Scattering Amplitudes in the Yang-Mills sector of Quantum Chromodynamics

Abstract

We derive a new Minkowski space action for the pure gluonic sector of QCD that implements new interaction vertices local in the light-cone time with at least four legs and fixed helicities - the lowest vertex is the four-point MHV (Maximally Helicity Violating), higher point vertices include $\mathrm{N}^k \mathrm{MHV}$, where 1 $\leqslant$ k $\leqslant $ n-4 and n is the number of external legs. The abscense of triple point interaction vertices makes it efficient in calculating higher multiplicity pure gluonic scattering amplitudes. This formulation is obtained via a canonical transformation of the light-cone Yang-Mills action, with the field transformations based on Wilson line functionals. At the quantum level, the action can only provide cut-constructible parts of amplitudes in 4D. In order to remedy that, we constructed the one-loop effective action starting with the Yang-Mills theory, which explicitly provides the missing contributions. This work provides a new field-theory action-based method to efficiently calculate higher multiplicity pure gluonic scattering amplitudes up to one loop.