Initial stage jet momentum broadening in tBLFQ formalism

TL;DR

This work addresses the quantum dynamics of jet propagation in the early Glasma stage following heavy-ion collisions. It introduces the time-dependent Basis Light Front Quantization (tBLFQ) approach to evolve a jet’s light-front wavefunction in the classical Glasma background generated by Color Glass Condensate initial conditions and real-time lattice Yang-Mills evolution with the Glasma scale $Q_s=1.5$ GeV. Key results show that the transverse momentum broadening and jet quenching parameter computed from the quantum evolution align with classical canonical-momentum predictions, while also clarifying the distinction between canonical and kinetic momentum. The study establishes a quantum framework for jet–medium interactions in the pre-equilibrium phase and opens the way to include quantum radiation and energy loss in early-time jet phenomenology.

Abstract

We study the momentum broadening of a high-energy quark jet in the large density gluon medium created right after the collision of two ultrarelativistic heavy nuclei, the Glasma. Previous Glasma studies modeled the jet as a classical probe particle, for which position and momentum are simultaneously determined. In this work, we use the light-front QCD Hamiltonian formalism to treat the jet as a fully quantum state. We compute its real-time evolution while propagating through the Glasma classical background fields, which act as an interaction potential in the quantum evolution of the jet. We present results for the momentum broadening and jet quenching parameter of a jet at mid-rapidity, with special emphasis on the anisotropies between the longitudinal and transverse directions relative to the collision axis. In addition, we compare our results to classical calculations, and initiate a study of the distinction between kinetic and canonic momentum in the context of jet momentum broadening.

Figures (2)

• Figure 1: Evolution of the expectation value of the jet transverse momentum (on the left panel) and the jet quenching parameter (on the right panel). We define $\Delta \langle p_y^2 (x^+)\rangle = \langle p_y^2 (x^+)\rangle - \langle p_y^2 (0)\rangle$ to subtract the initial width of the wavefunction in momentum space and show only the broadening due to interactions with the medium. The result obtained using tBLFQ formalism is shown in solid triangle and the classical calculation result using Eq. (\ref{['eq:ClassicalCanonicMomentum']}) is shown in dashed line as a comparison.
• Figure 2: Comparison of the canonical and kinetic momenta in the classical formalism. The kinetic (canonical) momentum, shown with solid (dashed) lines, is calculated using Eq. \ref{['eq:ClassicalKineticMomentum']} [Eq. \ref{['eq:ClassicalCanonicMomentum']}]. Momenta in the $y-$ and $z-$ directions are indicated in red and blue, respectively. The $p_z$ line overlaps the horizontal axis, indicating no canonical momentum broadening in $z$.