Massive matter and the double copy: Bootstrapping amplitudes in gauge and gravity theories
Ingrid A. Vazquez-Holm
The LHC and the advent of gravitational wave observation have motivated tremendous progress in developing approaches to precision predictions in fundamental gauge theories and classical general relativity, and the two can be intimately connected. The color-kinematics duality of Bern, Carrasco, and Johansson (BCJ) for gauge theories is a duality where in amplitudes, graph-by-graph, kinematic weights obey the same general algebraic constraints as color weights. When arranged in such a representation the color-weights can be replaced by another copy of kinematic weights, generating diffeomorphic invariant scattering amplitudes for gravitational theories in a procedure known as double-copy construction. These gravitational amplitudes can then in turn be applied to predicting classical observables.
The color-dual form for gauge theory predictions means we only need to fix the physical information in a small number of basis graphs, and algebraic relations propagate this to the full prediction—both at tree-level and importantly at loop-level for the integrand description. This thesis develops a BCJ duality satisfying representation of tree- and loop-level amplitudes in massive scalar coupled QCD. The double-copy amplitudes are then relevant to non-rotating black hole scattering. We use the BCJ duality to reduce the set of graphs of amplitudes up to one-loop five-point to a smaller set of basis graphs, to which we give ansatze that are constrained by unitarity cuts and color-kinematics relations.
Our color-dual representations have an important feature. The same kinematic weights, graph by graph, are applicable to scalars regardless of whether they are charged in the fundamental or the adjoint. Indeed one can use adjoint-type ordered cuts to constrain these kinematic weights to be used for predictions in a multitude of theories, depending on which graphs you allow to contribute and how you weight their color.
The double copy construction maps from the scattering of gluons to the scattering of gravitons in N = 0 supergravity, with additional massless states beyond the graviton coupling to the massive scalars. At tree- and loop-level we show that a projective double copy, combining naive double-copy with an application of the method of maximal cuts, can be easily exploited to project out non-gravitational states from the naive double copy, bootstrapping the predictions associated with pure-gravitational interactions between massive scalars.
We expect that the integrands found in this thesis can be used to find one-loop five-point predictions towards radiative corrections to classical observables. With that in mind, we warm up by using the amplitudes found in this thesis to reproduce known results for the color-impulse at leading and next-to-leading order, and radiation at leading order.