge invariant but under the boundary operator or a change it is. I presume this is what you mean in the nonperturbative analogy CV page about losing potential energy information with the simple HO

    Lawrence B. Crowell

  • Mark

    It’d take a lot more space to explain anomalies fully Lawrence. I’d recommend picking up the second half of a quantum field theory text (one usually talks about anomalies in an advanced QFT course. My review article just covers some basic details of the one in the standard model, and not in any real detail.

  • Claire C Smith

    Topic here,

    VERy interesting…


  • Count Iblis

    Lawrence, I’m sure you know this. Just think about conformal field theories with some central charge. The central charge would be zero in a classical theory…

  • Lawrence B. Crowell

    Since this is tied to QFT anomalies this then appears to be due to a classical symmetry of the Lagrangian which does not show up in the quantization. This BAU anomaly breaking appears similar to Witten’s anomaly as well. The CS Lagrangian defines some cocycle which under the co-boundary map gives a cyclic group, or similar structure, between the 3-chain (cycle) and the 4-manifold (chain?) of the standard gauge Lagrangian. As Iblis says, the central charge of CFT is zero in the classical case, but not in quantization. So this is beginning to come to some light. So I presume that the cyclic group, or homotopy on the 3-sphere persists for N-large or for classical recovery.

    I need to read the Riotto-Trodden paper to get more of the details and how this plays out in baryogenesis.

    Lawrence B. Crowell


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About Mark Trodden

Mark Trodden holds the Fay R. and Eugene L. Langberg Endowed Chair in Physics and is co-director of the Center for Particle Cosmology at the University of Pennsylvania. He is a theoretical physicist working on particle physics and gravity— in particular on the roles they play in the evolution and structure of the universe. When asked for a short phrase to describe his research area, he says he is a particle cosmologist.


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