Three particles in finite volume

• Applicant: Dr. Maxim Mai
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2016 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 299534482

The physical world manifests itself via four fundamental forces: gravitation, the weak, electromagnetic and the strong force. The latter, strong interaction is described by a non-Abelian gauge theory called Quantum Chromodynamics (QCD) and sets the general framework of the present project. Its force mediators (gluons) can interact among each other, which leads to the fact that the strong coupling is small at high energies and large at low energies. This implies that no matter- (quarks) or gauge-fields of QCD can be observed directly. Indeed, it appears that all quarks are confined in hadrons, such as, e.g., protons. The mass of these can be up to a hundred of times larger than the mass of individual quarks. The understanding of these effects, mass generation and confinement, has been the main endeavor of theoretical hadron physics of the last four decades. It has also driven an unprecedented experimental effort at facilities like ELSA (Bonn), MAMI (Mainz), and JLab (USA) to explore the so-called intermediate energy region characterized by a rich spectrum of excited hadrons.There are many approaches to address the inherently non-perturbative dynamics of QCD in this energy region and explore the nature of hadronic resonances. During his PhD the applicant has performed various studies of such resonances from the point of view of effective field theories using unitarization techniques. However, the only ab-initio method to address the dynamics of QCD is given by numerical simulations on discretized space-time, the so-called Lattice QCD. Such calculations are performed typically at unphysical quark masses and in a finite volume. While calculations at the physical quark masses are just a matter of computational cost, the finite-volume effects become even more pronounced at lower quark masses. In the three-particle systems these artefacts are not under control yet.To extract physical quantities, one needs a three-body amplitude whose free parameters are adapted to measured Lattice QCD data. The first part of the project is dedicated to the construction of such an amplitude, including established physical principles like unitarity, but avoiding model bias as far as possible. Subsequently, the breakdown of rotational symmetry due to the finite, cubic volume will be determined. The last part is dedicated to the analysis of real data on the a1(1260) meson that decays into three pions. These data are still rare and their analysis will require sophisticated statistical tools beyond chisquare and F-tests. However, the ongoing simulations of several Lattice QCD groups in this sector make the proposed project a sustainable investment for future research.

• DFG Programme: Research Fellowships
• International Connection: USA
• Host: Professor Dr. Michael Ulrich Döring