Relations Between Anomalous Dimensions in the Regge Limit

Abstract

We extend the recent formalism developed for computing rapidity anomalous dimension of form factors using unitarity to the problem of high-energy near forward scattering. By combining the factorization of $2\rightarrow 2$ scattering in the effective field theory (EFT) for Glauber operators with definite signature amplitudes, we derive an expression that relates anomalous dimensions (including Regge trajectories) to cut amplitudes, leading to significant computational simplifications. We demonstrate this explicitly by computing the one and two-loop Regge trajectories. Our formalism can also be used to bootstrap anomalous dimensions of operators not related by symmetries. As an example, we show that the full anomalous dimensions (including both the Regge pole and cut pieces) of the two Glauber operator anti-symmetric octet operator, can be determined from the anomalous dimension of the single Glauber exchange operator. Many other such relations exist between other color channels at each order in $\alpha$.