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How quarks electric charge directly have been measured when quarks never directly observed in isolation? (Due to a phenomenon known as color confinement.)

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Well, in high-energy scattering, you sort of observe the quarks separately. More generally, QCD - the theory that describes the dynamics of quarks as well as the bound states of quarks - agrees with all the observations of the related processes we have done which would be highly unlikely if something were seriously wrong about QCD. This validated theory also implies particular charges of the quarks so they're indirectly validated by the experiments, too. –  Luboš Motl Apr 7 '13 at 17:46
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The cross-section for $$ e^+ + e^- \to q + \bar{q} $$ goes by the square of the quark charge (times the number of colors). Now, the quarks can not be observed in isolation because they hadronize.

However the cross-section for $$ e^+ + e^- \to \mu^+ + \mu^- $$ is identical except for going by the muon charge squared.

So, a measurement of $$ R = \frac{\sigma_{e^+ + e^- \to \text{hadrons}}}{\sigma_{e^+ + e^- \to \mu + \mu^-}} $$ is a measurement of $$ \frac{\text{# of colors} \times \sum_\text{accessible flavors} q^2_\text{flavor}}{q^2_\mu} = \frac{\text{# of colors} \times \sum_\text{accessible flavors} q^2_\text{flavor}}{1} \quad .$$

The accessible flavors depend on the center of mass energy, so it is possible to observe the increases as the energy rises past successive quark masses (times 2).

See for instance figure 8.3 of www.itp.phys.ethz.ch/education/hs10/ppp1/PPP1_8.pdf (PDF link I'm afraid)

The results are consistent with three colors and the usual charge assignments (up-like quarks are +2/3 and down-like quarks are -1/3) from the baryon spectrum.

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The history of the proposal of the quark model of hadrons is interesting.

The quark model was independently proposed by physicists Murray Gell-Mann and George Zweig in 1964. The proposal came shortly after Gell-Mann's 1961 formulation of a particle classification system known as the [Eightfold Way]—or, in more technical terms, SU(3) flavor symmetry. Physicist Yuval Ne'eman had independently developed a scheme similar to the Eightfold Way in the same year.

At the time of the quark theory's inception, the "particle zoo" included, amongst other particles, a multitude of hadrons. Gell-Mann and Zweig posited that they were not elementary particles, but were instead composed of combinations of quarks and antiquarks. Their model involved three flavors of quarks—up, down, and strange—to which they ascribed properties such as spin and electric charge. The initial reaction of the physics community to the proposal was mixed. There was particular contention about whether the quark was a physical entity or an abstraction used to explain concepts that were not properly understood at the time.

The story goes on, but it was the classification of the plethora of hadrons into representations of an SU(3) symmetry group that simplified the particle zoo. Identifying the vectors entering SU(3)_flavor as "quarks" became acceptable because of the symmetry. The charges of the quarks are defined from this symmetry, otherwise the "eightfold way" classification would not work.

In a sense then the measurement of the charges of the quarks comes from the various SU(3) representations of the composite hadrons:

octed decuplet

----------meson octet -------------------------------baryon decuplet

--------charge is on diagonal--------

The reality of the existence of quarks as particles ( not as convenient mathematical tools) came by probing the protons with high energies and studying the interaction products, which could be identified as quarks and gluon jets of QCD, the strong interaction. See also Lubos' comment to your question.

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