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

TL;DR

The paper develops a nonperturbative, real-time lattice framework to study small-x gluon dynamics in ultrarelativistic nuclear collisions, treating wee partons as classical Weizsäcker–Williams fields within a 2+1D Yang–Mills theory coupled to an adjoint scalar. Initial conditions are derived from light-cone color sources, and the forward light-cone evolution is simulated to compare with perturbative mini-jet predictions at large transverse momentum while revealing nonperturbative behavior for soft modes. Gauge-invariant observables, including energy-energy correlators, are used to characterize the time evolution and energy distribution of produced gluons. The work provides qualitative insights into nonperturbative gluon production and space–time dynamics, outlining clear paths toward more quantitative future studies with larger gauge groups and relaxed boost-invariance assumptions.

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 $α_Sμ$, where $μ$ 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, $k_t\geq μ$, 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 $k_t\sim α_Sμ$. Gauge invariant energy-energy correlators are used to estimate energy distributions evolving in proper time.

Figures (7)

• Figure 1: The lattice size dependence of the scalar kinetic energy density, expressed in units of $\mu^4$ for $\mu=0.0177$ (pluses) and $\mu=0.035$ (diamonds). The solid line is the LPTh prediction. The error bars are smaller than the plotting symbols.
• Figure 2: Normalized field intensity of a hard ($k_t=2.16{\rm GeV}$) mode vs proper time $\tau$ in units of fm (diamonds). Solid line is the LPTh prediction.
• Figure 3: Field intensity over $\mu^4$ as a function of $k_t$ for $\mu=200 {\rm MeV}$ (squares), $\mu=100 {\rm MeV}$ (pluses), and $\mu=50 {\rm MeV}$ (diamonds). Solid line is the LPTh prediction. The field intensity is in arbitrary units and $k_t$ is in GeV.
• Figure 4: Normalized field intensity of a soft ($k_t=108{\rm MeV}$) mode vs proper time $\tau$ (in units of fm) for $\mu=200{\rm MeV}$ (squares), $\mu=100{\rm MeV}$ (pluses), and $\mu=50{\rm MeV}$ (diamonds). Solid line, nearly coinciding with the $\mu=50{\rm MeV}$ curve, is the LPTh prediction.
• Figure 5: Time history of the energy density in units of $\mu^4$ for $\mu=200{\rm MeV}$ (squares), $\mu=100{\rm MeV}$ (pluses), and $\mu=50{\rm MeV}$ (diamonds). Error bars are smaller than the plotting symbols. Proper time $\tau$ is in fm.