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# A relativistic dissipative hydrodynamic description for systems including particle number changing processes

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### Abstract

Relativistic dissipative hydrodynamic equations are extended by taking into account particle number changing processes in a gluon system, which expands in one dimension boost-invariantly. Chemical equilibration is treated by a rate equation for the particle number density based on Boltzmann equation and Grad's ansatz for the off-equilibrium particle phase space distribution. We find that not only the particle production, but also the temperature and the momentum spectra of the gluon system, obtained from the hydrodynamic calculations, are sensitive to the rates of particle number changing processes. Comparisons of the hydrodynamic calculations with the transport ones employing the parton cascade BAMPS show the inaccuracy of the rate equation at large shear viscosity to entropy density ratio. To improve the rate equation, the Grad's ansatz has to be modified beyond the second moments in momentum.

### Most cited references3

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### Elliptic flow at large transverse momenta from quark coalescence

,   (2003)
We show that hadronization via quark coalescence enhances hadron elliptic flow at large pT relative to that of partons at the same transverse momentum. Therefore, compared to earlier results based on covariant parton transport theory, more moderate initial parton densities dN/d\eta(b=0) ~ 1500-3000 can explain the differential elliptic flow v_2(pT) data for Au+Au reactions at s^1/2=130 and 200 AGeV from RHIC. In addition, v2(pT) could saturate at about 50% higher values for baryons than for mesons. If strange quarks have weaker flow than light quarks, hadron v_2 at high pT decreases with relative strangeness content.
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### Scaling behavior at high p_T and the p/pi ratio

,   (2002)
We first show that the pions produced at high $$p_T$$ in heavy-ion collisions over a wide range of high energies exhibit a scaling behavior when the distributions are plotted in terms of a scaling variable. We then use the recombination model to calculate the scaling quark distribution just before hadronization. From the quark distribution it is then possible to calculate the proton distribution at high $$p_T$$, also in the framework of the recombination model. The resultant $$p/\pi$$ ratio exceeds one in the intermediate $$p_T$$ region where data exist, but the scaling result for the proton distribution is not reliable unless $$p_T$$ is high enough to be insensitive to the scale-breaking mass effects.
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### Shear viscosity and out of equilibrium dynamics

(2008)
Using Grad's method, we calculate the entropy production and derive a formula for the second-order shear viscosity coefficient in a one-dimensionally expanding particle system, which can also be considered out of chemical equilibrium. For a one-dimensional expansion of gluon matter with Bjorken boost invariance, the shear tensor and the shear viscosity to entropy density ratio $$\eta/s$$ are numerically calculated by an iterative and self-consistent prescription within the second-order Israel-Stewart hydrodynamics and by a microscopic parton cascade transport theory. Compared with $$\eta/s$$ obtained using the Navier-Stokes approximation, the present result is about 20% larger at a QCD coupling $$\alpha_s \sim 0.3$$(with $$\eta/s\approx 0.18$$) and is a factor of 2-3 larger at a small coupling $$\alpha_s \sim 0.01$$. We demonstrate an agreement between the viscous hydrodynamic calculations and the microscopic transport results on $$\eta/s$$, except when employing a small $$\alpha_s$$. On the other hand, we demonstrate that for such small $$\alpha_s$$, the gluon system is far from kinetic and chemical equilibrium, which indicates the break down of second-order hydrodynamics because of the strong noneqilibrium evolution. In addition, for large $$\alpha_s$$ ($$0.3-0.6$$), the Israel-Stewart hydrodynamics formally breaks down at large momentum $$p_T\gtrsim 3$$ GeV but is still a reasonably good approximation.
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### Author and article information

###### Journal
1007.0705
10.1016/j.nuclphysa.2010.09.011

High energy & Particle physics, Nuclear physics