# Is there an explanation for the 3:2:1 ratio between the electron, up and down quark electric charges?

I understand that the NNG formula relates $Q$, $I_3$, and $Y$ and can be derived in QCD; does this unambiguously predict the electric charge ratios without making assumptions about the definitions of isospin and hypercharge?

If so, this is unintuitive to me! Why does a particle carrying $SU(3)$ color charge care what charge it has under the totally separate electroweak $U(1)\times SU(2)~$ symmetries?

If not, is there a name for the "problem" of explaining the charge ratios?

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–  Qmechanic Mar 28 '12 at 13:41

There is a nontrivial relation between the electric charge and the strong business, namely that there are instantons which will cause proton decay. So it is not completely true that there are no relations--- the requirement of anomaly cancellation requires that the proton decay process conserve charge, and so relates the total charge on the proton to the total charge on the electron.

The U(1) numbers are completely crazy. The only sensible explanation is that they come from an SU(5) GUT (or SO(10) or E6 or some higher version of the SU(5) idea). The reduction of charges from SU(5) is explained in this answer: Is there a concise-but-thorough statement of the Standard Model?

This gives the 1,2,3,6 ratios of the hypercharge assignments in nature, and completely explains the crazy quark charges. It is also an automatic way of ensuring anomaly cancellation. This, and approximate coupling constant unification, are the two strongest bits of evidence for a GUT at a scale of $10^16$ GeV or thereabouts.

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First of all there are no crazy quark charges. This 1/3 is an unphysical scaling factor unknowingly having been introduced when declaring the electron charge the unit charge. This seemed to be reasonable, because no other charge show up in nature than integer multiples of the electron charge. The reason for this is that no free quarks exist in nature. They are bound in neutron and proton hadron quark trinities. It was only when the existence of quarks was realized that smaller electric charges were found to exist. Relative to the electron charge of -1 they are -1/3 (d) and +2/3 (u). The elctron charge of -1 can be written as -3/3. This shows that the scaling factor of 1/3 is unphysical. the true charges are: electron -3, down quark -1 and up quark +2. All are integer multiples of a unit charge of -1 carried by the d-quark. Defining it as +1 would have been more reasonable.

Now to your 3 2 1 question: The reason is an underlying logical struture, relating electrons and quarks of matter and antimatter. The electron and positron define a minimal frequency bandwidth of minimal energy between -3 an +3 that still allows the incertion of just two additional frequencies - mirrored for matter and antimatter - which do not descructively interfere. The mathematically uniquely possible positions are -1 and +2 (matter) and complementary at +1 and -2 (antimatter).

The logic is a unique solution to a combinatorial problem. It ensures a maximal irregularity in the electric charges of leptons and quarks.It does not only determine the possible number of fundamental particles - one lepton and two quarks (the neutrino is no lepton!) but also determines the frequency relations between these particles. The fascinating aspect of this logic is that it was discovered to exist metaphysically as a mathematical object.

All this will be described in detail in a book on demand,to be released this year

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You answer 1) necros a question that seems to have already found a satisfactory answer 2) quibbles about what the 'fundamental' charge is (if the answer depends on whether we write the electron charge as -1 or -3, then the theory has a problem) and then 3) launches into an insufficiently justified pseudo-mathematical 'explanation'. –  Kevin Driscoll Apr 13 at 21:16