TY - JOUR

T1 - The role of Glauber exchange in soft collinear effective theory and the Balitsky-Fadin-Kuraev-Lipatov Equation

AU - Fleming, Sean

N1 - Funding Information:
I would like to thank A. Stasto and T. Mehen for helpful discussions. This work was supported in part by the Director, Office of Science, Office of Nuclear Physics, of the U.S. Department of Energy under grant number DE-FG02-04ER41338 .

PY - 2014/7/30

Y1 - 2014/7/30

N2 - 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-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 counter-term 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.

AB - 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-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 counter-term 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.

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U2 - 10.1016/j.physletb.2014.06.045

DO - 10.1016/j.physletb.2014.06.045

M3 - Article

AN - SCOPUS:84903551546

VL - 735

SP - 266

EP - 271

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

ER -