S-matrix of Quantum field theory has an intricate Analytic structure . In the last few years, there has been a striking development in defining the S-matrix of scalar quantum field theories as volume of certain polytopes known as Accordiohedra. These polytopes live in the kinematic space parametrized by Mandelstam invariants and many of the fundamental properties of the S-matrix such as locality and unitarity emerge from simple combinatorial properties of such polytopes.
In this talk, we will review some recent ideas to extend the positive geometry program to multi-scalar field amplitudes with scalar fields having distinct masses. In particular, we will analyze scattering involving two scalars with unequal masses and find the class of polytopes whose volume generates S-matrix for such theories. We will also argue that ``integrating out the heavier field" induces a map between different accordiohedra, thus giving some preliminary insight into geometrisation of effective field theory.
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Recordings of past talks can be found here: www.youtube.com/channel/UCw9LdPQ5t7Q7muD0qzn70TA