# The weak SU(2) instanton proposed by Belavin Polyakov Schwarz and Tyupkin

## Main Question or Discussion Point

I ran accross the following passage in the Wikipedia article on mass-energy equivalence:

Since most of the mass of ordinary objects resides in protons and neutrons, in order to convert all ordinary matter to useful energy, the protons and neutrons must be converted to lighter particles. In the standard model of particle physics, the number of protons plus neutrons is nearly exactly conserved. Still, Gerard 't Hooft showed that there is a process which will convert protons and neutrons to antielectrons and neutrinos. This is the weak SU(2) instanton proposed by Belavin Polyakov Schwarz and Tyupkin. This process, can in principle convert all the mass of matter into neutrinos and usable energy, but it is normally extraordinarily slow. Later it became clear that this process will happen at a fast rate at very high temperatures, since then instanton-like configurations will be copiously produced from thermal fluctuations. The temperature required is so high that it would only have been reached shortly after the big bang.
This level of physics is way over my head, but I'm wondering: "What happens to the quarks that comprise the protons and neutrons?" Are they conserved in the neutrinos and antielectrons?

Chris

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Ben Niehoff
Gold Member
LOL, what? You don't need instantons. Just the weak force will do. The W and Z bosons couple to quarks, leptons, and neutrinos, allowing those three to be interconverted.

Instantons are something else entirely...a useful tool for calculating the path integral of a gauge theory in the saddle point approximation.

LOL, what? You don't need instantons. Just the weak force will do. The W and Z bosons couple to quarks, leptons, and neutrinos, allowing those three to be interconverted.
It's not that simple. You cannot annihilate the quarks in protons and neutrons into leptons, since none of them are anti-quarks. The Standard Model conserves total lepton number.

...except for some business to do with chiral anomalies, which is connected back to instantons, which I understand to be indeed important for baryogenesis.

So now my question is:"Is the process described in the Wikipedia article accepted (theoretical) physics?" It seems that it's not well known to kuros and Ben Niehoff (thanks for your replies).

I'm wondering if this process, if it's real, might be one possible fate for matter subjected to the extreme conditions at (or immediately before) the point of a black hole singularity.

Chris

So now my question is:"Is the process described in the Wikipedia article accepted (theoretical) physics?" It seems that it's not well known to kuros and Ben Niehoff (thanks for your replies).
I believe it is well known to those who study baryogenesis. I am not one of these people, however. What I am saying is that I am inclined to believe wikipedia on this one :p.

And to comment on your initial question ("What happens to the quarks that comprise the protons and neutrons? Are they conserved in the neutrinos and antielectrons?"), no the quarks are certainly not 'conserved' in the lepton products, these are all fundamental particles; leptons cannot 'contain' quarks. So this process indeed violates conservation rules as they are understood in the Standard Model (baryon/lepton number conservation), however these are perturbative rules, that only apply to evaluating Feynman diagrams and the like. Instantons are a non-perturbative phenomenon (so we cannot write down a feynman diagram for this process you are talking about), and so they have some room to violate these perturbative rules, but I don't know any more details than that.

Thanks, Kuros, for your reply. I'm clearly over my head on this so it won't serve any purpose for me to speculate any further. At this point I'll accept that the author of the Wikipedia article knows what he or she is talking about.

If anyone in Physics Forums is familiar with this process I would be interested in a layman's explanation of how it works (if that's possible). At this point it seems that under extreme conditions it has significance in baryogenesis and, possibly, in the reverse process as well.

Chris

I also would like a layman's explanation! It seems like dark magic to me at the moment.

tom.stoer

http://en.wikipedia.org/wiki/Sphaleron

The idea behind these sphalerons is that they induce baryon-number non-conservation. Think about a potential V(x) looking like a cosine V(x) = V cos(x); to every minimum you assign a 'quantum number' n counting the minima at xn = nπ (for n = ±1, ±3, ...).

A sphaleron induces something like a tunneling between vacua n → n' = n±2. This n of our simplified model is something like the baryon number.

Dark magic, indeed. From a layman's point of view this process certainly seems to be one of those quantum physics ideas that is "way out there". The description that comes closest to a layman's explanation that I can find is contained in a May, 1993 paper by Glennys R. Farrar and M. E. Shaposhnikov entitled "Baryon Asymmetry of the Universe in the Minimal Standard Model", which can be found here:
http://arxiv.org/pdf/hep-ph/9305274v1.pdf

The passage that I think summarizes the essence of the idea is found on page 5.

Once again, I wonder if this process is one possible fate of matter as it approaches a black hole singularity. Like most laymen, it is hard for me to imagine the "stuff" of 3 or 4 suns (let alone 3 or 4 million suns) squashed into a point. Somehow it seems more imaginable if all that stuff is in the form of energetic photons and antineutrinos.

Chris

... Somehow it seems more imaginable if all that stuff is in the form of energetic photons and antineutrinos...

Chris
The above excerpt from my previous post should have read "...energetic photons and neutrinos...". The energetic photons would be from both the process itself and from the annihilation of the antielectrons produced with the original electrons comprising the matter.

Chris