6533b828fe1ef96bd128907e
RESEARCH PRODUCT
Wave functions of composite hadron states and relationship to couplings of scattering amplitudes for general partial waves
F. AcetiEulogi Osetsubject
PhysicsNuclear and High Energy PhysicsMesonFOS: Physical sciencesFísicaPosition and momentum spaceScattering amplitudeHigh Energy Physics - PhenomenologyHigh Energy Physics - Phenomenology (hep-ph)Quantum mechanicsBound stateSum rule in quantum mechanicsConnection (algebraic framework)Coordinate spaceWave functiondescription
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 $\ensuremath{\rho}$ meson indicating that it is not a composite particle of $\ensuremath{\pi}\ensuremath{\pi}$ and $K\overline{K}$ but something else.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-01-01 |