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I don't understand something about the wave functions of mesons. In my notes it's said that (u,s,d) mesons are composed of pairs $|q\overline q\rangle$ so there are 9 possible states which break into an octet and a singlet. But then it's said that we can form a nonent of pseudoscalar mesons (spin=0) and a nonet of vecttor mesons (spin=1) , but how's that possible if the whole wave function $|\psi\rangle = |space\rangle|flavor\rangle|spin\rangle|color\rangle$ has to be symmetric? Shouldn't the symmetry of the wave function change since the spin wave function for spin 0/1 is antisymmetric/symmetric ? What is the symmetry of the flavor part of the meson wave function, for the 9 possible states ? Can someone please explain this without the group theory math...

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  • $\begingroup$ WP or the excellent textbook of Perkins illustrates how octets and the singlet mix, give the approximate nature of flavor SU(3), and how symmetries are satisfied. There are several allowable combinations of the variables you wrote down to satisfy the quark-antiquark symmetry constraints. $\endgroup$ – Cosmas Zachos Jul 13 '17 at 15:13
  • $\begingroup$ Related physics.stackexchange.com/questions/96046/… ? $\endgroup$ – SRS Aug 19 '17 at 4:57
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A meson wavefunction does not have to be symmetric or anti-symmetric under interchange of the $q$ and $\bar{q}$, because quarks and antiquarks are not identical particles.

You are probably thinking of baryons. Being composed of three quarks, their wavefunctions must be totally anti-symmetric.

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