  The amplitude A(s,t) for ultra-high energy scattering can be found in the
leading eikonal approximation by considering propagation in an Aichelburg-Sexl
gravitational shockwave background. Loop corrections in the QFT describing the
scattered particles are encoded for energies below the Planck scale in an
effective action which in general exhibits causality violation and Shapiro time
advances. In this paper, we use Penrose limit techniques to calculate the full
energy dependence of the scattering phase shift Theta_scat(hat_s},, where the
single variable hat_s = Gs/m^2 b^(d-2) contains both the CM energy s and impact
parameter b, for a range of scalar QFTs in d dimensions with different
renormalizability properties. We evaluate the high-energy limit of
Theta_scat(hat_s) and show in detail how causality is related to the existence
of a well-defined UV completion. Similarities with graviton scattering and the
corresponding resolution of causality violation in the effective action by
string theory are briefly discussed.
