By C. DeWitt, Claude Itzykson

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The vector mesons are more massive than their pseudoscalar counterparts. For example, the pmeson has a rest mass energy of 767 MeV and the w-meson has 782 MeV, In contrast, the pion rest mass energies are 140 MeV for and 135 MeV for T O . As far as their wave functions are concerned, the vector and pseudoscalar mesons differ only in their total intrinsic spin, with S = 1 for the former and S = 0 for the latter. The large difference in their masses must come from the differences in the interaction between a quark and an aritiquark in the S = 0 and S = 1 states.

They are therefore “scalar” particles, as their wave functions are invariant under a rotation of the spatial coordinate system. However, unlike ordinary scalars, their wave functions change sign under a parity transformation. This may be seen in the following way. The parity of the pion is given by the product of the int,rinsic parities of the quark ($1) and the antiquark (-1) and the parity of the spatial wave function of the (@)-pair. The property of the spatial wave function under a parity transformation is related to the orbital angular momentum C and is given by (-l)t, the same a3 spherical harmonics of order e discuseed in $A-1.

A simple quark model of mesons, therefore, involves a quark and an antiquark moving with respect to each other with orbital angular momentum 4. The total angular momentum, or spin, of the system is J = 4 f S , where S = sq ST is the sum of the intrinsic spins of the quark and the antiquark. Since sq = ST = f , the possible value of S for a qpsystem is either 0 (singlet state) or 1 (triplet state). As for the spatial part of the wave function, it has been found that mesons with relative orbital angular momentum t = 0 are lower in energy, the same as in the case of atomic levels.