[Hybrid RBRC seminar] Computing scattering amplitudes made easy using field transformations

by Piotr Kotko (AGH UST)

Thursday 25 Jul 2024, 12:30 → 13:30 US/Eastern

2-160 ( https://bnl.zoomgov.com/j/1619458475?pwd=Z1VDdXVXcWF1eUhsRDZObVJnME4rUT092-160)

As is well known, computing multi-leg QCD scattering amplitudes using the standard elementary three and four-gluon vertices is cumbersome even at tree level, due to the fact that number of diagrams grows dramatically with each external state. Over the last two decades, the problem was addressed in essentially two ways. The first approach are the on-shell methods that try to eliminate fields as degrees of freedom whatsoever (unitarity methods, BCFW recursion, Grassmannian geometry, etc.). Second approach is to construct a new field theory that contains new degrees of freedom that are more efficient in computing scattering amplitudes. One such example is the MHV action, which is based on the light-cone Yang-Mills action and where the new fields interact via multileg vertices related to the maximally-helicity-violating (MHV) amplitudes. We discuss a further extension of such theory, called the Z-field theory, which is obtained via field transformation based on Wilson lines. Classically, it contains no triple couplings and thus is very efficient in computing tree amplitudes. However, at loop level, the classical action alone is not capable of reproducing rational contributions to QCD amplitudes, due to a quantum anomaly in the self-dual sector of the Yang-Mills theory. We describe one possible solution to that problem and discuss applicability of the new formulation in QCD computations.