The Role of Exotic Mesons and Final State Interactions in e+e− Collisions
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Abstract
In recent years, a plethora of new resonances has been discovered in the charmonium region, which cannot be interpreted in a simple quark model picture as states consisting of a charm quark and an anti-charm quark.
A study of the reaction dynamics through which such states are produced is crucial to understand the intrinsic properties of these exotic resonances and for shedding light on their nature.
A powerful non-perturbative tool to analyze hadronic processes is the dispersive formalism, which is based on the fundamental physical principles of causality, crossing symmetry and unitarity of the S-matrix.
In this thesis we apply this formalism to investigate three reactions in which charged exotic mesons were observed by the BESIII Collaboration.
We account for these exotic mesons explicitly as intermediate states in the process and incorporate final state interactions (FSI) through a Muskhelishvili-Omnès approach in order to provide a physical description of the experimental data.
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First, we study the process $e^+ e^- \to \psi(2S) \, \pi^+ \pi^-$ at four different electron-positron center of mass energies $q$ for which data exists.
For this reaction, the $\pi\pi$-FSI can be accounted for through a single channel formalism.
We observe a distinct behavior for each energy, indicating a change of the underlying physical process.
For the lowest energies $q=4.226$ GeV and $q=4.258$ GeV, considering the $Z_c(3900)$ as the intermediate state is essential to describe the invariant mass distributions.
In contrast, at $q=4.358$ GeV, there is no evidence of any intermediate states and the line shape of the data can be described with good precision using only the $\pi\pi$-FSI.
For the highest energy $q=4.416$ GeV, a new heavier state is necessary to describe the experimental data. After performing a scan search we find that a charged intermediate state with mass $4.016(4)$ GeV and width $52(10)$ MeV provides the best description of the peaks in the $\psi(2S) \pi^\pm$ mass distribution.
We observe that the $\pi\pi$-FSI is essential to explain the $\pi^+ \pi^-$ invariant mass distribution for all energies.
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We next extend the formalism to a $\pi\pi / K \bar{K}$ coupled-channel FSI and consider the $Z_c(3900)$ as the intermediate state, in order to investigate the process $e^+ e^- \to J/\psi \, \pi^+ \pi^-$ at $q=4.23$ GeV and $q=4.26$ GeV. Since the phase space for this reaction is much larger, we need to consider the $\pi\pi$ and $K\bar{K}$ rescattering simultaneously.
The formalism not only allows to describe the $J/\psi \pi^\pm$ and $\pi^+ \pi^-$ invariant mass distributions very well, but also predicts the $J/\psi K$ and $K \bar{K}$ line shapes.
Furthermore, we also use the formalism to predict the angular distributions of $J/\psi$ and $Z_c(3900)$.
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For the third process $e^+ e^- \to h_c \, \pi^+ \pi^-$, studied at $q=4.23$ GeV and $q=4.26$ GeV, we account for a relative angular momentum between the pion-pair and $h_c$. Furthermore, we also consider explicitly the charged exotic meson $Z_c(4020)$ as an intermediate state and investigate scenarios with and without including the $Z_c(3900)$. Assuming the $Z_c(4020)$ as an axial-vector, we predict the angular distributions of $h_c$.