Longitudinal rescaling and high-energy effective actions

Under a longitudinal rescaling of coordinates ${x}^{0,3}\ensuremath{\rightarrow}\ensuremath{\lambda}{x}^{0,3}$, $\ensuremath{\lambda}\ensuremath{\ll}1$, the classical QCD action simplifies dramatically. This is the high-energy limit, as $\ensuremath{\lambda}\ensuremath{\sim}{s}^{\ensuremath{-}1/2}$, 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 $\ensuremath{\lambda}$ in this action, with $\ensuremath{\lambda}<1$. 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 $|\mathrm{ln}\ensuremath{\lambda}|\ensuremath{\ll}1$, which is essential for the validity of perturbation theory. If $\ensuremath{\lambda}$ is sufficiently small (so that $|\mathrm{ln}\ensuremath{\lambda}|\ensuremath{\gg}1$), then the perturbative renormalization group breaks down. This is due to uncontrollable fluctuations of the longitudinal chromomagnetic field.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.