Meson-Baryon Scattering from Threshold to the Second Resonance Region
Final Report Abstract
Although Quantum Chromodynamics (QCD) provides the theory of the strong interaction, it has the particular and unique feature among the fundamental forces that it is well-understood at very high energies, but poorly at the much lower energies of matter as we know it. In the transition from very high to low energies, the non-linear QCD dynamics causes the phenomenon of confinement, i.e. that quarks are always confined in colorless composite objects like the proton. The details of this mechanism are not understood. Similarly, at intermediate energies the very light quarks are dressed such that the proton weights fifty times more than the sum of three current quark masses. Adressing these fundamental questions by studying the intermediate energy region, in experiment and theoretically, is thus one of the prime interests in modern hadronic physics. To understand the wealth of data produced in pion- and photon-induced reactions in dedicated experimental programs, one needs to understand the reaction dynamics and perform a partial wave analysis. The goal of this project was to provide a comprehensive theoretical framework to simultaneously analyze the world data in the intermediate energy region. To set up this framework, a prerequisite was to understand the constraints on the amplitude provided by general theoretical requirements from scattering theory. In a first step, we have, thus, investigated the analytic structure of the scattering amplitude to implement the principles of unitarity (in the two-body but also three-body sense), analyticity, as well as approximations of the left-hand cut and the correct low- and high-energy behavior. It turned out that the only way to provide a clear definition of a resonance is to determine the associated position of its pole, and, for the decay modes of the resonance, the residue. This has been discussed in our first publication in 2009. The next step, also carried out from 2007 to 2009, was, thus, the analytic continuation of the amplitude to complex energies. In an extensive study, we determined the resonance pole properties of our amplitude, published in 2009. At the same time, we also followed other paths outlined in the original project proposal. A major step was to include more data in the analysis, apart from the reaction πN → πN. The analysis of πN → πN together with π + p → K + Σ+ could be achieved in 2010. Around the same time, we implemented the interaction with the photon in a strictly gauge invariant way, enabling the analysis of pion photoproduction. Within the framework of dynamical coupledchannel approaches, the work represents the first analysis of this kind. A major advance could be made through the simultaneous analysis of the reactions πN → πN , π − p → ηn, K 0 Λ, K 0 Σ0 , K + Σ− , and π + p → K + Σ+. Apart from following the ideas of the original proposal, we have realized that our framework provides also the opportunity to connect to the rapidly evolving field of lattice gauge theory that is an ab-initio approach to solve QCD at intermediate energies. As shown in a series of publications, the analysis tools developed for pion- and photon-induced reactions can be used in the analysis of the complex pattern of lattice eigenvalues.
Publications
- Coupled-channel dynamics in the reactions πN → πN, ηN, KΛ, KΣ, Eur. Phys. J. A
D. Rönchen, M. Döring, F. Huang, H. Haberzettl, J. Haidenbauer, C. Hanhart, S. Krewald, U.-G. Meißner and K. Nakayama
- Analytic properties of the scattering amplitude and resonance parameters in a meson exchange model, Nucl. Phys. A 829, 170 (2009)
M. Döring, C. Hanhart, F. Huang, S. Krewald and U.-G. Meißner
- The role of the background in the extraction of resonance contributions from mesonbaryon scattering, Phys. Lett. B 681, 26 (2009)
M. Döring, C. Hanhart, F. Huang, S. Krewald and U.-G. Meißner
- Dynamical coupled-channel approaches on a momentum lattice, Eur. Phys. J. A 47, 163 (2011)
M. Döring, J. Haidenbauer, U.-G. Meißner and A. Rusetsky
- The reaction π + p → K + Σ+ in a unitary coupled-channels model, Nucl. Phys. A 851, 58 (2011)
M. Döring, C. Hanhart, F. Huang, S. Krewald, U.-G. Meißner, D. Rönchen
- Pion photoproduction in a dynamical coupled-channels model, Phys. Rev. C 85, 054003 (2012)
F. Huang, M. Döring, H. Haberzettl, J. Haidenbauer, C. Hanhart, S. Krewald, U.-G. Meißner and K. Nakayama
(See online at https://doi.org/10.1103/PhysRevC.85.054003)
