Friction terms in multi-fluid description of heavy-ion collisions

TL;DR

This work develops a charge-transfer friction mechanism for a three-fluid hydrodynamic description of low-energy heavy-ion collisions and implements it in MUFFIN with a chiral equation of state. It shows that CT friction allows finite baryon density in the fireball and introduces α and β to control energy transfer and momentum-space assignment, but CT alone underpredicts midrapidity entropy and struggles to fit both charged-hadron and net-proton data. Introducing shear viscosity with a μ_B-dependent η enhances charged-hadron yields and sharpens the net-proton distribution, underscoring the importance of dissipative effects in multi-fluid dynamics. The study points to the need for bulk viscosity and diffusion in future work and highlights the challenge of achieving simultaneous agreement across multiple observables and collision energies.

Abstract

In multi-fluid description of heavy-ion collisions, the primary scatterings and particle production are described in terms of interaction between fluids, so called friction. These friction terms can be derived from kinetic theory, but they are not unique. We compare different approaches to derive the friction terms, introduce a new ``charge transfer" friction, which allows to move charge to the midrapidity fireball, and implement them in the MUFFIN model. The charge transfer friction is more consistent with the assumption of three fluids clearly separated in momentum space, and allows better comparisons of the experimental data and underlying equation of state. It also leaves room for entropy generation due to dissipation in individual fluids, and we present the first results obtained using viscous multi-fluid dynamics.

Figures (6)

• Figure 1: Pseudo-rapidity distributions of all charged hadrons (left) and rapidity distribution of net protons (right) with the Csernai, IMS and CT friction models using parameter values $\xi_{\rm pt}=1.0$, $\xi_{\rm f}=0.1$ for all models and $\alpha = 0.7$, $\beta = 0.1$ for CT friction. The data are by the PHOBOS PHOBOS:2010eyu and the NA49 NA49:1998gaz collaborations.
• Figure 2: Pseudo-rapidity distributions of all charged hadrons (left) and rapidity distribution of net protons (right) with the CT friction model. Scans over the $\beta$ and $\alpha$ parameters are conducted using $\xi_{\rm pt}=1.0$, $\xi_{\rm f}=0.1$, $\alpha=0.7$ (for top row) and $\beta=0.1$ (for bottom row). The data are by the PHOBOS PHOBOS:2010eyu and the NA49 NA49:1998gaz collaborations.
• Figure 3: Same quantities as in Fig. \ref{['fig:alpha-beta-scan']}, but simulated with different projectile-target friction scaling ($\xi_{\rm pt}$, top row) and different projectile-fireball friction scaling ($\xi_{\rm f}$, bottom row). The other friction settings are $\xi_{\rm f}=0.1$ for the top row ($\xi_{\rm pt}$ scan) and $\xi_{\rm pt}=1.0$ for the bottom row ($\xi_{\rm f}$ scan), and $\alpha=0.7$, $\beta=0.1$ for all plots. The data are by the PHOBOS PHOBOS:2010eyu and the NA49 NA49:1998gaz collaborations.
• Figure 4: Comparison of results from multi-fluid simulations with ideal fluids to fluids with baryon chemical potential dependent shear viscosity from Eq. \ref{['eq:etaS']}. Friction settings $\alpha=0.7$, $\beta=0.1$, $\xi_{\rm pt} = 1.0$, $\xi_{\rm f}=0.1$ are used for this comparison.The data are by the PHOBOS PHOBOS:2010eyu and the NA49 NA49:1998gaz collaborations.
• Figure 5: Best fit to the experimental data, achieved with the friction terms settings $\alpha=0.8$, $\beta=0.1$, $\xi_{f\alpha}=0.1$, $\xi_{pt}=1.0$. For $\sqrt{s_{\rm NN}}=62.4$ GeV, an alternation $\alpha=0.75$, $\xi_{pt}=0.8$ is used. Fluids are evolved with temperature- and baryon chemical potential dependent shear viscosity from Eq. \ref{['eq:etaS']}. Data are by the PHOBOS PHOBOS:2010eyu, NA49 NA49:1998gazBlume:2007kw and BRAHMS BRAHMS:2009wlg collaborations.