[Paper Review] Monitoring parton equilibration in heavy ion collisions via dilepton polarization

Edward Shuryak|arXiv (Cornell University)|Mar 5, 2012

High-Energy Particle Collisions Research3 citations

TL;DR

This paper proposes using dilepton polarization angular distributions as a probe to monitor parton equilibration in heavy ion collisions. By analyzing the mass-dependent anisotropy parameter $ a(M) $, it shows that dileptons from different stages—Drell-Yan (high mass, $ a \approx 1 $), pre-equilibrium (intermediate mass, $ a \approx -0.2 $), and equilibrated plasma (low mass, $ a \to 0 $)—provide a clock-like signal of thermalization, with experimental measurement of $ a(M) $ offering direct insight into the degree of local parton equilibration.

ABSTRACT

In this note we discuss how angular distribution of the dileptons produced in heavy ion collisions at RHIC/LHC energies can provide an information about a degree of local equilibration of the quark-gluon plasma produced at different invariant mass regions.

Motivation & Objective

• To develop an experimental observable sensitive to the degree of local parton equilibration in quark-gluon plasma formed in heavy ion collisions.
• To link the angular distribution of dileptons to the equilibration stage of the plasma via the anisotropy parameter $ a(M) $.
• To provide a measurable signature—$ a(M) $—that evolves from $ a \approx 1 $ (Drell-Yan) to $ a \approx -0.2 $ (pre-equilibrium) to $ a \to 0 $ (equilibrated) as a function of dilepton invariant mass.
• To motivate experimental measurement of $ a(M) $ to test theoretical models of parton thermalization.
• To highlight the limitations of translating stress tensor anisotropy into parton distribution anisotropy in strongly coupled systems.

Proposed method

• Modeling the angular distribution of dileptons using a one-parameter form $ W \sim \exp[-\alpha \cos^2\theta_p] $, where $ \alpha $ characterizes parton momentum anisotropy.
• Deriving the effective anisotropy parameter $ a(\alpha) $ from the differential cross-section $ d\sigma/d\Omega_k \sim 1 + a(\alpha)\cos^2\theta_k $.
• Using the temperature profile function $ \Phi(T) \sim T^{-p} $ and production rate $ W \sim \exp(-M/T) $ to link dilepton invariant mass $ M $ to the proper time of production via $ T^* = M/p $.
• Analyzing the dependence of $ a(M) $ on $ M $, with $ M > 4\,\text{GeV} $ corresponding to early Drell-Yan emission ($ a \approx 1 $), intermediate $ M $ to pre-equilibrium ($ a \approx -0.2 $), and $ M < 1\,\text{GeV} $ to equilibrated plasma ($ a \to 0 $).
• Establishing that the anisotropy parameter $ a(M) $ serves as a clock for equilibration, with its evolution reflecting the transition from early to late stages of the collision.
• Highlighting the need for direct calculation of vector channel spectral functions in strongly coupled plasma, as stress tensor anisotropy may not directly map to parton distribution anisotropy in such systems.

Experimental results

Research questions

• RQ1 How can the angular distribution of dileptons in heavy ion collisions be used to monitor the degree of local parton equilibration?
• RQ2 What is the quantitative relationship between dilepton invariant mass and the equilibration stage of the quark-gluon plasma?
• RQ3 Can the anisotropy parameter $ a(M) $ serve as a clock to track the transition from pre-equilibrium to equilibrated phases?
• RQ4 How do the assumptions linking stress tensor anisotropy to parton distribution anisotropy break down in strongly coupled systems?
• RQ5 What experimental observable can best distinguish between early, pre-equilibrium, and equilibrated stages of the plasma?

Key findings

• The anisotropy parameter $ a(M) $ evolves from $ a \approx 1 $ for high-mass dileptons ($ M > 4\,\text{GeV} $) produced via the Drell-Yan process, indicating strong angular anisotropy from collimated partons.
• For intermediate-mass dileptons ($ m_\phi < M < m_{J/\psi} $), $ a \approx -0.2 $, corresponding to a pre-equilibrium state with transverse pressure dominance and large positive $ \alpha $.
• For low-mass dileptons ($ M < 1\,\text{GeV} $), $ a \to 0 $, indicating isotropic parton distributions consistent with local thermal equilibrium.
• The functional dependence $ a(\alpha) $, derived from the angular distribution model, shows that $ a(\alpha \to \infty) = -1/3 $, representing the extreme pre-equilibrium limit.
• The mass dependence of $ a(M) $ provides a clock-like signal with a sharp transition from positive to negative anisotropy, useful for experimental monitoring of equilibration.
• Theoretical challenges remain in translating stress tensor anisotropy to parton distribution anisotropy in strongly coupled systems, particularly due to non-local effects and channel dependence in spectral functions.