I need to know the relation of wave function and vertex function of mesons. Any one give me an explanation of them. Are they same? in some journals their expressions are the same and in other papers the wave function expresses as a function of the vertex function of meson. Which one is the correct? THANK YOU!!
I find it difficult to get a clue what you are asking about. Vertex functions appear in renormalizable field theories in higher order pertubation theory as corrections to vertices in Feynman diagrams. However, there is no such field theory dealing mesons as fundamental particles - the standard model is about quarks and leptons. I don't see an obvious relation between these vertex functions and the wave function of a particle. Can you give a link?
For instance, on the leptonic decays of mesons, the Bethe-Salpeter wave function expresses in terms of the hadron quark-antiquark vertex function of mesons. see the following journal on google; A.N. Mitra, S. Bhatnagar, Intl. J. Mod. Phys. A7, 121(1992)