Note on the absence of R2 corrections to Newton's potential

Manuel Accettulli Huber, Andreas Brandhuber, Stefano De Angelis, Gabriele Travaglini
2020 Physical Review D  
We consider Einstein gravity with the addition of R 2 and R μν R μν interactions in the context of effective field theory, and the corresponding scattering amplitudes of gravitons and minimally coupled heavy scalars. First, we recover the known fact that graviton amplitudes are the same as in Einstein gravity. Then we show that all amplitudes with two heavy scalars and an arbitrary number of gravitons are also not affected by these interactions. We prove this by direct computations, using field
more » ... ations, using field redefinitions known from earlier applications in string theory, and with a combination of factorization and power-counting arguments. Combined with unitarity, these results imply that, in an effective field theory approach, the Newtonian potential receives neither classical nor quantum corrections from terms quadratic in the curvature.
doi:10.1103/physrevd.101.046011 fatcat:4wtrqhvmungndkn3juosbefzea