Causality and the Equivalence Principle for Higher Energy Scattering

Abstract

Recently, it was proposed that the leading high-energy behavior of scattering amplitudes is universal, independent of charge, thereby extending the equivalence principle beyond the graviton pole. In this Letter, we derive a sharper causality constraint on such behavior by studying the Regge limit of colored scattering. Parameterizing a trajectory by $s^{\alpha (t)}$ with $\alpha (0)=2-\delta$, we analyze the Shapiro/Wigner--Smith time-delays in the irreducible scattering channels. We show that any non-singlet trajectory with $\delta <1/2$ produces a growing sign-indefinite time-delay (with $\delta =1/2$ a marginal, dimension-dependent case), which becomes dominant in the Regge diffusion region in the weak-gravity regime. The essential point is that, while the eikonal phase is naturally organized in $t$-channel irreducible representations, the physical time-delays are its eigenvalues in the $s$-channel. A non-singlet exchange therefore recouples into the physical channels with both signs, inevitably producing a negative time-delay in at least one channel.

5 pages + appendix, 2 figures