Dispersive analysis of J/Ψ → γπ 0 π 0 at low pion-pion invariant mass

In this thesis, we analyze the $J/\psi \to \gamma\pi^0\pi^0$ decay process, for which relevant data were collected by the BESIII (Beijing Spectrometer) experiment in 2015. We construct a model for the decay amplitude using a dispersive formalism that minimizes model dependence and is founded on fundamental physical principles, such as unitarity, crossing symmetry, and the analyticity properties of the $S$-matrix. The main goal of this work is to reproduce both the decay rate and the phase-shifts, with particular focus on the latter, which exhibit a $9\sigma$ discrepancy with previous theoretical predictions. Our results show a significant improvement in the description of the phase, thanks to the implementation of the Muskhelishvili–Omnès formalism. This approach allows us to incorporate both intermediate vector-meson exchange and final-state pion rescattering effects. The shape of the decay rate is also successfully reproduced, although further work is needed to match the model with normalized data. This work extends the existing dispersive formalism, previously applied to processes involving space-like photons, to the case of time-like photons. Furthermore, it contributes to the study of the light isoscalar scalar meson spectrum, which is of interest in the search for glueball states, which are hypothetical bound states of gluons whose discovery would provide a crucial test of QCD in the non-perturbative regime. This work represents a first step toward developing a comprehensive analysis framework that can be used to describe the precise datasets expected from upcoming experimental runs.