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We derive the collision term in the Boltzmann equation using the equation of motion for the Wigner function of massive spin-1/2 particles. To next-to-lowest order in h, it contains a nonlocal contribution, which is responsible for the conversion of orbital into spin angular momentum. In a proper choice of pseudogauge, the antisymmetric part of the energy-momentum tensor arises solely from this nonlocal contribution. We show that the collision term vanishes in global equilibrium and that the spin potential is, then, equal to the thermal vorticity. In the nonrelativistic limit, the equations of motion for the energy-momentum and spin tensors reduce to the well-known form for hydrodynamics for micropolar fluids.
The amount of proton stopping in central Pb+Pb collisions from 20 160 A·GeV as well as hyperon and antihyperon rapidity distributions are calcu- lated within the UrQMD model in comparison to experimental data at 40, 80 and 160 A·GeV taken recently from the NA49 collaboration. Further- more, the amount of baryon stopping at 160 A·GeV for Pb + Pb collisions is studied as a function of centrality in comparison to the NA49 data. We find that the strange baryon yield is reasonably described for central colli- sions, however, the rapidity distributions are somewhat more narrow than the data. Moreover, the experimental antihyperon rapidity distributions at 40, 80 and 160 A·GeV are underestimated by up to factors of 3 - depending on the annihilation cross section employed - which might be addressed to missing multi-meson fusion channels in the UrQMD model. PACS 25.75.+r
We study central collision of Pb + Pb at 20, 40, 80 and 160 A·GeV within the UrQMD transport approach and compare rapidity distributions of ,K+,K and with the recent measurements from the NA49 Collaboration at 40, 80 and 160 A·GeV. It is found that the UrQMD model reasonably describes the data, however, systematically overpredicts the yield by < 20%, whereas the K+ yield is underestimated by < 15%. The K yields are in a good agreement with the experimental data, the yields are also in a reasonable correspondence with the data for all energies. We find that hadronic flavour exchange reactions largely distort the information about the initial strangeness production mechanism at all energies considered. PACS: 25.75.+r
We calculate p, ±,K± and (+ 0) rapidity distributions and compare to experimental data from SIS to SPS energies within the UrQMD and HSD transport approaches that are both based on string, quark, diquark (q, ¯q, qq, ¯q ¯q) and hadronic degrees of freedom. The two transport models do not include any explicit phase transition to a quark-gluon plasma (QGP). It is found that both approaches agree rather well with each other and with the experimental rapidity distributions for protons, s, ± and K±. In- spite of this apparent agreement both transport models fail to reproduce the maximum in the excitation function for the ratio K+/ + found experimen- tally between 11 and 40 A·GeV. A comparison to the various experimental data shows that this failure is dominantly due to an insu cient description of pion rapidity distributions rather than missing strangeness . The modest di erences in the transport model results on the other hand can be attributed to di erent implementations of string formation and frag- mentation, that are not su ciently controlled by experimental data for the elementary reactions in vacuum.
ϕ-meson production in In–In collisions at Elab=158A GeV: Evidence for relics of a thermal phase
(2010)
Yields and transverse mass distributions of the ϕ-mesons reconstructed in the ϕ→μ+μ− channel in In+In collisions at Elab=158A GeV are calculated within an integrated Boltzmann+hydrodynamics hybrid approach based on the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) transport model with an intermediate hydrodynamic stage. The analysis is performed for various centralities and a comparison with the corresponding NA60 data in the muon channel is presented. We find that the hybrid model, that embeds an intermediate locally equilibrated phase subsequently mapped into the transport dynamics according to thermal phase-space distributions, gives a good description of the experimental data, both in yield and slope. On the contrary, the pure transport model calculations tend to fail in catching the general properties of the ϕ meson production: not only the yield, but also the slope of the mT spectra, compare poorly with the experimental observations at top SPS energies.
We investigate the effect of large magnetic fields on the (2 + 1)-dimensional reduced-magnetohydrodynamical expansion of hot and dense nuclear matter produced in √sNN = 200 GeV Au+Au collisions. For the sake of simplicity,we consider the casewhere themagnetic field points in the direction perpendicular to the reaction plane. We also consider this field to be external, with energy density parametrized as a two-dimensional Gaussian. The width of the Gaussian along the directions orthogonal to the beam axis varies with the centrality of the collision. The dependence of the magnetic field on proper time (τ ) for the case of zero electrical conductivity of the QGP is parametrized following Deng et al. [Phys. Rev. C 85, 044907 (2012)], and for finite electrical conductivity following Tuchin [Phys. Rev. C 88, 024911 (2013)].We solve the equations of motion of ideal hydrodynamics for such an external magnetic field. For collisions with nonzero impact parameter we observe considerable changes in the evolution of the momentum eccentricities of the fireball when comparing the case when the magnetic field decays in a conducting QGP medium and when no magnetic field is present. The elliptic-flow coefficient v2 of π− is shown to increase in the presence of an external magnetic field and the increment in v2 is found to depend on the evolution and the initial magnitude of the magnetic field.
In this paper a new method of experimental data analysis, the Particle-Set Identification method, is presented. The method allows to reconstruct moments of multiplicity distribution of identified particles. The difficulty the method copes with is due to incomplete particle identification – a particle mass is frequently determined with a resolution which does not allow for a unique determination of the particle type. Within this method the moments of order k are calculated from mean multiplicities of k-particle sets of a given type. The Particle-Set Identification method remains valid even in the case of correlations between mass measurements for different particles. This distinguishes it from the Identity method introduced by us previously to solve the problem of incomplete particle identification in studies of particle fluctuations.
We investigate the long-standing question of the effect of proton-antiproton annihilation on the (anti-)proton yield, while respecting detailed balance for the five-body back-reaction for the first time in a full microscopic description of the late stages of heavy-ion collisions. This is achieved by employing a stochastic collision criterion in a hadronic transport approach (SMASH), which is used to account for the regeneration of (anti-)protons via 5π→p¯p. We investigate Au+Au and Pb+Pb collisions from √sNN=17.3GeV−5.02 TeV in a viscous hybrid approach. Our results show that back-reactions happen for a fraction of 15%–20% of all annihilations, independent of the beam energy or centrality of the system. The inclusion of the back-reaction results in the regeneration of half of the (anti-)proton yield lost to annihilations at midrapidity. We also find that, concerning the multiplicities, treating the back-reaction as a chain of two-body reactions is equivalent to a single 5-to-2 reaction.
We study the diffusion properties of the strongly interacting quark-gluon plasma (sQGP) and evaluate the diffusion coefficient matrix for the baryon (B), strange (S) and electric (Q) charges—κqq′ (q,q′=B,S,Q) and show their dependence on temperature T and baryon chemical potential μB. The nonperturbative nature of the sQGP is evaluated within the dynamical quasiparticle model (DQPM) which is matched to reproduce the equation of state of the partonic matter above the deconfinement temperature Tc from lattice QCD. The calculation of diffusion coefficients is based on two methods: (i) the Chapman-Enskog method for the linearized Boltzmann equation, which allows to explore nonequilibrium corrections for the phase-space distribution function in leading order of the Knudsen numbers as well as (ii) the relaxation time approximation (RTA). In this work we explore the differences between the two methods. We find a good agreement with the available lattice QCD data in case of the electric charge diffusion coefficient (or electric conductivity) at vanishing baryon chemical potential as well as a qualitative agreement with the recent predictions from the holographic approach for all diagonal components of the diffusion coefficient matrix. The knowledge of the diffusion coefficient matrix is also of special interest for more accurate hydrodynamic simulations.
Using combined data from the Relativistic Heavy Ion and Large Hadron Colliders, we constrain the shear and bulk viscosities of quark-gluon plasma (QGP) at temperatures of ∼150–350 MeV. We use Bayesian inference to translate experimental and theoretical uncertainties into probabilistic constraints for the viscosities. With Bayesian model averaging we propagate an estimate of the model uncertainty generated by the transition from hydrodynamics to hadron transport in the plasma’s final evolution stage, providing the most reliable phenomenological constraints to date on the QGP viscosities.