Gluon scattering on self-dual radiative gauge fields

Tim Adamo, Lionel Mason, Atul Sharma

Published 2020-10-28Version 1

We present all-multiplicity formulae for the tree-level S-matrix of gluons in self-dual radiative backgrounds, which are chiral, asymptotically flat gauge fields characterised by their free radiative data. Twistor theory captures the underlying integrability of these backgrounds, and the tree-level scattering amplitudes are written as integrals over the moduli space of holomorphic maps from the Riemann sphere to twistor space, with the degree of the map related to the helicity configuration of the external gluons. In the MHV sector, our formula is derived from first principles; for general helicities the formulae are motivated by twistor string theory and shown to pass several consistency tests. Unlike amplitudes on a trivial background, there are residual integrals due to the functional freedom in the self-dual scattering background, but for scattering of momentum eigenstates we are able to do many of these explicitly and even more is possible in the special case of plane wave backgrounds. In general, the number of these integrals is always less than expected from standard perturbation theory, but matches the number associated with space-time MHV rules in a self-dual background field, which we develop for self-dual plane wave backgrounds.