Initial energy density of gluons produced in very-high-energy nuclear collisions

Quasiclassical Gluon Fields and Low's Soft Theorem at Small Momentum-Fraction x

In the high-energy limit, soft gluons can be approximately described by quasiclassical gluon fields. It is well known that the gluon field is a pure gauge field on the transverse plane at eikonal order. We derived the complete next-to-eikonal order solutions of the classical Yang-Mills equations for soft gluons in the dense nuclear regime. Utilizing these solutions, it is shown that Low's soft theorem at small x can be obtained by considering off-diagonal matrix elements of quasiclassical chromoelectric field between single-gluon states in the dilute regime. We further propose on extending Low's soft theorem at small x to incorporate the effects of gluon saturation in the dense regime.

Effect of Longitudinal Fluctuations of 3D Weizsäcker-Williams Field on Pressure Isotropization of Glasma

We investigate the effects of boost invariance breaking on the isotropization of pressure in the glasma, using a 3+1D glasma simulation. The breaking is attributed to spatial fluctuations in the classical color charge density along the collision axis. We present numerical results for pressure and energy density at mid-rapidity and across a wider rapidity region. It is found that, despite varying longitudinal correlation lengths, the behaviors of the pressure isotropizations are qualitatively similar. The numerical results suggest that, in the initial stage, longitudinal color electromagnetic fields develop, similar to those in the boost invariant glasma. Subsequently, these fields evolve into a dilute glasma, expanding longitudinally in a manner akin to a dilute gas. We also show that the energy density at mid-rapidity exhibits a 1/τ decay in the dilute glasma stage.

Some aspects of the theory of heavy ion collisions

We review the theoretical aspects relevant in the description of high-energy heavy ion collisions, with an emphasis on the learnings about the underlying quantum chromodynamics phenomena that have emerged from these collisions.

Importance of the Bulk Viscosity of QCD in Ultrarelativistic Heavy-Ion Collisions

We investigate the consequences of a nonzero bulk viscosity coefficient on the transverse momentum spectra, azimuthal momentum anisotropy, and multiplicity of charged hadrons produced in heavy ion collisions at LHC energies. The agreement between a realistic 3D hybrid simulation and the experimentally measured data considerably improves with the addition of a bulk viscosity coefficient for strongly interacting matter. This paves the way for an eventual quantitative determination of several QCD transport coefficients from the experimental heavy ion and hadron-nucleus collision programs.

Event-by-event anisotropic flow in heavy-ion collisions from combined Yang-Mills and viscous fluid dynamics

Anisotropic flow coefficients v(1)-v(5) in heavy ion collisions are computed by combining a classical Yang-Mills description of the early time Glasma flow with the subsequent relativistic viscous hydrodynamic evolution of matter through the quark-gluon plasma and hadron gas phases. The Glasma dynamics, as realized in the impact parameter dependent Glasma (IP-Glasma) model, takes into account event-by-event geometric fluctuations in nucleon positions and intrinsic subnucleon scale color charge fluctuations; the preequilibrium flow of matter is then matched to the music algorithm describing viscous hydrodynamic flow and particle production at freeze-out. The IP-Glasma+MUSIC model describes well both transverse momentum dependent and integrated v(n) data measured at the Large Hadron Collider and the Relativistic Heavy Ion Collider. The model also reproduces the event-by-event distributions of v(2), v(3) and v(4) measured by the ATLAS Collaboration. The implications of our results for better understanding of the dynamics of the Glasma and for the extraction of transport properties of the quark-gluon plasma are outlined.

Fluctuating glasma initial conditions and flow in heavy ion collisions

We compute initial conditions in heavy ion collisions within the color glass condensate framework by combining the impact parameter dependent saturation model with the classical Yang-Mills description of initial Glasma fields. In addition to fluctuations of nucleon positions, this impact parameter dependent Glasma description includes quantum fluctuations of color charges on the length scale determined by the inverse nuclear saturation scale Q(s). The model naturally produces initial energy fluctuations that are described by a negative binomial distribution. The ratio of triangularity to eccentricity ε(3)/ε(2) is close to that in a model tuned to reproduce experimental flow data. We compare transverse momentum spectra and v(2,3,4)(p(T)) of pions from different models of initial conditions using relativistic viscous hydrodynamic evolution.

Collective non-Abelian instabilities in a melting color glass condensate

We present first results for (3 + 1)D simulations of SU(2) Yang-Mills equations for matter expanding into the vacuum after a heavy ion collision. Violations of boost invariance cause a non-Abelian Weibel instability leading soft modes to grow with proper time tau as exp(gamma square root(g2 mu tau)), where g2 mu is a scale arising from the saturation of gluons in the nuclear wave function. The scale for the growth rate gamma is set by a plasmon mass, defined as omega(pl) = kappa0 square root(g2 mu/tau)), generated dynamically in the collision. We compare the numerical ratio gamma/kappa0 to the corresponding value predicted by the hard thermal loop formalism for anisotropic plasmas.

Coherent gluon production in very-high-energy heavy-ion collisions

The early stages of a relativistic heavy-ion collision are examined in the framework of an effective classical SU(3) Yang-Mills theory in the transverse plane. We compute the initial energy and number distributions, per unit rapidity, at midrapidity, of gluons produced in high-energy heavy-ion collisions. We discuss the phenomenological implications of our results in light of the recent Relativistic Heavy-Ion Collider data.

Energy and centrality dependence of rapidity densities at RHIC energies

The energy and centrality dependence of the charged multiplicity per participant nucleon is shown to be able to differentiate between final state saturation and fixed scale perturbative QCD models of initial entropy production in high-energy heavy-ion collisions. The energy dependence is shown to test the nuclear enhancement of the minijet component of the initial conditions, while the centrality dependence provides a key test of whether gluon saturation is reached at RHIC energies. The HIJING model predicts that the rapidity density per participant increases with centrality, while the saturation model prediction is essentially independent of centrality.

Initial gluon multiplicity in heavy-ion collisions

The initial gluon multiplicity per unit area per unit rapidity, dN/L2/d eta, in high energy nuclear collisions, is equal to f(N)(g(2)mu L) (g(2)mu)(2)/g(2), with mu(2) proportional to the gluon density per unit area of the colliding nuclei. For an SU(2) gauge theory, we compute f(N)(g(2)mu L) = 0.14 +/- 0.01 for a wide range in g(2)mu L. Extrapolating to SU(3), we predict dN/L2/d eta for values of g(2)mu L relevant to the Relativistic Heavy Ion Collider and the Large Hadron Collider. We compute the initial gluon transverse momentum distribution, dN/L2/d(2)k( perpendicular), and show it to be well behaved at low k( perpendicular).