# Fractionally charged Quarks

Just wondering what the evidence is for fractionally charged quarks, is it simply enough to say that as we see deep inelastic scattering of electrons (at high energies) off the nucleus of an atom (protons and neutrons) we must assume that there are three constituent components of protons/neutrons and must therefore be fractionally charged?

Is it just that because we see three constituent flavours of quark (and then assuming they are integer charge like the electron) that we couldn't add up three combinations to equal that of the neutron (i.e., 0). If it were integer spin we would always see +1 and -1 hadrons made from three quarks?

• maybe a distinct question for the spins ?
– user46925
Feb 10, 2016 at 13:07
• A proton is not made of 3 quarks. It consists. many hadrons and 3 valence quarks. Feb 10, 2016 at 14:40
• It you won't accept the group theoretical argument (as you tell anna v below) then the question is a duplicate of How quark electric charge directly have been measured?. Feb 10, 2016 at 14:42
• The original data that convinced the world of physicists that quarks were real were generated by two groups lead by Henry Kendall at MIT and Richard Taylor at Stanford. I was present in the Fall of 1973 when these results were revealed at an MIT seminar. The data showed that: 1) protons consisted of three point-like constituents, and 2) the charges of these constituents are fractional ($\frac{1}{3}, \frac{2}{3}$). Most physicists viewed quarks only as a mathematical classification scheme until then. I felt the hair on the back of my neck rise as these data were presented. Feb 10, 2016 at 16:03
• @LewisMiller Do you know the original source for the graph I exhibit in the question I linked? I'm trying to run down a proper citation and as my copy of Perkin's has walked out of my office I'm a bit lost. Feb 10, 2016 at 18:51

The quarks have fractional charge not only because of fitting proton and neutron constituents. There is a huge data base of hadronic resonances that gave rise to to the quark model , the standard SU(3)xSU(2)x(U(1) of particle physics.

The quantum numbers assigned to the quarks are important, among them the 1/3 and 2/3 charge and the color assignements. The representations of the resonances would not fit the model with different charges.

An example of the symmetries that led to the quark model" The S = 3⁄2 baryon decuplet

The Omega minus was one of the first predictions of the quark model, before it was found in Brookhaven bubble chamber data.

Why is the above decouplet structure ( and all the other representations in the link ) "evidence" for the fractional charge of quarks?

These structures are described by a group called SU(3) . This has a rigid representational structure, more complicated than a crystal which has simple symmetries. The fact that all the known hadronic resonances have a niche in one of these representations, allows to identify the constituents of the hadrons with the basic unit vectors of the SU(3) symmetry, as three "quarks".

The resonances in their niches have charges. In order for the charges to be consistent the quarks have to be identified with fractional charge , to add up to 1 and -1 and 0 ( integer numbers), and in addition, the complexity of the representations (each niche is accompanied by group constants) imposes the fractions to be either +/- 1/3 or +/-2/3 in order to fit the resonances in the appropriate niches with the correct charge. Otherwise the symmetry would break, the puzzle pieces would not fit.

The fact that the Omega minus was predicted and then was discovered, clinched the model, although the beautiful symmetries had already convinced most physicists at the time.

• I can't accept this answer as I would like experimental evidence to make up the model. Feb 10, 2016 at 13:13
• The plot above, and the ones in the link, are the results of a great number of experiments in the 1950's and 1960's. Did you read the link? Feb 10, 2016 at 13:18
• @garyp If you consider a plethora of experimental values from a plethora of experiments you must have a very strange idea about experimental evidence. The evidence is in the symmetries seen experimentally that are explained by the specific quark model SU(3)xSU(2)xU(1), and not another. Similar to crystal symmetries , that define the crystal. Feb 10, 2016 at 14:34
• @garyp Note that the group theoretical model anna presents here predicted the existence of the (then unknown) $\Omega^-$ (including its charge, spin, parity and approximate mass) which was then sought and found. Historically that a was a watershed moment for the quark model being taken seriously. Feb 10, 2016 at 15:05
• @dmckee It just seems to me that this answer is "the evidence for fractional charge is that it the theory that includes the existence of fractional charge correctly predicts experimental results". My interpretation of the OP's question is "what's that evidence". He probably accepts the fact that theory and experiment agree. It's probably too large a question for a small space, though. Feb 11, 2016 at 16:43

1) The spin of the proton and neutron is 1/2. The deep inelastic scattering (DIS) experiments in the seventies (and later) showed that the proton (neutron) is made of charged subparticles being also fermions, the quarks. The rule of the addition of angular momentum thus constrains the number of quarks (talking only about valence quarks) in the proton and the neutron to be an odd number. 1 is excluded since the proton/neutron would be elementary. The next one is 3.

2) Now the charge of the proton is 1 while the one of the neutron is 0. Isospin symmetry conservation in strong interaction (verified experimentally much before the 70s) suggested that neutron and proton must be made of the same kind of quarks. The charge constraint imposes at minima 2 kinds of quarks, that we call now u and d with respectively the charge 2/3 and -1/3.

3) In addition, DIS constrained the structure functions of the proton (and neutron). The analysis of these structure functions (obtained from the measurement of the cross-section of the scattering of an electron with the proton) confirmed that in the proton there are twice more u-quarks (of charge 2/3) that d-quark (of charge -1/3, but the sign doesn't matter since only the charges squared matter in the structure functions) an twice more d in the neutron than u-quark.

• It would be great to understand more "what the hell you SEE" in DIS experiments. WHAT tracks do you see? As I understand it, quarks are never seen. But something else happens, at a certain angle (or whatever) and this implies such-and-such. Feb 12, 2016 at 19:37
• @JoeBlow: what is measured is the differential scattering cross-section of $e+p$ as function of the scattered electron energy, its angle and the mass of decay product of the proton. If the proton was structureless, the cross section would drop very fast as function of the momentum transfer. The way it behaves gives indication of the proton substructure. In order to go further, I would need to develop the DIS formalism... Feb 12, 2016 at 19:45