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We construct the on-shell amplitude basis and the corresponding effectiveoperators for generic modified gravity theory, such as pure gravity with higherderivatives, scalar-tensor gravity, Einstein-Yang-Mills, etc. Taking the Weyltensor as the building block, we utilize the Young tensor technique to obtainindependent operators, without equation of motion and total derivativeredundancies. We update our algorithm and vastly increase the speed for findingthe monomial basis (m-basis) of effective operators expressed in terms of Weyltensors with Lorentz indices, the familiar form for the General Relativitycommunity. Finally, we obtain the complete and independent amplitude andoperator basis for GRSMEFT and GRLEFT up to mass dimension 10.

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