B How Does Nucleon Shape Relate to Quark Number and Electric Quadrupole Moment?

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If a nucleon is let say made of 3 quarks then they rather build a triangle than a tetrahedron, so they are flat ? Why is there not 4 quarks ?
 
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They don't have any particular arrangement. They don't even have a well-defined position in a proton (except from "everywhere in the proton", if you prefer that view).

4 quarks cannot form a color-neutral hadron. Two quarks and two antiquarks can, you get short-living tetraquarks in that case.
 
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A proton and electron in a protium atom are on a line at any moment, except when the electron is at the cusp. But they do not have a preferred spatial direction at their ground state of 1s - over time, the electron can be in any direction. The He nucleus and two electrons are always on a flat triangle, but in their ground state (both 1s) do not have a preferred spatial orientation either.
 
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Do spin 1/2 baryons such as nucleons possesses electric quadrupole moment?
Do spin 3/2 baryons such as omega hyperon and delta resonances possesses electric quadrupole moment?
 
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I'm following this paper by Kitaev on SL(2,R) representations and I'm having a problem in the normalization of the continuous eigenfunctions (eqs. (67)-(70)), which satisfy \langle f_s | f_{s'} \rangle = \int_{0}^{1} \frac{2}{(1-u)^2} f_s(u)^* f_{s'}(u) \, du. \tag{67} The singular contribution of the integral arises at the endpoint u=1 of the integral, and in the limit u \to 1, the function f_s(u) takes on the form f_s(u) \approx a_s (1-u)^{1/2 + i s} + a_s^* (1-u)^{1/2 - i s}. \tag{70}...
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