On-shell Operator Construction in the Effective Field Theory of Gravity

We construct the on-shell amplitude basis and the corresponding effective operators for generic modified gravity theory, such as pure gravity with higher derivatives, scalar-tensor gravity, Einstein-Yang-Mills, etc. Taking the Weyl tensor as the building block, we utilize the Young tensor technique to obtain independent operators, without equation of motion and total derivative redundancies. We update our algorithm and vastly increase the speed for finding the monomial basis (m-basis) of effective operators expressed in terms of Weyl tensors with Lorentz indices, the familiar form for the General Relativity community. Finally, we obtain the complete and independent amplitude and operator basis for GRSMEFT and GRLEFT up to mass dimension 10.