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)?

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.

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?

Regards,

Paul

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.

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!

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.

Thanks!

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?

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 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

$latex
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

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

L. C.

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

http://arxiv.org/PS_cache/hep-ph/pdf/9901/9901362v2.pdf

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

Topic here,

VERy interesting…

Claire

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