Unitary Bethe-Salpeter Methods in Two- and Three-Body Systems
- George Washington Univ., Washington, DC (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
The study of resonances, unstable particles formed in particle scattering, is motivated by the questions about the strong interaction and the composition of hadrons. In order to advance this study in the intermediate energy region, a variety of techniques are used. In this thesis, we present work done on two different analyses that use the principle of unitarity and the Bethe-Salpeter equation to study the resonances Lambda(1405), Sigma(1385), and a1(1260). Firstly, we perform a simultaneous analysis of Sand P-waves of the Strangeness = -1 two-body meson-baryon scattering amplitude using all low-energy data. For the first time, differential cross section data are included for chiral unitary coupled-channel models. From this model, S- and P-wave amplitudes are extracted and we observe both well-known I(JP)=0(1/2^-) S-wave states as well as a new I(JP)=1(1/2^+) state absent in quark models and lattice QCD results. Multiple statistical and phenomenological tests suggest that, while the data clearly require an I =1 P-wave resonance, the new state just accounts for the absence of the decuplet Sigma(1385)3/2+ in the model which is subsequently included in the parameterization. Secondly, we formulate the final state interaction of the a1(1260) resonance decay in a manifestly three-body-unitary parameterization and fit it to the a1(1260) lineshape measured by the ALEPH experiment. Dalitz plots calculated from this fit are presented. The work demonstrates the feasibility to numerically solve a previously derived amplitude and its generalization to isobars with spin and coupled channels. The model is a good test case because it can also be applied to other meson decays including exotic states and modified for the finite-volume problem as it arises in lattice QCD due to its manifest unitarity. The understanding of the resonances being analyzed in both the two-body work and the three-body work gives a better understanding of intermediate energy QCD.
- Research Organization:
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- DOE Contract Number:
- AC05-06OR23177
- OSTI ID:
- 1728591
- Report Number(s):
- JLAB-THY-20-3113; DOE/OR/23177-5089
- Country of Publication:
- United States
- Language:
- English
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