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I have a basic question about pseudoscalar mesons wavefunction.

As I understand it, mesons are bosons so they have a total symmetric wavefunction under exchange of particles.

For pseudoscalar mesons, the spacial wavefunction is anti-symmetric because the parity is negative ($P=(-1)^{L+1}$ and $L=0$ ).

The spin wavefunction is antisymmetric because it's in the singlet state.

The Color wavefunction is symmetric for all mesons.

That leaves me with the flavor wavefunction - for the octet particles, the flavor seems anti-symmetric, and the total wave function is antisymmetric.

How is it possible ?

Diyanko Bhowmik
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Noam Chai
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  • You might be in confusion about the symmetry of the total wavefunction w.r.t. interchanges with other particles (your red herring 2nd paragraph) versus interchanges of constituents within this wf. Further be advised the η' is a flavor singlet, unlike the iso-, U- and V- triplets, actually flavor symmetric, you are considering in isolation. Any book on the quark model should clarify all symmetry issues for you. Identical to the equally malformed question. – Cosmas Zachos Apr 28 '17 at 13:24
  • O.k, I understand know the difference between changing particles or their constituents. From that counclusion, the total wave function must be anti-symmetric under exchange of two quarks because quarks are fermions. In the ground state, the spin wavefunction is anti-symmetric, the radial wavefunction of each quark is symmetric and the color is symmetric also. It means that the flavor wavefunction must be symmetric for exchange but it fits only the $\eta ' $ particle. Is something worng with this path of thinking? – Noam Chai Apr 28 '17 at 14:20
  • Or maybe i'm wrong about the flavor wavefuctions. In the literature the flavor wavefunction is written as $|u\bar{d}>$ but maybe it's a linear combination of both orders? – Noam Chai Apr 28 '17 at 14:33
  • Yes, you are confused about flavor. There is a minor sign wrinkle with antiquarks. Skip SU(3) and focus on isospin that you have spin experience with. The π+ so isotriplet you write is flavor symmetric. Lichtenberg, Kokkedee, etc... any book, not paper, on the subject should work. – Cosmas Zachos Apr 28 '17 at 16:17
  • This question 226493 might help with pseudoreality, a sub-question that I feel coming... – Cosmas Zachos Apr 28 '17 at 16:31

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the parity for the spacial part is not what your wrote. It is actually P=(−1)^L making it symmetrical. After that everything fits!

Angelos
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