New constraints on equation of state of hot QCD matter

TL;DR

This work tackles constraining the QCD equation of state (EoS) at finite baryon density by linking longitudinal fluctuations in event-by-event mean $p_T$ to the EoS stiffness. The authors implement a parametric NEOS-BQS-based EoS modified by a stiffness parameter $\alpha$, enabling controlled variation of $c_s^2$ within a (3+1)D viscous hydrodynamic framework and thermodynamic consistency. They show that decorrelations of mean $p_T$—quantified by $R_{p_T}$ and $r_{p_T}$—are strong EoS probes, especially at large rapidity separations, while anisotropic-flow decorrelations $R_{v_n}$ and $r_{v_n}$ are largely insensitive to the EoS and viscosities, highlighting the role of finite-$\mu_B$ dynamics. The results, including implications for BES, FAIR-CBM, NICA, and HIAF programs, suggest forward-rapidity $p_T$ decorrelations as a practical observable to map the QCD phase diagram and constrain the high-density EoS.

Abstract

The longitudinal structure of the quark-gluon plasma(QGP) remains a key challenge in heavy-ion physics. In this Letter, we propose a novel observable, event-by-event mean transverse momentum fluctuations Var$_{\langle p_{T} \rangle}$, which is sensitive to the local pressure gradients and serves as a probe of longitudinal dynamics in the initial state of QGP. We demonstrate that the covariance of averaged transverse momentum at two rapidities $\mathrm{Cov}_{\langle p_T \rangle}(η_1, η_2)$ and its associated decorrelation measures, $R_{p_T}(η_1, η_2)$ and $r_{p_T}(η, η_{\mathrm{ref}})$, exhibit strong sensitivity to the stiffness of equation of state (EoS) of QGP, while showing negligible dependence on the QGP transport coefficients. This distinctive behavior, revealed through state-of-the-art (3+1)-dimensional hydrodynamic simulations, establishes a powerful approach for constraining the EoS of QCD matter. In the meantime, our results provide new insights into the longitudinal structure of the QGP and its properties under high baryon density.

Figures (6)

• Figure 1: Squared speed of sound ($c_s^2$) as a function of temperature, computed under the isentropic condition $s/n_B = 51$ for $^{197}$Au+$^{197}$Au collisions at $\sqrt{s_{\rm NN}} = 19.6\ \mathrm{GeV}$ using different EoS parametrizations. The fireball effective temperature can be estimated via the approximate relation $T_\mathrm{eff} \approx \left\llangle p_T\right\rrangle / 3 \approx 0.18~\mathrm{GeV}$Gardim:2019xjs.
• Figure 2: The pseudorapidity $\eta$ distribution of anisotropic flow coefficients $v_2^2$ (a) and $v_3^2$ (b) on in 0-10% central $^{197}$Au+$^{197}$Au collisions at 19.6 GeV with different EoS and viscosity parameters presented in Table \ref{['tab:parameters']}. The STAR data is taken from Refs. STAR:2017idkSTAR:2016vqt.
• Figure 3: The pseudorapidity $\eta$ distribution of mean transverse momentum $\left\llangle p_T\right\rrangle_\eta$ (a) and it's covariance $\operatorname{Var}_{\left\langle p_T\right\rangle} \left({\eta}\right)$ (b) in 0-10% central $^{197}$Au+$^{197}$Au collisions at 19.6 GeV.
• Figure 4: Mean transverse momentum decorrelation coefficients in 0--10% central $^{197}$Au+$^{197}$Au collisions. Panels (a) and (b) show $\operatorname{Cov}_{\left\langle p_T\right\rangle}(\eta_1, \eta_2)$ with $\eta_1 = -0.5$ and $\eta_1 = -1$, respectively; Panels (c) and (d) show $R_{p_T}(\eta_1, \eta_2)$ with $\eta_1 = -0.5$ and $\eta_1 = -1$, respectively; Panels (e) and (f) present $r_{p_T}(\eta, \eta_{\mathrm{ref}})$ with $\eta_{\mathrm{ref}} = 0.5$ and $\eta_{\mathrm{ref}} = 1$, respectively.
• Figure 5: $v_2$ decorrelation coefficients $R_{v_2}$ and $r_{{v_2}}$ in 0--10% central $^{197}$Au+$^{197}$Au collisions at $\sqrt{s_{\rm NN}}=$ 19.6 GeV. Panels (a) and (b) show $R_{v_2}(\eta_1, \eta_2)$ with $\eta_1 = -0.5$ and $\eta_1 = -1$, respectively; Panels (c) and (d) present $r_{v_2}(\eta, \eta_{\mathrm{ref}})$ with $\eta_{\mathrm{ref}} = 0.5$ and $\eta_{\mathrm{ref}} = 1$, respectively.