# Why we never see a rational charge?

1. Nov 1, 2015

### SlowThinker

There is a question that has been puzzling me for quite a few years by now, since the moment I've heard that quarks have charge $-e/3$, $2e/3$ etc. There seem to be 2 independent answers to the title:
1. There is a Charge Censorship Principle, where you can never observe a charge $e/3$ and the like, only integer multiples of $e$.
2. Quantum chromodynamics, with 3 colors, 3 anticolors and the colorless principle, only mixes quarks into integer multiples of the electron's charge.

I'm not asking "how" (2) implies (1), but "if" that is indeed the case, or just a funny coincidence. I've never seen this mentioned in popular books, or the introductory courses that I have watched.

A supplementary question would be, are there any attempts to explain the quark behavior based on (1) rather than (2), or is QCD accepted by all serious physicists as the answer?

2. Nov 1, 2015

### vanhees71

QCD is very well accepted, and in a way it answers your question, because from lattice-QCD simulations it is clear that QCD shows confinement, i.e., observables are always color-neutral states, and the hadronic spectrum (i.e., the masses of all the hadrons listed in the particle data book and even predictions for some not (yet?) observed) comes out pretty well. Together with also the successes of perturbative QCD, showing asymptotic freedom, explaining Bjorken scaling and its breaking, etc. also very well, this makes physicists pretty confident about the correctness of QCD, at least on the energy scales available in today's acclerators (particularly the LHC with the so far highest available beam energies).

Another question is, why the charge pattern of the elementary particles, i.e., the quarks, leptons, the gauge bosons, and the Higgs boson(s), is as it is. On the first glance one would think, it's totally arbitrary and just taken from observations in nature, as all the observable parameters like coupling constants have to be taken from experiment. At the second glance there is a restriction, because the weak interaction is based on a socalled chiral local gauge symmetry, which must never ever be explicitly broken by anything in the formalism, and one danger with the particular gauge group of the electroweak part of the standard model is that it could be explicitly broken by a socalled anomaly.

A theory has a symmetry, if the equations of motion of the dynamical degrees of freedom, which are in this case all the fields, describing the elementary particles and their interactions, do not change their form when one does some non-trivial transformation. The electroweak standard model is constructed on the classical level such that it obeys this chiral local gauge symmetry, which means (loosely speaking) a symmetry under rotations of all the matter fields in a particular way, and these rotations can even depend on space and time variables. This is a pretty strong constraint on the theory, but it leaves also enough freedom to implement all the so far observed facts about the particles and their weak and electromagnetic interactions.

Now this classical field theory is not directly useful to describe high-energy collisions. Only the electromagnetic interaction has a very well-known classical limit, namely classical electrodynamics, which governs all our electronic devices around us. For the high-energy particle physics, however, one must use it as the starting point to build a quantum field theory. A quantum field theory is just the quantum theory of many particles, which are described as specific excitations of the quantum fields, that can also describe the creation and annihilation of particles, which is exactly what's happening in collisions at high (relativistic) energies. Now there's a mathematical recipe to make a classical field theory a quantum field theory, and you can derive the famous Feynman rules of perturbation theory from it, which tells you how to predict cross sections for scattering processes.

Now there's the danger that the symmetry, the classical field theory obeys by construction, gets lost in the quantization process. This is called an anomaly. If this happens to a local gauge symmetry, it's a desaster, because then the theory produces totally non-sensical results, where the probabilities for all possible scattering processes are not adding up to 1 as it should be, or they become even negative. So one has to avoid this desaster of anomalous breaking of the local gauge symmetry. The mathematics behind it, group theory, tells us, when such symmetries can occur. Some groups are anomaly safe to begin with. Unfortunately the electroweak gauge group is not such a nice one, but it can potentially be anomalously broken just by quantizing it. Another theorem, however, tells us, how to efficiently check, whether this desaster really occurs. One has to calculate only a specific set of one-loop diagrams. This calculation shows that one can perhaps avoid the anomaly by choosing the right pattern of charge values of particles, and amazingly, the charge pattern of the standard model is precisely such that the anomaly is cancelled! For me that's one of the most beautiful outcomes of theoretical physics! Indeed it happens that just because each flavor family has one lepton with a charge -e, its neutral neutrino (and the corresponding anti-particles) and two quarks, one with -1/3 e and one with 2/3 e charges coming in three "copies" (i.e., each quark carries also three color charges, which is the coupling of the strong force in the strong sector of the Standard Model, QCD) and the corresponding anti-quarks with the opposite charges and anti-colors. This charge pattern is such that the anomaly cancelled, and the Standard Model is thus free of anomalies of its fundamental local gauge symmetries. One should however say, that the particular charge pattern is not the only one that prevents the anomalous breaking of the electroweak theory. So there remains still the question, why nature has chosen the observed charge pattern of elementary particles and not just another one.

One should mention that sometimes anomalies are also good! E.g., in the Standard Model there are also accidental symmetries. The most important example is the approximate chiral symmetry of the light-quark sector of QCD. This allows one to build effective hadronic models, i.e., to describe hadrons, which are composite objects made of quarks and gluons, as elementary particles at low energies, and the residual strong interactions among the hadrons is ruled by this approximate chiral symmetry. On the other hand, chiral symmetry is also a problem, because it predicts the decay rate for the process $\pi^0 \rightarrow 2 \gamma$ (the decay of a neutral pion to two photons) way too low. However, the pion is a pseudoscalar particle, and there's a particular anomaly which leads to the correct value for this decay rate. Here, nothing is destroyed by the anomaly, because it violates a symmetry of the classical theory which is unimportant for the mathematical consistency and physical interpretabilty of the corresponding quantum theory.

3. Nov 1, 2015

### SlowThinker

I see why it's not discussed in the introductory texts
Yet I'm still not sure what the answer is. I understand I'd have to learn all the gory details of QCD to appreciate your previous and probably next answer, but is it possible to pick one of the 5 choices?
A) Charge Censorship Principle implies Colorless Principle
B) Colorless Principle implies Charge Censorship Principle
C) Both are implied by a greater principle (avoid infinities, make theory logically consistent, etc.)
D) It's a coincidence
E) Charge Censorship Principle does not always hold

From what I could understand from your answer, it looks like (A) or (C) is correct, but that's probably not what you meant?

4. Nov 1, 2015

### SlowThinker

Perhaps
C') They are two sides of one coin
?

5. Nov 1, 2015

### DennisN

Thanks for you description vanhees! I got a crash course in quark charges and anomaly cancellation three years ago in this thread (Empirical tests of quark charges, any info?), and now you have expanded my understanding more... thanks!

6. Nov 1, 2015

Staff Emeritus
The "Charge Censorship Principle" seems to be your own invention, and not part of mainstream physics.

7. Nov 1, 2015

### SlowThinker

Yes, I thought it's obvious that it's my shortcut for "the fact that we never see a rational charge". If there is an experiment showing the existence of a free 1/3 charge, that would answer my question.
I've read through DennisN's thread but while interesting, it does not really prove that QCD is the only possible explanation for what we observe.
So I just wanted a confirmation that QCD is the only possible, and complete, explanation for the fact that we never see a rational charge.

8. Nov 1, 2015

Staff Emeritus
It's not. Suppose there were a 100 TeV particle with charge +1/5 and another with charge -1/5. No reason that couldn't happen.

Last edited: Nov 2, 2015
9. Nov 5, 2015

### SlowThinker

Yes, I'm not quite happy with the "answer" I received, but clearly I'm not going to get any better around here.
So I decided to abandon the thread... for now.

10. Nov 5, 2015

### Mister T

I hope you didn't get "because we say so" out of those explanations. The real reason we don't see free particles with fractional charges isn't because someone said so. It's the same reason we don't see little green men on the moon. Maybe they're there but when we look for them we don't see them.

That's nature.

Your question, I think it seemed to everyone, is not a question about nature. It's about the models used by physicists to describe nature.

I think both are generalizations from observation. (1) is simply a statement, (2) is a fully-developed model. I would say that (1) follows from (2). It's certainly no coincidence because you were already aware that (2) predicts the idea embodied in (1) when you went through the process of creating (1).

11. Nov 5, 2015

### SlowThinker

Well, the thread linked by DennisN leads to some systems of equations where it is shown that the charges 2/3e and -1/3e satisfy them, but
- it's not clear if these are the only solutions,
- it seems the equations are derived from QCD, rather than directly from observation.
I admit my knowledge of QCD is pretty much non-existent, which is why I wasn't asking for a detailed answer. Clearly I'll have to have a look at it before I can ask the question again.

*I* certainly did not derive (1) from (2).
My original question can be rephrased as "What other things does QCD explain besides quark confinement and (1)?" Is there a computation of neutron's half-time of life? Or Tritium half-time of life? Of deuterium rest mass? Anything like that?

12. Nov 5, 2015

### Mister T

I don't know how one would derive an equation from an observation. Certainly not using the same meaning for "derive" that's used in the context of deriving an equation from a theory such as, for example, QCD.

Deriving an equation from a theory is a deductive process, inferring an equation from observations is an inductive process.

Tons and tons of other stuff. Like the way an atomic nucleus is structured and decays. Nuclear fusion and fission. The number of neutrinos emitted by the sun.

I really don't have much more than a layman's understanding of QCD, but my detailed knowledge of other areas of physics helps me see where it fits into the bigger picture.