Motivation

MotivationWe study the dynamics of the quark-gluon plasma, as created in heavy-ion collisions usingreal-time lattice calculations of coupled particle-field systems in classical SU(N) gauge theory.Because occupation numbers are large in the infra-red, the classical field approximation becomes reasonable. Away from the infra-red however, the degrees of freedom should bedescribed by particles.

We present first results of real-time simulations of the QCD-Boltzmann-Vlasov equationcombining both limits by including the effects of elastic particle collisions and field-particle

interactions. We introduce a separation scale, on the particle momentum transferwhere is the lattice spacing. Above particles undergo point-like binary scatterings and below scatterings occur via self-consistent field deflections. We demonstrate that in an isotropic plasma particle momentum-space diffusion is independent of the lattice spacing in this scheme. Extending this to anisotropic plasmas we determine the effect of binary collisions on theChromo-Weibel-instability and study the influence of instabilities on jet broadening.

Real-time Lattice Simulationsof Heavy-Ion Collisions

CPIC- Colored Particle In Cell method:

The test-particle ansatz allows for a numerical solution of the Vlasov equation and in the collisionless limit leads toWong's equations:

with the coordinates , , and of test particle . is the number of test particles per physical particle.

The time evolution of the Yang-Mills field is determined by the standard Hamiltonian method in gauge.In lattice units the Kogut-Susskind Hamiltonian reads:

with the number of colors .

Inclusion of binary collisions

In addition to the field-particle interaction described above, we include elastic particle-particle collisions with momentum exchange above the intermediate scale .

The total cross section is calculated from the differential pQCD cross section for the diagrams shown above:

Momentum space diffusion

We measure the momentum broadening of hard particles that are placed in a bath of Boltzmann distributed particles and distributed fields, these distributions being the two limits of the Bose-distribution. We set the initial energy density of the fields equal to that in Bose distributed particles up to momentum . As shown on the right this leads to approximate independence of the separation scale in the observable , the average squared transverse momentum gained by the hard particles.

particle-field interaction only

particle-field interaction and hard collisions

Initial setup for the measurement

For the physically mostsensible choice ,about 25% of the momentum diffusion is due to particle-field interactions.

We find a lattice independent value for

for

in an SU(2) plasma and with

For SU(3) a correction due to a color factor applies.

Jet broadening in unstable non-Abelian plasmas

Conclusion We extended the CPIC-simulation by hard particle collisions, which lead to

a new kind of parton-cascade including fields and collective phenomena. Lattice independent results for in an isotropic plasma were determined. Instabilities in an anisotropic plasma create large domains of strong

chromo-fields that cause stronger broadening of jets in than in .

For weakly-coupled anisotropic plasmas the local rotational symmetry in momentum space is broken. The fields develop unstable modes, forming configurations where and . This provides a possible explanation for the experimental observation that high-energy jets traversing the plasma perpendicular to the beam axis experience much stronger broadening in rapidity than in azimuth.

Weibel-instability and filamentation

Mechanism of filamentation

Current filaments and B-field-domains in the simulation during instability growth.

The field configurations during instability growth are such that particles are deflected preferentially in the longitudinal direction (to restore isotropy).

Growing field components.

Stronger longitudinal broadening:

Star preliminary

Observed additional near-side long range correlation in .

Au+Au 0-10%