Quantum corrected gravitational potential beyond monopole-monopole interactions

Abstract

We investigate spin-and velocity-dependent contributions to the gravitational interparticle potential. The methodology adopted here is based on the expansion of the effective action in terms of form factors encoding quantum corrections. Restricting ourselves to corrections up to the level of the graviton propagator, we compute, in terms of general form factors, the nonrelativistic gravitational potential associated with the scattering of spin-0 and-1=2 particles. We discuss comparative aspects concerning different types of scattered particles and we also establish some comparisons with the case of electromagnetic potentials. Moreover, we apply our results to explicit examples of form factors based on nonperturbative approaches for quantum gravity. Finally, the cancellation of Newtonian singularity is analyzed in the presence of terms beyond the monopole-monopole sector.

Graviton-mediated scattering amplitudes from the quantum effective action

“…Generically non-localities appear in the form factors if a theory contains massless modes, e.g., the logarithms above. Both fundamental and phenomenological aspects of more general non-local terms have been discussed in the literature [66][67][68][69][70]. Some non-local terms may have interesting consequences for the universe at large scales [71][72][73], potentially providing an explanation of dark energy.…”