Remarks on pole trajectories for resonances

© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license. We are particularly thankful towards R.L. Jaffe for his participation at early stages of this work. The research was in part supported by the Spanish project FPA2011-27853-C02-02, DFG funds to the Sino-German CRC 110 “Symmetries and the Emergence of Structure in QCD”, and the EU I3HP “Study of Strongly Interacting Matter” under the Seventh Framework Program of the EU.
We discuss in general terms pole trajectories of resonances coupling to a continuum channel as some strength parameter is varied. It is demonstrated that, regardless of the underlying dynamics, the trajectories of poles that couple to the continuum in a partial wave higher than s-wave are qualitatively the same, while in case of s-waves the pole trajectory can reveal important information on the internal structure of the resonance. In addition we show that only molecular (or extraordinary) states appear near thresholds naturally, while more compact structures need a significant fine tuning in the parameters. This study is of current relevance especially in strong interaction physics, since lattice QCD may be employed to deduce the pole trajectories for hadronic resonances as a function of the quark mass thus providing additional, new access to the structure of s-wave resonances.
DFG
Seventh Framework Program of the EU
Depto. de Estructura de la Materia, Física Térmica y Electrónica
Fac. de Ciencias Físicas
TRUE
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