Bootstraping Gauge Theories

In this text we consider the S-Matrix bootstrap of the 2−2 Pion amplitude as introduced on [2]. We start by considering the general constraints of analyticity, crossing symmetry and unitarity and further restrict the space of amplitudes to match the UV (QCD) and IR (Chiral Perturbation Theory) symmetry information where many results can be found in the literature and are well understood. The crucial realization, for which this work became feasible, is that one can extract information out of these theories using a procedure known as the Form Factor bootstrap to constrain the space of allowed amplitudes matching the IR and UV information. In this work we keep exploring the framework proposed in [2, 3] by describing the amplitude functions in terms of a discrete basis. This allow us first, to check the consistency of the results and, secondly to efficiently explore the poles of the S−Matrix. As expected from [3] we found great agreement with experimental/phenomenological data [4–6] on the partial waves of the S−Matrix and on the poles in the S−Matrix found in the PDG data [7], where we identified the σ, ρ(770) and the f2(1270) mesons.

We continue in this exploration…