Authors:	Deineka, Oleksandra
Title:	Coupled-channel dynamics in hadronic systems
Online publication date:	5-May-2023
Year of first publication:	2023
Language:	english
Abstract:	The description of the hadron dynamics still challenges modern theoretical physics. The current approaches are striving to meet the demands of increasing experimental precision. They either incorporate the massive amounts of data in various channels or rely on the theoretical assumptions, which are valid only in a limited number of cases. In this context, it is crucial to develop techniques which allow the accurate description of the existing data and simultaneously have a predictive power achieved through their model-independent nature. This thesis is dedicated to the partial-wave dispersion relation approach, which is built upon the fundamental properties of the scattering matrix, such as unitarity and analyticity. We first apply this approach to study the $S$-wave $\pppp$ and $\pkpk$ reactions, in which the lightest scalar resonances $\sfz$, $\fz$ and $\kks$ show up. The contributions from the left-hand cuts are accounted for using the power expansion in a suitably constructed conformal variable. The expansion coefficients are determined in a data-driven manner by fitting the phase shifts to experimental and lattice data as well as Roy analyses. For the $\pi\pi$ scattering, we present both a single- and coupled-channel analysis by additionally including the $K\bar{K}$ channel. For the latter, the central result is the Omn\`es matrix, which is consistent with the most recent dispersive results on $\pi\pi \to \pi\pi$ and $\pi\pi \to K\bar{K}$, respectively. By performing an analytic continuation to the complex plane, we found poles associated with the resonances $\sfz$, $\fz$ and $\kks$ for the physical pion mass value and in the case of $\sigma/f_0(500)$, $\kappa/K_0^*(700)$ also for unphysical pion mass values. The knowledge of the $\pppp$ amplitude allows us to perform a dispersive analysis of the double-virtual photon-photon scattering to two pions which is very sensitive to hadronic final state interaction through unitarity. This process is particularly important since it contributes to the hadronic light-by-light scattering part of the anomalous magnetic moment of the muon. For the $S$-wave, we use the obtained coupled-channel $\pi\pi,\, K\bar{K}$ Omn\`es matrix to account for the $\sfz$ and $\fz$ resonances simultaneously. For higher energies, the $f_2(1270)$ resonance shows up as a dominant structure which we approximate by a single channel $\pi\pi$ rescattering in the $D$-wave. In the dispersive approach, the latter requires taking into account $t$- and $u$-channel vector-meson exchange left-hand cuts, which exhibit an anomalous-like behaviour for large space-like virtualities. We show how to incorporate such behaviour using an appropriate contour deformation. We also focus on the kinematic constraints of helicity amplitudes and explicitly show their correlations. We furthermore extend the dispersive approach to the $\gamma\gamma\to D^+D^-$ and $\gamma\gamma\to D^0\bar{D}^0$ processes, which are expected to contain the two charmonium resonances: $\chizero$ and $\chitwo$. While the latter is relatively well established from both experimental and theoretical sides, the identification of the former remains dubious. For the $S$-wave contribution, we again adopt a partial-wave dispersive representation and the $D$-wave $\chi_{c2}(3930)$ state is described as a Breit-Wigner resonance. The resulting fits are consistent with the data on the invariant mass distribution of the $e^+e^- \to J/\psi D\bar{D}$ process. Performing an analytic continuation to the complex $s$-plane, we find no evidence of a pole corresponding to the $\chizero$ candidate $X(3860)$ reported by the Belle Collaboration. Instead, we find a clear bound state below the $D\bar{D}$ threshold at $\sqrt{s_B} = 3695(4)$ MeV, confirming the previous phenomenological and lattice predictions.
DDC:	530 Physik 530 Physics
Institution:	Johannes Gutenberg-Universität Mainz
Department:	FB 08 Physik, Mathematik u. Informatik
Place:	Mainz
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-8981
URN:	urn:nbn:de:hebis:77-openscience-e95890f9-cb84-4fc8-b293-03eb8ab888295
Version:	Original work
Publication type:	Dissertation
License:	CC BY
Information on rights of use:	https://creativecommons.org/licenses/by/4.0/
Extent:	149 Seiten
Appears in collections:	JGU-Publikationen