Executive Summary : | Scattering amplitudes are key observables in high energy experiments and of fundamental interest in quantum field theory. Conventional method of evaluating scattering amplitudes in Lagrangian formulation using Feynman diagrammatic is computationally challenging. Modern on-shell techniques provide efficient and convenient methods for calculating scattering amplitudes. Lagrangian formulation suffers from the problem of field redefinition which makes Feynman diagrams ambiguous at individual level. On-shell formalisms are free from such redundancies due to field redefinition. Spinor helicity method, BCFW recursion relation, CHY formalism and positive geometry are some of the well known on-shell techniques developed in recent years. Several significant properties of scattering amplitudes like color-kinematic duality, soft and collinear factorizations are remarkably manifested in these on-shell methods which are otherwise obscured in the usual Lagrangian framework. In four dimension little group of massive fields, unlike that in massless case, is non-abelian. Although lot of progress has been made in the context of scattering amplitudes involving massless states, massive case remains largely unexplored. My research project primarily focuses on exploring on-shell methods, mainly spinor helicity and CHY formalisms, for scattering amplitudes consisting of massive fields. This will be useful in studying amplitudes in standard model, supersymmetric field theories and string theory. Our plan is to study loop level amplitudes in standard model using on-shell methods by applying generalized unitarity principle. On-shell recursive relations are available for tree amplitudes - by deforming the momenta of external states in the complex plane and applying Cauchy's residue theorem, one can build up higher point amplitudes from lower point ones. Spinor helicity variables are most suitable for obtaining these recursion relations. It will be interesting to develop loop level recursion relations for massive amplitudes. This will have significant consequence in understanding standard model physics, as an example we would like to compute anomalous magnetic moment of muon which is interesting because of the discrepancy between theoretical prediction and observed data. Massive spinor helicity is well suited for representing on-shell higher spin fields, which are important in supergravity theories, string theory and black hole scattering. Four-point amplitudes can be expanded in the basis of partial waves, supersymmetry constrains the coefficients of the partial waves due to exchange of different spinning particles. The partial waves play important role in S-matrix bootstrap program. Using on-shell methods, our goal is to study four-graviton amplitudes in supergravity theories where poles come from exchange of massive spinning particles. Since supergravity theories are low energy limits of string theory, we can use our result to check unitarity in string theory answer. |