New infra-red enhancements in 4-derivative gravity

4-derivative gravity provides a renormalizable theory of quantum gravity at the price of introducing a physical ghost, which could admit a sensible positive-energy quantization. To understand its physics, we compute ghost-mediated scatterings among matter particles at tree-level, finding a new power-like infra-red enhancement typical of 4-derivative theories, that we dub '$ghostrahlung$'. Super-Planckian scatterings get downgraded to Planckian by radiating hard gravitons and ghosts, which are weakly coupled and carry away the energy.