Loop celestial amplitudes for gauge theory and gravity

Scattering amplitudes of massless particles in Minkowski space can be expressed in a conformal basis by Mellin transforming the momentum space amplitudes to correlation functions on the celestial sphere at null infinity. In this paper, we study celestial amplitudes of loop-level gluons and gravitons. We focus on the rational amplitudes that carry all-plus and single-minus external helicities. Because these amplitudes are finite, they provide a concrete example of celestial amplitudes of Yang- Mills and gravity theory beyond tree level. We give explicit examples of four- and five-point functions and comment on higher point amplitudes.