Correlations of conserved quantities at finite baryon density

Oleh Savchuk and Scott Pratt

Phys. Rev. C 109, 024910 – Published 14 February 2024

Abstract

Correlations involving the seven conserved quantities, namely energy, baryon number, electric charge, strangeness, and the three components of momentum, give rise to correlations in heavy-ion collisions. Through the utilization of a simple one-dimensional hydrodynamic model, we calculate the evolution of the entire $7 \times 7$ matrix of correlations as a function of relative spatial rapidity. This comprehensive analysis accounts for finite baryon density, which results in off-diagonal correlations between the charge-related quantities and the energy-momentum quantities. These correlations in coordinate space are subsequently transformed into correlations in momentum space using statistical weighting. The entire matrix of correlations is revealed to be highly sensitive to the equation of state, viscosity, and diffusivity.

Received 14 November 2023
Accepted 16 January 2024

DOI:https://doi.org/10.1103/PhysRevC.109.024910

Physics Subject Headings (PhySH)

Equations of state of nuclear matter QCD phenomenology Relativistic heavy-ion collisions

Relativistic hydrodynamics

Fluid DynamicsStatistical Physics & ThermodynamicsNuclear Physics

Authors & Affiliations

Oleh Savchuk^1,2,* and Scott Pratt^3,1

¹Facility for Rare Isotope Beams, Michigan State University, East Lansing, Michigan 48824, USA
²Bogolyubov Institute for Theoretical Physics, 03680 Kyiv, Ukraine
³Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA

^*Corresponding author: savchuk@frib.msu.edu

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Vol. 109, Iss. 2 — February 2024

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Images

Figure 1
The speed of sound is displayed for a noninteracting (ideal) hadron resonance gas and a hadronic fluid with two illustrative cases for interactions. The equation of state that includes interactions can be either stiffer (Hard-EoS) or softer (Soft-EoS) compared to the noninteracting one (ideal HRG).
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Figure 2
The susceptibilities of energy-energy (a), energy-baryon density (b), baryon-baryon densities (c), and momentum-momentum (d) are shown for the three equations of state that were considered. The difference between different EoS is reflected in the susceptibilities of conserved charges.
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Figure 3
Green's functions, denoted as $G_{Y X} (τ_{source} = 1 fm / c, τ = 11 fm / c, Δ η)$ , represent the response to a perturbation in $X$ , initiated at $1 fm / c$ at $η = 0$ and observed in $Y$ at $Δ η$ . Panels (a)–(d) display $G_{Y X}$ for $Y = E, P_{η}, P_{x}$ , and $B$ , respectively. For each $Y$ , each panel shows the nonzero Green's functions for the quantities described in the legends. These functions are computed for the soft version of the equation of state, and further details can be found in the accompanying text. Cross-correlations between different conserved charges are considered, including longitudinal energy-momentum, baryon, and electric charges. To enhance visibility, some of the functions were scaled by large factors.
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Figure 4
The matrix of two-point correlations for energy, longitudinal momentum, and baryon, electric, and strange charges is presented as a function of space-time rapidity distance at the freeze-out time $τ = 11 fm / c$ . The considered equations of state include the ideal hadron resonance gas (in blue), hard hadronic fluid (in orange), and soft hadronic fluid (in green). Transverse fluctuations of the system are decoupled from other observables and can be found in a separate plot. $N_{ch}$ is charged particle multiplicity per unit of $η$ as predicted from statistical hadronization at $T = 150$ MeV with transverse area $S = 100$ ${fm}^{2}$ .
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Figure 5
Balancing part for the correlations of transverse momentum $P_{x, y}$ as function of space-time (left) or momentum (right) rapidity differences. As predicted from hydrodynamic evolution with thermal sources before (left) and after particle creation (right). $N_{ch}$ is charged particle multiplicity per unit of $η$ as predicted from statistical hadronization at $T = 150$ MeV with transverse area $S = 100$ ${fm}^{2}$ .
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Figure 6
The matrix of two-point correlations for energy, longitudinal momentum, and baryon, electric, and strange charges is presented as a function of momentum rapidity at the freeze-out time $τ = 11 fm / c$ , computed after sampling all charged particles. The equations of state considered include the ideal hadron resonance gas (in blue), interacting hadronic fluid (in orange), and a fluid with a phase transition (in green). It is important to note that transverse fluctuations of the system do not affect the longitudinal observables, and momentum fluctuations completely cancel out. $N_{ch}$ is charged particle multiplicity per unit of $η$ as predicted from statistical hadronization at $T = 150$ MeV with transverse area $S = 100$ ${fm}^{2}$ .
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