The role of Glauber Exchange in Soft Collinear Effective Theory and the Balitsky-Fadin-Kuraev-Lipatov Equation

Abstract: In soft collinear effective theory (SCET) the interaction between high energy quarks moving in opposite directions involving momentum transfer much smaller than the center-of-mass energy is described by the Glauber interaction operator which has two-dimensional Coulomb-like behavior. Here, we determine this $n$-$\bar{n}$ collinear Glauber interaction operator and consider its renormalization properties at one loop. At this order a rapidity divergence appears which gives rise to an infrared divergent (IR) rapidity anomalous dimension commonly called the gluon Regge trajectory. We then go on to consider the forward quark scattering cross section in SCET. The emission of real soft gluons from the Glauber interaction gives rise to the Lipatov vertex. Squaring and adding the real and virtual amplitudes results in a cancelation of IR divergences, however the rapidity divergence remains. We introduce a rapidity counterterm to cancel the rapidity divergence, and derive a rapidity renormalization group equation which is the Balitsky-Fadin-Kuraev-Lipatov Equation. This connects Glauber interactions with the emergence of Regge behavior in SCET.