Proton electric dipole moment... what's that all about?
Be more specific. What is it that you don't understand? Have you tried looking for information about it? What wasn't clear from explanations elsewhere?
You can't really come in and ask such a broad question and expect a detailed explanation. We don't know your level of knowledge and ability to understand. And nobody is going to write a chapter of textbook just to explain something.
What is it? How is it? Why is it? How can it be said particle with elementary charge of +1e has one more plus charge and also one negative charge? Doe that mean there are all together three electric fields around proton, with their own center of origin? What shape is this magnetic dipole moment? What orientation? Wouldn't this dipole electric moment impact proton elementary charge, or is it maybe already accounted for when we say proton has charge of +1 e? Where this dipole comes from? How could we possibly know to be measuring proton elementary charge and not one of its dipole electric moments? Does electron too have electric dipole moment beside its elementary charge?
Proton's valence quarks have charges of +2/3, +2/3, and -1/3, for a total of +1. Furthermore, it has a bunch of quarks and anit-quarks besides these. The total charge is still +1, but there is enough going on in there to contribute to a total dipole. Neturon is also predicted to have an electric dipole, despite being neutral. The "why?" has to do with quantum field theory. I am not familiar with this particular computation, however.
You explain it as if elementary proton charge is net effect of three charged quarks, but they say there is elementary charge, and then there is also this dipole moment, given by some upper limit estimation. It is listed as separate property, like magnetic moment, so it doesn't sound as something that is already accounted for by proton elementary electric charge.
A molecular ion like NO+ also has one elementary charge and a dipole moment. So they are in principle independent.
Now there is a theorem that any vectorial quantity has to be proportional to the spin (=angular momentum in the rest frame).
Now the dipole moment transforms differently from the spin vector under e.g. parity.
In molecules, parity is broken within the Born-Oppenheimer approximation, so there is no problem to observe a dipole moment. However in a proton, an electric dipole moment can only be due to the small explicit breaking of parity. Hence observation of the electric dipole moment of the proton would allow to deduce the strength of that parity breaking effect. However, I think it has not yet been measured.
Not only parity, a nonzero electric dipole moment would break CP. The standard model predicts an extremely small effect, coming from the CP-violating part of the weak interaction. But actually it's experimentally much easier to look for the neutron's electric dipole moment. See this Wikipedia page.
...or equivalently T, which is maybe easier to visualize.
The only thing I really want to know right now is whether proton elementary charge and its dipole electric moment are two separate properties. Like, there is proton elementary charge +1e, and then there is ALSO this electric dipole moment with it own magnitude? Is it like that?
What do you mean with "two separate properties"?
A proton could have a non-zero dipole moment even with a net charge of 0 (see neutron), but it needs some charged components in it: quarks.
Let me try like this. Are both, proton elementary charge and proton dipole moment, direct consequence of the three quarks and their three electric fields? Indirect consequence would be anything less, like if it was due to quarks rotation rather than simply just position.
The total charge is a direct consequence of the three valence quarks.
It is not useful to try to model its field as sum of three electric fields from quarks - those are not stationary objects in a proton, and you have additional virtual quarks in a proton as well.
The dipole moment is a result of the quarks (both valence quarks and virtual quarks) and their interactions in quantum chromodynamics.
It is hard to measure a dipole moment, as the monopole moment (the total charge) dominates effects of the electric field.
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