[Submitted on 17 Mar 2016] (cross-list from hep-ph)
General considerations on the nature of and from their pole positions
Xian-Wei Kang🇪🇸 · Zhi-Hui Guo🇩🇪 · J. A. Oller🇪🇸
The nature of the bottomonium-like states and is studied by calculating the compositeness () in those resonances. We first consider uncoupled isovector -wave scattering of within the framework of effective-range expansion (ERE). Expressions for the scattering length () and effective range () are derived exclusively in terms of the masses and widths of the two states. We then develop compositeness within ERE for the resonance case and deduce the expression , which is then applied to the systems of interest. Finally, the actual compositeness parameters are calculated in terms of resonance pole positions and their experimental branching ratios into by using the method of Ref.[1]. We find the values and for the and , respectively. We also compare the ERE with Breit-Wigner and Flatté parameterizations to discuss the applicability of the last two ones for near-threshold resonances with explicit examples.
- Comments:
- 15 pages, 1 figure
- Subjects:
- High Energy Physics — Phenomenology (hep-ph); High Energy Physics — Experiment (hep-ex); High Energy Physics — Lattice (hep-lat); Nuclear Theory (nucl-th)
- arXiv:
- 1603.05546 [pdf]