Non-perturbative computation of gluon mini-jet production in nuclear collisions at very high energies

Abstract

At very high energies, in the infinite momentum frame and in light cone gauge, a hard scale proportional to the high parton density arises in QCD. In an effective theory of QCD at small $x$, this scale is of order ${\alpha }_S\mu$, where $\mu$ is simply related to the gluon density at higher rapidities. The ab initio real time evolution of small $x$ modes in a nuclear collision can be described consistently in the classical effective theory and various features of interest can be studied non-perturbatively. In this paper, we discuss results from a real time lattice computation of the production of gluon jets at very high energies. At very large transverse momenta, $k_t\ge \mu$, our results match the predictions from pQCD based mini-jet calculations. Novel non-perturbative behaviour of the small $x$ modes is seen at smaller momenta $k_t\sim {\alpha }_S\mu$. Gauge invariant energy-energy correlators are used to estimate energy distributions evolving in proper time.

50 pages Latex, includes 7 figures, revised version, Nuclear Physics B, in press

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