What Part of the Wavefn Ensures Symmetry for Rho^0 and Pi^0 Bosons?

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SUMMARY

The discussion centers on the symmetry requirements of the wave function for Rho^0 and Pi^0 bosons, which are both required to have an overall symmetric wave function due to their bosonic nature. The Pi^0 is in an anti-symmetric S=0 state, while the Rho^0 is in a symmetric S=1 state. The key distinction lies in the quark composition of the mesons; since the quarks (and antiquarks) are distinguishable, their combination does not necessitate symmetry. This clarification resolves the confusion regarding the symmetry requirements of multi-boson wave functions versus the wave functions of quarks within a single meson.

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Both Rho^0 and Pi^0 are bosons so require an overall symmetric wavefn. However, they are in different spin states: the Pi is in the anti-symmetric S=0 state and the Rho is in one of the symmetric S=1 states.

Which other part of the overall wavefn (color, flavor, spatial) differs between the two such that their wavefn's have the required symmetry? As far as I know they should be identical in all other respects!
 
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The wave function of a state with *several* identical bosons must be symmetric under exchanging those bosons. It sounds like you are mixing up this multi-boson wave function with the wave function of the quark and antiquark inside a single meson.
 
I was mixing it up yes! So but taking the overall wavefn of the quarks then. As fermions they must be anti-symmetric overall. If the spins are different for the two mesons, then what else is also different?
 
Actually i think i know what the answer is. Since the quarks inside the mesons are distinguishable (antiquark and quark) then their combination doesn't have a symmetry requirement.
 

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