Proton Decay At The Highest Possible Energies

[ohwilleke]

Proton decay has not been observed and has been constrained to be extremely rare in ordinary low temperature situations, if it happens at all (the Standard Model says it doesn't happen at all, because there are no lighter decay products that would not violate conservation of baryon number).

But, we know that all of physical constants of the Standard Model change with energy scale, as a physical consequence of renormalization. So, could it be possible the protons decay at higher energies but not at lower ones, either in the Standard Model or with New Physics?

Following this train of thought further, however, it occurred to me that at some energy scale that is high enough, talking about a proton ceases to be meaningful, because you get quark-gluon plasma instead.

So, my question is, what do the physical constants of the Standard Model (which might be relevant to proton decay) look like at the energy scale just below the threshold of quark-gluon plasma, since this is the highest energy scale at which something which could be meaningfully called proton decay could occur? And, with these values, is proton decay prohibited in the Standard Model or under popular BSM theories?

Also, have we reproduced experimentally the energy scales at which protons cease to exist in favor of quark-gluon plasmas experimentally? Or, can this question be answered solely based upon theoretical calculations?

 

[mfb]

Also, have we reproduced experimentally the energy scales at which protons cease to exist in favor of quark-gluon plasmas experimentally?

We have produced quark-gluon plasmas.
Yes, clearly.

This energy scale is far away from anything where the baryon number violation might become relevant.

 

[mitchell porter]

mfb, ohwilleke isn't just talking about the creation of QGP in collisions; he seems to be arguing that proton decay should be impossible because it involves high-energy virtual processes, but at those energies (he says) "talking about a proton ceases to be meaningful, because you get quark-gluon plasma instead".

ohwilleke: first of all, proton decay involves quarks becoming non-quarks. So whether you mean GUT proton decay caused by superheavy leptoquark gauge bosons, or nonperturbative SM proton decay caused by sphaleron field configurations... analyzing the proton into a quark-gluon sea, doesn't do anything to make those processes impossible. You still have quarks in your physical picture, so those processes can still happen.

Second, the proton is a quark-gluon sea, not a quark-gluon plasma. I don't quite know how to contrast sea vs plasma in a first-principles way, but empirically, the DGLAP equations for the parton distribution functions are different when a QGP is formed (maybe mfb knows more).

 

[ohwilleke]

first of all, proton decay involves quarks becoming non-quarks. So whether you mean GUT proton decay caused by superheavy leptoquark gauge bosons, or nonperturbative SM proton decay caused by sphaleron field configurations... analyzing the proton into a quark-gluon sea, doesn't do anything to make those processes impossible. You still have quarks in your physical picture, so those processes can still happen.

The point I was getting at, which admittedly isn't a terribly deep one, is that proton decay involves quarks becoming non-quarks from protons. So, if proton decay is limited to processes that can only happen at QGP temperatures, it isn't really proton decay anymore. Instead, it is really QGP decay at that point, because the proton itself no longer exists. There might be baryon number violating processes that occur in a QGP at a high enough temperature, but those processes, by definition, can't be proton decay.

My thought was that it wouldn't be implausible that a proton on the verge is dissolving into QGP might have somewhat different properties than a "cold" proton and that the differences in those properties might shed light on the kind of BSM physics that might make proton decay possible at the highest possible energies at which a proton was still a proton.

Second, the proton is a quark-gluon sea, not a quark-gluon plasma. I don't quite know how to contrast sea vs plasma in a first-principles way, but empirically, the DGLAP equations for the parton distribution functions are different when a QGP is formed (maybe mfb knows more).

This is totally not what I was getting at or talking about. I was talking about QGP at which point a proton ceases to be a proton.

 

[mitchell porter]

if proton decay is limited to processes that can only happen at QGP temperatures

It's not. If proton decay is possible, then a single proton just sitting there in empty space will eventually decay.

 

[mfb]

The point I was getting at, which admittedly isn't a terribly deep one, is that proton decay involves quarks becoming non-quarks from protons. So, if proton decay is limited to processes that can only happen at QGP temperatures, it isn't really proton decay anymore. Instead, it is really QGP decay at that point, because the proton itself no longer exists. There might be baryon number violating processes that occur in a QGP at a high enough temperature, but those processes, by definition, can't be proton decay.

The d to u quark transition involves a virtual W boson, where W bosons have a mass of 80 GeV - it still occurs in decays of free neutrons at much lower energies.

Proton decays would look similar.