[Paper Review] Can Binary Bound States in a Strongly Coupled Quark-Gluon Plasma be observed via dileptons and photons?

Jorge Casalderrey-Solana, Edward Shuryak|ArXiv.org|Aug 16, 2004

High-Energy Particle Collisions Research2 references3 citations

TL;DR

This paper proposes detecting binary bound states in a strongly coupled quark-gluon plasma (sQGP) via dilepton and photon spectra, focusing on modified $ houn$ and $ ho$ resonances near $T_c$ and threshold enhancements at $M \sim 1.5-2$ GeV. Using non-relativistic Green's functions and fireball averaging, it shows that peaks from bound states and near-threshold states can survive smearing and may be observable in dilepton spectra, though $̳\gamma\gamma$ signals are strongly suppressed by chiral symmetry restoration.

ABSTRACT

Recently there was a significant change of views on physical properties and underlying dynamics of Quark-Gluon Plasma at $T=170-350 MeV$, produced in heavy ion collisions at RHIC. Instead of weakly coupled gas of quasiparticles, it is rather a liquid-like matter with multiple bound states. In this paper we discuss how one can test these ideas experimentally, using the ``penetrating probes'' and looking for certain peaks at some invariant masses. In dileptons the most promising are modified $ρ,ω$, with $M(T\approx T_c)\sim .5 GeV$ and also near zero binding at $M(T\approx (1.5-2)T_c)=1.5-2 GeV$. We also discuss the observability of peaks corresponding to scalar/pseudoscalar mesons in the two-photon channel.

Motivation & Objective

• To investigate whether binary bound states in a strongly coupled quark-gluon plasma (sQGP) can be probed experimentally using dileptons and photons.
• To identify specific invariant mass regions where bound states or threshold enhancements might produce observable peaks in dilepton spectra despite thermal smearing.
• To assess the feasibility of detecting scalar and pseudoscalar mesons via the two-photon decay channel in sQGP.
• To evaluate the impact of quark masses, in-medium modifications, and chiral symmetry restoration on the observability of these signals.
• To provide a theoretical framework for interpreting future experimental data from RHIC and LHC in terms of sQGP structure.

Proposed method

• Uses the dilepton production rate formula $ dR/d^4x d^4q = \alpha^2/(48\pi^4) \cdot 1/(e^{q_0/T}-1) \cdot F $, with $ F $ representing form factors for $ \rho, \omega $ and weakly coupled QGP.
• Applies non-relativistic Green's functions to compute annihilation rates in the sQGP, including both bound and unbound states.
• Performs space-time averaging over an expanding fireball using RHIC parameters, integrating over $ t \sim 5\,\text{fm} $ and $ T \sim 170-350\,\text{MeV} $.
• Evaluates the two-photon decay rate $ dR/d^4x d^4q \propto \Gamma_{\gamma\gamma} \cdot n \cdot t_{\text{QGP}} $, with suppression from chiral symmetry restoration.
• Compares rates to a 'standard candle' wQGP model with $ F_{\text{wQGP}} = 24 $, normalizing predictions.
• Uses lattice QCD-inspired estimates for in-medium spectral functions and accounts for $ T $-dependent quark masses and widths.

Experimental results

Research questions

• RQ1 Can binary bound states in sQGP produce observable peaks in dilepton spectra despite thermal smearing during fireball expansion?
• RQ2 Are there specific invariant mass regions—such as near $ T_c $ or at $ M \sim 1.5-2\,\text{GeV} $—where modified $ \rho, \omega $ resonances or threshold enhancements are most likely to be detected?
• RQ3 To what extent are $ \gamma\gamma $ signals from scalar and pseudoscalar mesons like $ \eta, \eta' $ observable in sQGP, given suppression from chiral symmetry restoration?
• RQ4 How do in-medium modifications of quark masses and interactions affect the spectral functions and production rates of dileptons and photons?
• RQ5 Can non-relativistic Green's functions accurately describe the annihilation rates of bound states in a strongly coupled medium?

Key findings

• Peaks in dilepton spectra from modified $ \rho, \omega $ resonances are most prominent near $ T_c \approx 170\,\text{MeV} $, with invariant masses $ M \sim 0.5\,\text{GeV} $, and near $ (1.5-2)T_c $, with $ M \sim 1.5-2\,\text{GeV} $.
• The time-integrated fireball averaging does not fully wash out the peaks from bound states or threshold enhancements, especially near the two endpoints of the sQGP regime.
• The two-photon signal from $ \eta, \eta' $ mesons is suppressed by about four orders of magnitude due to the smallness of $ \Gamma_{\gamma\gamma} $ in the chirally symmetric phase.
• The suppression factor for $ \gamma\gamma $ widths at $ T > T_c $ is estimated as $ \sim (m_s/M)^2 $, reducing the signal by an order of magnitude for strange mesons.
• Additional states such as scalars and plasminos could enhance the $ \gamma\gamma $ rate by a factor of 8, but this is offset by strong suppression from chiral symmetry.
• The paper concludes that while dilepton signals from bound states are potentially observable, the $ \gamma\gamma $ channel remains highly challenging due to background and suppression.