MSc defense by Alicia Astorga Elcarte
On-shell methods for anomalous dimensions and beta functions
On-shell methods have proven to be a powerful alternative to Feynman diagrams for the calculation of scattering amplitudes. They can also be applied to partially off-shell quantities, such as form factors of gauge invariant local composite operators. The discontinuities of these quantities can be computed via phase-space integrals that are related to the anomalous dimensions of these operators as well as the beta functions of the corresponding couplings.
We review the parametrizations of these phase space integrals at one-loop and at the simplest two-loop case, involving the triple cut in the two-particle channel. The utility of these computations will be further explained with some examples. We will finally study the two-loop parametrization of the triple cut in the three-particle channel, that would allow to fully extend these methods to the second order in perturbation theory.