I was wondering if there was a relation between the fractional coefficients $$2/3, 1/3$$ obtained when calculating color potential for quarks and the value of electric charge for the up and down quark. Is there a reason these numbers are the same or is it just a coincidence?
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What do you mean by the "color potential for quarks"? QCD has many expansions and approximations. – Mitchell Porter Oct 21 '18 at 00:34
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Does it involve Casimir operators? Please provide a reference or tell us exactly what potential you mean. – Mitchell Porter Oct 21 '18 at 02:39
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Possible duplicate of Why do electron and proton have the same but opposite electric charge? – Stéphane Rollandin Oct 21 '18 at 20:12
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2Possible duplicate of Is it a coincidence that quarks have exactly -1/3 or 2/3 the electron's charge? – Oct 22 '18 at 12:15
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1Neither of those is a duplicate of this question. For one thing, it says absolutely nothing about electrons. – Mitchell Porter Oct 23 '18 at 05:12
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First, the Baryon number for quarks, that you refer to, as color potential, is 1/3 for quarks. it is because all Baryons are made up of three quarks.
Now the electric charge of the quarks can be 2/3 or -1/3. Why it is exactly one third (or two thirds) of the elementary charge of the electron, well that is more complicated. But the proton and the neutron have integer e charges, so since they are made up of three quarks, the constituting quarks must have electric charge of one or two thirds of the electron's elementary charge.
You are asking for a reason why it is so. Otherwise we would not have stable atoms. You are asking but why were the electron made so that quarks have exactly 1/3 or 2/3 the electron's electric charge. Two independent elementary particles, the electron, and the quark(s) have exactly a relation on their electric charge of -1/3 or 2/3. If this was not so, we would not have stable atoms. All the experimental data fits the math that Baryons consist of three valence quarks, and that quarks can have either 2/3 or -1/3 the electron's charge.
But for your question, let's assume that this was not so. Let's assume that the quarks could have 3/4 or -1/4 the electron's charge. Would it be possible in this case to have a Baryon made up of four quarks? So that the Baryon would have again an integer charge, just like the electron. This way we could build stable atoms again. I do not think anybody knows exactly why quarks have 2/3 or -1/3 the electron's charge, maybe Baryons automatically adopted to the electron's charge, and quarks teamed up in teams of three. But all the experimental data suggests that this is how Baryons are made.
Árpád Szendrei
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