Asymmetric transverse momentum broadening in an inhomogeneous medium

Abstract

Gradient jet tomography in high-energy heavy-ion collisions utilizes the asymmetric transverse momentum broadening of a propagating parton in an inhomogeneous medium. Such broadening is studied within a path integral description of the evolution of the Wigner distribution for a propagating parton in medium. Going beyond the eikonal approximation of multiple scattering, the evolution operator in the transverse direction can be expressed as the functional integration over all classical trajectories of a massive particle with the light-cone momentum $\omega$ as its mass. With a dipole approximation of the Wilson line correlation function, evolution with the light-cone time $t$ is determined by the jet transport coefficient $\hat{q}$ that can vary with space and time. In a uniform medium with a constant ${\hat{q}}_0$, the analytical solution to the Wigner distribution becomes a typical drifted Gaussian in both transverse momentum and coordinate with the diffusion width $\sqrt{{\hat{q}}_{0}t}$ and $\sqrt{{\hat{q}}_0{t}^3/3{\omega }^2}$, respectively. In the case of a simple Gaussian-like transverse inhomogeneity with a spatial width $\sigma$ on top of a uniform medium, the final asymmetrical momentum distribution can be calculated semi-analytically. The transverse asymmetry defined for jet gradient tomography that characterizes the asymmetrical distribution is found to linearly correlate with the initial transverse position of the propagating parton within the domain of the inhomogeneity. It decreases with the parton energy $\omega$, increases with the propagation time initially and saturates when the diffusion distance is much larger than the size of the inhomogeneity or $t^3\gg 3{\omega }^2{\sigma }^2/{\hat{q}}_0$. The transverse momentum broadening due to the inhomogeneity also saturates at late time in contrast to the continued increase with time if the drifted diffusion in space is ignored.

16 pages in ReVTeX with 5 figures

References in corpus (11)

• Glauber Modeling in High Energy Nuclear Collisions
• Dihadron Tomography of High-Energy Nuclear Collisions in NLO pQCD
• Determining the jet transport coefficient $\hat{q}$ from inclusive hadron suppression measurements using Bayesian parameter estimation
• Tomography of high-energy nuclear collisions with photon-hadron correlations
• Mach cone induced by $\gamma$-triggered jets in high-energy heavy-ion collisions
• Higher twist jet broadening and classical propagation
• Ab Initio Coupling of Jets to Collective Flow in the Opacity Expansion Approach
• The Transverse-momentum-dependent Parton Distribution Function and Jet Transport in Medium
• Search for the elusive jet-induced diffusion wake in $Z/\gamma$-jets with 2D jet tomography in high-energy heavy-ion collisions
• Jet broadening in dense inhomogeneous matter
• Quantum partonic transport in QCD matter

Cited by in corpus (8)

• Probing the Short-Distance Structure of the Quark-Gluon Plasma with Energy Correlators
• Medium induced gluon spectrum in dense inhomogeneous matter
• Jet quenching in anisotropic flowing matter
• Deep learning assisted jet tomography for the study of Mach cones in QGP
• Inconsistencies in, and short pathlength correction to, $R_{AA}(p_T)$ in $\mathrm{A}+\mathrm{A}$ and $\mathrm{p}+\mathrm{A}$ collisions
• Bayesian Constraints on Pre-Equilibrium Jet Quenching and Predictions for Oxygen Collisions
• In-medium gluon radiation spectrum with all-order resummation of multiple scatterings in longitudinally evolving media
• QCD antenna radiative spectrum in dense media within the Improved Opacity Expansion