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Since quarks always form bound states, how do we know the spin of a single quark is $\frac{1}{2}$ experimentally?

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That quarks have spin $\frac{1}{2}$ is inferred from the structure of the hadron families (octets of mesons and spin $\frac{1}{2}$ baryons, decouplets of spin $\frac{3}{2}$ baryons). If the quark spin were different the families of hadrons would be structured differently (here is a link that describes this in detail: eightfold way). BTW the quark color is inferred from the fact that three quarks can fit in the lowest bound state to form the lowest mass hadrons. So experimentally the individual quark color and spin cannot be measured, but theoretically these assignments are justified.

When the quark model was first proposed by Gell-Mann (1962) it was viewed as nothing more than a mathematical curiosity (even by Gell-Mann himself). Gell-Mann was interested in categorizing the recently discovered mesons and baryons into families. He sought to describe these hadrons as composite particles made up of more fundamental entities and inquired about the properties the fundamental entities must possess. He found that by assuming three quark flavors (up, down, strange) all with spin $\frac{1}{2}$, with fracional charges of $\frac{1}{3}$ and $\frac{2}{3}$ the known baryons could be described as bound states of these three quarks and the known mesons could all be described as quark-antiquark bound states. For the baryons of spin $\frac{3}{2}$ he noticed an entry in the decouplet with strangeness 3 and charge -1 that did not exist in the experimental data. When such a particle was discovered ($\Omega^-$) in 1964 the quark model began to transcend its original descriptive motivation; however, it was not until the early 1970s when high energy scattering of electrons off protons showed evidence of point-like constituents within the proton that the reality of quarks became fully accepted.

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  • $\begingroup$ Am I right to say that the observation of eight hadrons in an octet can tell people that quarks have half spin? Can you explain the details somehow? $\endgroup$ – taper May 6 '18 at 13:54
  • $\begingroup$ You are correct. I'm not able to give the details at the moment, but I will edit my answer later. $\endgroup$ – Lewis Miller May 6 '18 at 14:16

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