A bstract It has been suggested that logarithmically enhanced infra-red loop corrections arising in theories with four derivatives correspond to a physical running of couplings, rendering quadratic gravity asymptotically free. We find that these effects depend on the gauge and on the field parameterisation. We compute physical on-shell amplitudes and find genuine infra-red log-enhanced loop corrections, that are process-dependent and cannot be absorbed into running couplings. As a byproduct, we show that the effective action of quadratic gravity at tree level and without matter fields is just Einstein gravity, so positivity bounds are satisfied despite the presence of ghosts.
Salvio et al. (Thu,) studied this question.