Validation and improvement of the ZPC parton cascade inside a box

Abstract

Cascade solutions of the Boltzmann equation suffer from causality violation at high densities and/or scattering cross sections. Although the particle subdivision technique can reduce the causality violation, it alters event-byevent correlations and fluctuations and is also computationally expensive. Here we evaluate and then improve the accuracy of the ZPC parton cascade for elastic scatterings inside a box without using parton subdivision. We first test different collision schemes for the collision times and ordering time and find that the default collision scheme does not accurately describe the equilibrium momentum distribution at large opacities. We then find a specific collision scheme that can describe very accurately the equilibrium momentum distribution as well as the time evolution towards equilibrium, even at large opacities. We also calculate the shear viscosity and the η/s ratio of the parton systems and confirm that the new collision scheme is more accurate. In addition, we use a novel parton subdivision method to obtain the "exact" evolution of the system. This subdivision method is valid for such box calculations and is so much more efficient than the standard subdivision method that we use a subdivision factor of 10 6 in this study.

Further developments of a multi-phase transport model for relativistic nuclear collisions

“…We see that the time evolution of the p T variance from the default scheme deviates significantly from the ''exact'' parton subdivision result, although the time evolutions of hp T i are close to each other (mostly due to the conservation of total momentum). In contrast, the time evolution of the p T variance from the new scheme [261] is very close to the parton subdivision result, which at late times agrees with theoretical expectation (diamond). By examining cases of different parton densities and cross sections [261], we find rather surprisingly that the new scheme for ZPC gives very accurate results (i.e., very close to parton subdivision results and/or theoretical values) even at very large opacities, such as the case of T ¼ 0:7 GeV and r p ¼ 10 mb.…”

“…In contrast, the time evolution of the p T variance from the new scheme [261] is very close to the parton subdivision result, which at late times agrees with theoretical expectation (diamond). By examining cases of different parton densities and cross sections [261], we find rather surprisingly that the new scheme for ZPC gives very accurate results (i.e., very close to parton subdivision results and/or theoretical values) even at very large opacities, such as the case of T ¼ 0:7 GeV and r p ¼ 10 mb.…”

“…19a that the final distribution from the default ZPC scheme deviates considerably from the expected thermal distribution (dotted curve). On the other hand, we find that a new collision scheme, which uses minðct 1 ; ct 2 Þ as both the collision time and ordering time, gives a final distribution very close to the thermal distribution [261]. The causality violation usually suppresses collision rates, which is the case for the default ZPC scheme; it is therefore understandable that choosing time minðct 1 ; ct 2 Þ instead of ðct 1 þ ct 2 Þ=2 enhances the collision rates and thus suppresses the causality violation.…”

“…Therefore, it is preferred to improve the parton cascade to yield solutions that are accurate enough without using parton subdivision. We have recently pursued this goal for box calculations [261].…”

“…However, because of the finite r p the two partons have different spatial coordinates in general; this collision time in the two-parton center of mass frame thus becomes two different collision times in the global frame (named here as ct 1 and ct 2 , respectively, for the two colliding partons) after the Lorentz transformation. The default collision scheme of ZPC [109] uses ðct 1 þ ct 2 Þ=2 as both the collision time and ordering time; this is the case for the AMPT model [13] Results from the default ZPC scheme [261] at r p ¼ 2:6 mb are shown in Fig. 19 (curves with open circles).…”