Gluon production at high transverse momentum in the McLerran-Venugopalan model of nuclear structure functions

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.

On transverse momentum broadening in real-time lattice simulations of the glasma and in the weak-field limit

In these proceedings, we report on our numerical lattice simulations of partons traversing the boost-invariant, non-perturbative glasma as created at the early stages of collisions at RHIC and LHC. Since these highly energetic partons are produced from hard scatterings during heavy-ion collisions, they are already affected by the first stage of the medium's time evolution, the glasma, which is the pre-equilibrium precursor state of the quark-gluon plasma. We find that partons quickly accumulate transverse momentum up to the saturation momentum during the glasma stage. Moreover, we observe an interesting anisotropy in transverse momentum broadening of partons with larger broadening in the rapidity than in the azimuthal direction. Its origin can be related to correlations among the longitudinal color-electric and color-magnetic flux tubes in the initial state of the glasma. We compare these observations to the semi-analytic results obtained by a weak-field approximation, where we also find such an anisotropy in a parton's transverse momentum broadening.

Progress on 3+1D Glasma simulations

We review our progress on 3+1D Glasma simulations to describe the earliest stages of heavy-ion collisions. In our simulations we include nuclei with finite longitudinal extent and describe the collision process as well as the evolution of the strongly interacting gluonic fields in the laboratory frame in 3+1 dimensions using the colored particle-in-cell method. This allows us to compute the 3+1 dimensional Glasma energy-momentum tensor, whose rapidity dependence can be compared to experimental pion multiplicity data from RHIC. An improved scheme cures the numerical Cherenkov instability and paves the way for simulations at higher energies used at LHC.

The Fragmentation Region of High Energy Nucleus-Nucleus and Hadron-Nucleus Collisions

The fragmentation region of particles produced in high energy nuclear collisions provides a laboratory for studying high baryon number density systems. This talk outlines work in progress that attempts to compute properties of the matter produced in these collisions at the highest energies.

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.

Forward quark jets from protons shattering the color glass condensate

We consider the single-inclusive minijet cross section in pA at forward rapidity within the color glass condensate model of high energy collisions. We show that the nucleus appears black to the incident quarks except for very large impact parameters. A markedly flatter p(t) distribution as compared to QCD in the dilute perturbative limit is predicted for transverse momenta about the saturation scale, which could be as large as Q(2)(s) approximately 10 GeV2 for a gold nucleus boosted to rapidity approximately 10 (as at the BNL-RHIC).

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.

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).

Geometric scaling for the total gamma(*)p cross section in the low x region

We observe that the saturation model of deep inelastic scattering predicts a geometric scaling of the total gamma(*)p cross section in the region of small Bjorken variable x. The geometric scaling in this case means that the cross section is a function of only one dimensionless variable tau = Q(2)R(2)(0)(x), where the function R(0)(x) decreases with decreasing x. We show that the experimental data from HERA in the region x<0.01 confirm the expectations of this scaling over a very broad region of Q(2). We suggest that the geometric scaling is more general than the saturation model.

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

In very-high-energy nuclear collisions, the initial energy of produced gluons per unit area per unit rapidity, (dE/L2)/deta, is equal to f(g(2)&mgr;L) (g(2)&mgr;)(3)/g(2), where &mgr;(2) is proportional to the gluon density per unit area of the colliding nuclei. For an SU(2) gauge theory, a nonperturbative computation of f(g(2)&mgr;L) shows that it varies rapidly for small g(2)&mgr;L but varies only by approximately 25%, from 0.208+/-0.004 to 0.257+/-0. 005, for a wide range 35.36- 296.98 in g(2)&mgr;L. This includes the range relevant for collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). Extrapolating to SU(3), we estimate dE/deta for Au-Au collisions in the central region at RHIC and LHC.