We congratulate Dr. Oleksandra Deineka on completing her dissertation titled

Coupled-channel dynamics in hadronic systems

This thesis is dedicated to the dispersion relation approach, which is built upon the  unitarity and analyticity properties of the scattering matrix.  We apply it to study the pion-pion and pion-kaon scattering, in which the lightest scalar resonances show up. The knowledge of the pion-pion amplitude allows us to perform an analysis of the double-virtual photon-photon scattering to two pions, which contributes to the hadronic light-by-light scattering part of the anomalous magnetic moment of the muon. We also consider the two photon fusion reaction with D-meson pair in the final state, which is expected to contain two charmonium resonances.

Short summary for scientists:

The description of the hadron dynamics still challenges modern theoretical physics. The current approaches are striving to meet the demands of increasing experimental precision. 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 pion-pion and pion-kaon scattering, in which the lightest scalar resonances f0(500), f0(980) and K*(700) 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 by fitting the phase shifts to the data. By performing an analytic continuation to the complex plane, we found poles associated with the light scalar resonances.

The knowledge of the pion-pion 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 Omnès matrix. For higher energies, the f2(1270) resonance shows up as a dominant structure which we approximate by a single channel pion-pion rescattering in the d-wave. 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 focus on the kinematic constraints of helicity amplitudes and explicitly show their correlations.

We furthermore extend the dispersive approach to the two photon fusion reaction with D-meson pair in the final state, which is expected to contain the two radially excited p-wave charmonium states. For the s-wave contribution, we again adopt a partial-wave dispersive representation and the d-wave state is described as a Breit-Wigner resonance. Performing an analytic continuation to the complex plane, we find no evidence of a pole corresponding to the X(3860) reported by the Belle Collaboration. Instead, we find a clear bound state below the D-pair threshold, confirming the previous phenomenological and lattice predictions.