1202.4607 (F. Aceti et al.)

Wave functions of composite hadron states and relationship to couplings
of scattering amplitudes for general partial waves    [PDF]

F. Aceti, E. Oset

In this paper we present the connection between scattering amplitudes in
momentum space and wave functions in coordinate space, generalizing previous
work done for s-waves to any partial wave. The relationship to the wave
function of the residues of the scattering amplitudes at the pole of bound
states or resonances is investigated in detail. A sum rule obtained for the
couplings provides a generalization to coupled channels, any partial wave and
bound or resonance states, of Weinberg's compositeness condition, which was
only valid for weakly bound states in one channel and s-wave. An example,
requiring only experimental data, is shown for the $\rho$ meson indicating that
it is not a composite particle of $\pi \pi$ but something else.

View original: http://arxiv.org/abs/1202.4607