Coupled channel partial wave analysis of two-photon reactions at BESIII

Within this thesis, the three two-photon reactions γγ → π${}^0$π${}^0$, π${}^0$η and K${}^{+}$K${}^{-}$ were investigated. All available data samples in the beam energy range between $\sqrt{s}$ = 3.7 - 4.7 GeV, corresponding to an integrated luminosity of 21.7 fb${}^{-1}$ collected by the BESIII experiment, were used. By applying sophisticated background rejection methods, very pure data samples have been selected. These selected data samples were then analyzed simultaneously in a coupled channel partial wave analysis. The resonance parameters were fixed to the result obtained form a recent coupled channel analysis. The data were described using the K-matrix formalism under the P-vector approach. The best fit hypothesis was obtained under all from the physical point of view reasonable other alternative hypothesis using the Bayesian and Akaike information criteria. For the resonances f${}_0$(980), f${}_0$(1370), f${}_0$(1500), f${}_0$(1710), a${}_0$(980), a${}_0$(1450), f${}_2$(1270), f'${}_2$ (1525), a${}_2$(1320) and a${}_2$(1700) two-photon coupling strengths have been determined by extracting the pole residues of the F-vector amplitude in the complex energy plane. The two-photon coupling strengths for both helicities λ = 0 and λ = 2 could be determined for the f'${}_2$(1525), a${}_2$(1320) and a${}_2$(1700) resonances for the first time. Within this thesis, the most precise measurements of the two-photon widths for the f${}_0$(1370), f${}_0$(1500), f${}_0$(1710), a${}_0$(980), f${}_2$(1270) and a${}_2$(1320) states can be reported. Furthermore, the total and differential cross sections were measured. The cross section limited by the detector acceptance was extracted in the angular ranges of |cos θ${}^{\ast }$| < 0.8 and |cosθ${}^{\ast }$| < 0.6 in case of the channels π${}^0$π${}^0$, π${}^0$η and K${}^{+}$K${}^{-}$, respectively. The results were found to be consistent with previous ones. The cross section results for the K${}^{+}$K${}^{-}$ channel below an invariant K${}^{+}$K${}^{-}$ mass of 1.5 GeV/c${}^2$ are the most precise measurement so far. Using the obtained partial wave analysis result, it was possible to extrapolate to the full angular range and thus to determine the total cross sections. In addition the differential cross sections depending on the invariant two-photon masses has been extracted. Finally, an extensive study of the statistical and systematic uncertainties was performed. In conclusion, the analysis performed in this thesis represents one of the most extensive analysis of two-photon data so far, using highly sophisticated methods to select and describe the experimental data, to extract the properties of the various contributing resonances and to determine the differential and total cross sections.