• analytic scattering amplitude
• bootstrap
• large-n qcd
• pion
• s-matrix
• s-matrix bootstrap
• scattering
• scattering amplitudes

This thesis investigates the space of meromorphic amplitudes through the modern S-matrix bootstrap approach.
In 1968, Lovelace and Shapiro introduced a model for the elastic pion-pion scattering in the large-N limit, which adheres to fundamental principles such as crossing symmetry, causality, unitarity, and obeys to a Regge behaviour across all channels. This model can be generalized by constructing amplitudes that combine LS-amplitudes with different Regge trajectories, weighted by appropriate coefficients. This generalisation allows the development of an innovative and intricate set of scattering amplitudes.
The resulting amplitudes simultaneously obey the Regge behaviour for each value of the Mandelstam variable t and exhibit the expected behaviour for the fixed-angle, high-energy scattering in both the physical and unphysical regions of t.
The generalised Lovelace-Shapiro amplitude must adhere to the fundamental requirements of S-matrix theory. While properties like crossing symmetry and the Regge behaviour are respected by construction, unitarity must be enforced by constraining the coefficients in the sum. Specifically, S-matrix unitarity requires that the coefficients in the partial wave expansion of the residues of the amplitude remain positive, providing a basis for bounding the parameter space.
The coefficients in the sum are matched to the low-energy expansion of the theory, allowing for a systematic exploration of the space of meromorphic effective field theories for massless pion-pion elastic scattering in the large-N limit of QCD. In particular, we compare our results with the allowed region identified by Albert and Rastelli, for a general meromorphic effective field theory, compatible with our requirements, in their recent work.
Additionally, we investigate how the parameter space evolves as the number of the free coefficients in the amplitude increases.