Argument against quarks being composite particles?

[throneoo]

So during a particle physics lecture, the lecturer used Heisenberg's uncertainty principle to set a lower limit on the KE of the quarks bound in a proton (given the mass,size of proton and the mass of u/d quarks), which is of the order of 100 MeV, while the mass of quarks is about several MeV/c^2. Then, he said given the small size and low mass of quarks, it is "unnatural" for them to be composite particles, and continued to elaborate. I failed to listen to the whole explanation and all I heard was "as it would require a fine-tuned balance between kinetic energy and potential energy". I didn't get the chance to ask him again and now I don't exactly know what that last statement would mean.

So I started to ponder for hours what that has to do with composite particles. I know that a bound system of particles need to have negative total energy (KE+PE, at least in classical mechanics). Suppose quarks are indeed composed of smaller particles. As far as I can tell, given the small size of quarks, these particles would have even larger minimum KE than the quarks do (>100 Mev) and the PE has to be very negative to make the total energy scale back to several MeV. I still fail to appreciate why KE and PE have to be balanced. I mean, the system is bound as long as the net energy is negative isn't it?

 

[The_Duck]

The point is that the total mass of a composite system, such as a composite particle, is exactly the total energy of all its constituents, via $E = mc^2$. If quarks have constituents, those constituents must have kinetic energies of order $10^6$ MeV or greater (I'm actually not sure what the limits on quark size are). But the up and down quarks have masses of only 2-5 MeV or so. So there would have to be a negative potential energy almost-but-not-quite cancelling out the $10^6$ MeV worth of kinetic energy to get a total of only a few MeV.

For example, the quarks in the proton have kinetic energies of order a few hundred MeV, and the proton has a mass of 938 MeV, which is reasonable. It would be really weird if the proton had a mass of, say, 0.001 MeV despite being composed of quarks with energies of a few hundred MeV each. To get a total energy of 0.001 MeV would require a strange cancellation of these large kinetic energies with some counterbalancing negative energy.

 

[throneoo]

The point is that the total mass of a composite system, such as a composite particle, is exactly the total energy of all its constituents, via $E = mc^2$. If quarks have constituents, those constituents must have kinetic energies of order $10^6$ MeV or greater (I'm actually not sure what the limits on quark size are). But the up and down quarks have masses of only 2-5 MeV or so. So there would have to be a negative potential energy almost-but-not-quite cancelling out the $10^6$ MeV worth of kinetic energy to get a total of only a few MeV.

Now that you've mentioned the order of magnitude of the KE of those constituent particles I begin the realize just how "unnatural" it would be for the potential energy to 'almost' balance the KE. Thanks for the help.

 

[Vanadium 50]

I would not think about kinetic energy.

We know that the constituents must be heavier than several hundred GeV, and most likely at least a few TeV. Let's say they weight exactly 1 TeV each and there are two per quark. Since the u and d quarks weigh around 5 MeV, that means they need to be bound by exactly 1,999,995 MeV. That seems, um, unusual. That's the "fine tuning" problem.

But let's take a step back. Why do we want quarks to be composite? One answer is that maybe we can explain why there are generations in terms of excited states of these composite quarks - the u is the ground state, the c is the first excited state, and so on. The problem is that if you have a potential this deep, it looks like a delta function, and a delta function has exactly one bound state. So this idea doesn't work.

You have all the problems of this model, and now none of the advantages.

 

[arivero]

I believe to remember that 't Hooft concept of naturalness was developed when people was trying to address this problem of composites, late seventies and early eighties. Was not the idea to look for some way for quarks to appear as "fermionic goldstone particles" or something so?

 

[arivero]

But let's take a step back. Why do we want quarks to be composite? One answer is that maybe we can explain why there are generations in terms of excited states of these composite quarks - the u is the ground state, the c is the first excited state, and so on. The problem is that if you have a potential this deep, it looks like a delta function, and a delta function has exactly one bound state. So this idea doesn't work.

We could want excited states if we want a whole tower of generations. But with only three generations, a delta-like well with a finite number of states looks more as a bless. And if we have more than one preon, we can use some combinatorics too.

 

[Vanadium 50]

s, a delta-like well with a finite number of states looks more as a bless

It would if the finite number were three. But it's not.

Yes, you can move the "why three?" level to the preons. But this doesn't solve the problem so much as move it down a level.

 

[arivero]

It would if the finite number were three. But it's not.

Yes, you can move the "why three?" level to the preons. But this doesn't solve the problem so much as move it down a level.

Well, it adds some playground for equations and combinatorics. Of course even with a single delta-well we can add some degeneracy group -not a real problem if the mass mechanism is elsewhere-... and now I think about of it, I have never seen the Dirac equation in a dirac delta potential.

A case where having an extra level fixes the number of generations was the idea I developed time ago in the BSM subforum: to build the scalar partners of supersymmetry as a composite sector. One assumes that the quarks divide in two sets, labeled as "massless" and "massive", and only allows the "massless set" to be bound by a new force; then the condition of matching bosonic and fermionic degrees of freedom translates to conditions in the size of the "massless set" and in the number of generations. And still each bound state only contains one level, as in the dirac delta example. Without supersymmetry it is not so easy to find a way to impose conditions relating the composite and the preonic states; we have the anomaly matching conditions, but it does not seem enough.