The discussion centers on the absence of nucleons composed of three up quarks or three down quarks, specifically addressing the implications of Fermi statistics and color charge in quantum chromodynamics. It is established that three up quarks create a totally symmetric isospin wavefunction, which conflicts with the requirement for a totally antisymmetric color wavefunction necessary for color neutrality. This leads to the conclusion that such configurations cannot exist as they would necessitate a spin of 3/2, violating Fermi-Dirac statistics for fermions. The requirement for hadrons to be colorless mandates that quarks must be in a totally antisymmetric state under the SU(3) color group.
PREREQUISITESThis discussion is beneficial for particle physicists, theoretical physicists, and students studying quantum mechanics and quantum field theory, particularly those interested in the behavior of quarks and the fundamental forces governing particle interactions.
okey I see. This might be a really stupid question to you, but why can't we have a symmetric color wave function? The antisymmetric one isBill_K said:Can't satisfy the Fermi statistics. (1) Three up quarks means the isospin part of the wavefunction is totally symmetric. (2) Must have three different colors red, green, blue, so the color part is totally antisymmetric. Conclusion: the spin part (3) must be totally symmetric. That requires it to be spin 3/2.