Drei-Teilchen-Systeme im endlichen Volumen
Zusammenfassung der Projektergebnisse
Four fundamental interactions build the groundwork of the world surrounding us. Gravity, describes the largest observed structures in the universe. The dynamics of the smallest structures in the universe are caused by the three other interactions. Together, the latter build a theory called The Standard Model of particle physics. Two of its parts unify to the so-called electroweak force, which is essentially perturbative. The remaining - strong interaction - behaves, however, entirely different. In particular, it is coupled weakly at high energies (small distances) and strongly at low energies (large distances). The effects leading to this counterintuitive behavior are also responsible for the generation of the largest part of the mass of hadrons such as protons as well as the non-trivial pattern of excited states. In the past, the exploration of the latter in the low- and intermediate energy regime has led to an enormous progress on the side of theory and experiments, and sets the general goals of this project. The quantum field theory of the strong interaction is called Quantum Chromodynamics (QCD). The only ab-initio approach to it at low energies are the numerical calculations of Lattice QCD. Being performed in the finite volume they lead to a discrete spectrum, which has to be mapped to the infinite-volume (continuous) spectrum, for a comparison with phenomenology and experiment. Such mapping is well known for systems with two hadrons. However, many systems of large contemporary interest are related to systems with three hadrons. For example the hypothetical spin-exotics (currently searched for in experiments at, e.g., CERN and Jefferson Laboratory) decay into three-pions such does also ordinary mesons. During the project a fully relativistic approach to such a mapping was developed and applied in a first-ever analysis of the finite-volume spectrum of a physical three-body system. This approach relies on a quantization of a fully relativistic, unitary infinite-volume threebody scattering amplitude, deduced in the first part of the project. This novel approach has already re-ignited the interest of the community in performing new lattice calculations with three hadrons. From the experience in the two-body sector, the understanding of the finite-volume spectra of systems with three hadrons will be the next milestone of the hadron spectroscopy. The novel results, obtained during this project are an essential step to this enterprise.
Projektbezogene Publikationen (Auswahl)
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“Three-body Unitarity in the Finite Volume,” Eur. Phys. J. A 53, no. 12, 240 (2017)
M. Mai and M. Döring
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“Three-body Unitarity with Isobars Revisited,” Eur. Phys. J. A 53, no. 9, 177 (2017)
M. Mai, B. Hu, M. Doring, A. Pilloni and A. Szczepaniak
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Finite-volume spectrum of π+ π+ and π+ π+ π+ systems
M. Mai and M. Doring
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“Three-body spectrum in a finite volume: the role of cubic symmetry,” Phys. Rev. D 97, no. 11, 114508 (2018)
M. Döring, H. W. Hammer, M. Mai, J.-Y. Pang, A. Rusetsky and J. Wu
