Comments on: Matter v Antimatter II: Electroweak Baryogenesis

By: Lawrence B. Crowell

Lawrence B. Crowell — Sun, 03 Aug 2008 16:34:57 +0000

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

By: Count Iblis

Count Iblis — Sun, 03 Aug 2008 13:28:18 +0000

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…

By: Claire C Smith

Claire C Smith — Sat, 02 Aug 2008 22:52:04 +0000

Topic here,

VERy interesting…

Claire

By: Mark

Mark — Sat, 02 Aug 2008 13:49:58 +0000

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.

By: Lawrence B. Crowell

Lawrence B. Crowell — Sat, 02 Aug 2008 12:45:39 +0000

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

By: Mark

Mark — Sat, 02 Aug 2008 04:28:36 +0000

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

By: Lawrence B. Crowell

Lawrence B. Crowell — Fri, 01 Aug 2008 22:22:01 +0000

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

L. C.

By: Mark

Mark — Fri, 01 Aug 2008 22:08:20 +0000

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.

By: Lawrence B. Crowell

Lawrence B. Crowell — Fri, 01 Aug 2008 21:58:35 +0000

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~+~{\bar\nu}_\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

By: Mark

Mark — Fri, 01 Aug 2008 21:43:58 +0000

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.