Longitudinal rescaling and high-energy effective actions

作者：Orland Peter^*; Xiao Jing

来源：Physical Review D - Particles, Fields, Gravitation and Cosmology, 2009, 80(1): 016005.

DOI：10.1103/PhysRevD.80.016005

Under a longitudinal rescaling of coordinates x(0,3)->lambda x(0,3), lambda < 1, the classical QCD action simplifies dramatically. This is the high-energy limit, as lambda similar to s(-1/2), where s is the center-of-mass energy squared of a hadronic collision. We find the quantum corrections to the rescaled action at one loop, in particular, finding the anomalous powers of lambda in this action, with lambda < 1. The method is an integration over high-momentum components of the gauge field. This is a Wilsonian renormalization procedure, and counterterms are needed to make the sharp-momentum cutoff gauge invariant. Our result for the quantum action is found, assuming vertical bar ln lambda vertical bar < 1, which is essential for the validity of perturbation theory. If lambda is sufficiently small (so that vertical bar ln lambda vertical bar 1), then the perturbative renormalization group breaks down. This is due to uncontrollable fluctuations of the longitudinal chromomagnetic field.

• 出版日期2009-7