Why Are There No 3 Up Quark Nucleons?

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Discussion Overview

The discussion revolves around the question of why there are no nucleons composed of three up quarks (or three down quarks) with spin 1/2, despite the existence of Delta particles made from up and down quarks with spin 3/2. The scope includes theoretical considerations related to particle physics and quark composition.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • Some participants note that having three up quarks results in a totally symmetric isospin part of the wavefunction, which conflicts with Fermi statistics.
  • It is argued that to satisfy color charge requirements, the three quarks must be of different colors (red, green, blue), leading to a totally antisymmetric color part of the wavefunction.
  • Consequently, the spin part of the wavefunction must be totally symmetric, which necessitates a spin of 3/2.
  • One participant questions the possibility of a symmetric color wave function and proposes an alternative symmetric combination, prompting further clarification.
  • Another participant clarifies that hadrons must be colorless, which requires the quarks to form a singlet state under the SU(3) color group, thus necessitating a totally antisymmetric state.

Areas of Agreement / Disagreement

Participants generally agree on the constraints imposed by Fermi statistics and color charge requirements, but there is some debate regarding the implications of these constraints and the nature of the wavefunctions involved.

Contextual Notes

The discussion highlights the complexities of quark combinations and the requirements for color neutrality, but does not resolve the underlying assumptions about the nature of wavefunctions or the implications for particle existence.

Kurret
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There are four Delta particles made up of down and up quarks and having spin 3/2, but there are only two nucleons, the proton and the neutron. Why are there no particles made up of three up (or down) quarks and having spin 1/2??
 
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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.
 
Bill_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.
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 is

RGB+BRG+GBR-RBG-BGR-GRB

why can't we have

RGB+BRG+GBR+RBG+BGR+GRB ?
 
Thanks, The requirement is that a hadron must be colorless, which is a stronger condition than what I said. Not only must the colors of the three quarks be different, they must form a singlet under the SU(3) color group, which requires them to be in the totally antisymmetric state. The totally symmetric color state on the other hand belongs to the 10 representation of color SU(3), and is not invariant, i.e. not "colorless".
 
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