Causal and unitary scattering amplitudes compliant with crossing symmetry at low energy

PhD ceremony: Ms. S. Stoica, 12.45 uur, Academiegebouw, Broerstraat 5, Groningen

Dissertation: Causal and unitary scattering amplitudes compliant with crossing symmetry at low energy

Promotor(s): prof. O. Scholten

Faculty: Mathematics and Natural Sciences

The AntiProton ANihilation at DArmstadt experiment features a broad scientific programme with key areas being the study of exotic hadrons strange and charmed baryons, charmonium spectroscopy, and the structure of the nucleon. Quantum Chromo Dynamics (QCD) is generally accepted to be the fundamental underlying theory of the strong interaction. The self-coupling of gluons in QCD allows the prediction of exotic hadronic systems that differ from the classical quark model. Results of high precision are a decisive element to be able to identify and extract features of these exotic states.

Our approach starts from the analytic properties of the most general scattering amplitude: unitarity, covariance, analyticity and crossing symmetry. The covariant partial-wave amplitudes are an excellent starting point for analyzing baryon-antibaryon scattering in a covariant coupled-channel approach that takes into account causality and coupled-channel unitarity. The kinematical constraints in the helicity partial-wave amplitudes are eliminated by means of nonunitary transformation matrices that map the initial and final helicity states to new covariant states. We have performed a series of calculations for a 2x2 coupled-channel interaction, investigating the effects of a weak, intermediate and strong coupling on the covariant partial-wave amplitudes calculated with the N/D method. As a next step, covariant partial-wave amplitudes must be used to extend the coupled-channel space with meson-nucleon states and meson-meson states.