Mikhasenko, Mikhail: Three-pion dynamics at COMPASS: resonances, rescattering and non-resonant processes. - Bonn, 2019. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-56606
@phdthesis{handle:20.500.11811/8115,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-56606,
author = {{Mikhail Mikhasenko}},
title = {Three-pion dynamics at COMPASS: resonances, rescattering and non-resonant processes},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2019,
month = dec,

note = {This thesis presents studies of the strong interaction in the non-perturbative regime by analyzing the properties of hadronic resonances. The basis for this research is the world's largest dataset on diffractive reactions, especially the $pi^-,ptopi^-pi^+pi^-,p$ channel with about ,$M events, measured with a high-energy pion beam by the COMPASS experiment at the CERN Super Proton Synchrotron. The three-pion final state couples to a variety of light isovector resonances, many of which are still poorly understood. Among these are a ground axial-vector state $a_1(1260)$, and the spin-exotic $pi_1(1600)$ that is a prime candidate for the lightest hybrid meson with explicit gluonic degrees of freedom. Recently, a new resonance-like signal with axial-vector quantum numbers was reported by COMPASS at a mass of 20,$MeV and called $a_1(1420)$. This state, if confirmed, is to be regarded as a candidate for a light tetraquark or molecular state because of its proximity to the $a_1(1260)$ ground state. % among other peculiarities. In order to disentangle the different spin-parity contributions to a given final state, a partial-wave analysis (PWA) of the data in small bins of the pi$ invariant mass and of the momentum transfer squared $t$ is performed. The results of this analysis are spin-density matrix elements, whose mass and $t$-dependences are subjected to phenomenological analysis to extract resonance parameters. We introduce the PWA technique and discuss several methods to obtain the resonance parameters. Instead of the traditional approach of coherently adding Breit-Wigner amplitudes, which violate the fundamental principle of unitarity, we study models that incorporate the unitarity constraints by construction and enable us to minimize systematic uncertainties of the pole positions of resonances.
Other effects which are traditionally ignored in the analyses are final-state interactions of the hadrons produced in the reaction. Due to the high energy of the beam particle, these effects are usually considered negligible. We show, however, that they do become important given the large datasets available. A distinct feature of the three-hadron final state that is not present in two-hadron final states is cross-channel rescattering. We find that a peculiar rescattering from $K^*bar{K} to f_0pi$ in a triangle loop produces a resonance-like signal with exactly the mass and width of the new $a_1(1420)$. We calculate the amplitude for this and other rescattering processes using different techniques and demonstrate that the final-state-interaction hypothesis is consistent with the COMPASS observations. A simple approach applied to the data is matched to the unitarity-based dispersive framework, known as the Khuri-Treiman model, which gives access to the ``higher orders'' of the rescattering corrections beyond the triangle graph.
In diffractive reactions, an additional complication arises from a coherent physical background due to non-resonant production of the pi$ system, the main part of which is the so-called Deck effect. We reveal its features using the COMPASS data and compare several theoretical models to describe it. This background accounts for a large fraction of the intensity in several important waves and has been one of the reasons for the poor knowledge of the $a_1(1260)$ from diffractive reactions. In order to obtain an independent extraction of $a_1$ pole parameters, we study the hadronic decays of $tau$-leptons from $e^+e^-$ collisions, $tau to pi^-pi^+ pi^-, nu_tau$, using data of the ALEPH experiment. In this case, the pi$-interaction is dominated by the $a_1(1260)$. Applying our unitarity approach we construct a $K$-matrix-based model and successfully extract the pole position of the $a_1(1260)$ for the first time.
Finally, using the S-matrix unitarity constraints for the system of three particles we derive a unified framework which combines the resonance physics (the short-range interaction) and the rescattering phenomena (the long-range exchanges). A factorization inspired by the Khuri-Treiman approach leads to a simplification of the three-body unitarity constraints and permits us to build a $K$-matrix-like model for the resonance physics with the rescattering terms entering the self-energy function.},

url = {http://hdl.handle.net/20.500.11811/8115}
}

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