Search Results (29 total)

We show that the enhancement of the saturation scale in large nuclei relative to the proton is significantly influenced by the effects of quantum evolution and the impact parameter dependence of dipole cross sections in high energy QCD. We demonstrate that there is a strong A dependence in diffractive deeply inelastic scattering and discuss its sensitivity to the measurement of the recoil nucleus.

Recent estimates that color glass condensate initial conditions may generate a larger initial eccentricity for noncentral relativistic heavy ion collisions (relative to the initial eccentricity assumed in earlier hydrodynamic calculations) have raised the possibility of a higher bound on the viscosity of the qark gluon plasma. We show that this large initial eccentricity results in part from a definition of the saturation scale as proportional to the number of nucleons participating in the collision. A saturation scale proportional to the nuclear thickness function (and therefore independent of the probe) leads to a smaller eccentricity, albeit still larger than the value used in hydrodynamic models. Our results suggest that the early elliptic flow in heavy ion collisions (unlike multiplicity distributions) is sensitive to the universality of the saturation scale in high-energy QCD.

We discuss results from 3+1-D numerical simulations of SU(2) Yang-Mills equations for an unstable glasma expanding into the vacuum after a high energy heavy-ion collision. We expand on our earlier work on a non-Abelian Weibel instability in such a system and study the behavior of the instability in greater detail on significantly larger lattices than previously. We establish the time scale for the onset of the instability and demonstrate that the growth rate is robust as one approaches the continuum limit. For large violations of boost invariance, non-Abelian effects cause the growth of soft modes to saturate. At late times, we observe significant creation of longitudinal pressure and a systematic trend towards isotropy. These time scales however are significantly larger than those required for early thermalization in heavy-ion collisions. We discuss additional effects in the produced glasma that may speed up thermalization.

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 τ as exp⁡(Γsqrt[g²μτ]), where g²μ is a scale arising from the saturation of gluons in the nuclear wave function. The scale for the growth rate Γ is set by a plasmon mass, defined as ω_pl=κ₀sqrt[g²μ/τ], generated dynamically in the collision. We compare the numerical ratio Γ/κ₀ to the corresponding value predicted by the hard thermal loop formalism for anisotropic plasmas.

We demonstrate the violation of k_⊥ factorization for quark production in high energy hadronic collisions. This violation is quantified in the color glass condensate framework and studied as a function of the quark mass, the quark transverse momentum, and the saturation scale Q_s, which is a measure of large parton densities. At x values where parton densities are large but leading twist shadowing effects are still small, violations of k_⊥ factorization can be significant—especially for lighter quarks. At very small x, where leading twist shadowing is large, we show that violations of k_⊥ factorization are relatively weaker.

We show that the weight functional for color sources in the classical theory of the color glass condensate (CGC) includes a term which generates odderon excitations. Remarkably, the classical origin of these excitations can be traced to the random walk of partons in the two dimensional space spanned by the SU(3) Casimirs. We compute dipole and baryon odderon operators in the CGC and show that contributions from the classical color sources to these are suppressed in the limit of very large parton densities.

The effective action for wee partons in large nuclei includes a sum over static color sources distributed in a wide range of representations of the SU(N_c) color group. The problem can be formulated as a random walk of partons in the N_c-1 dimensional space of the Casimir operators of SU(N_c). For a large number of sources, k≫1, we show explicitly that the most likely representation is a classical representation of order O(sqrt[k]). The quantum sum over representations is well approximated by a path integral over classical sources with an exponential weight whose argument is the quadratic Casimir operator of the group. The contributions of the higher N_c-2 Casimir operators are suppressed by powers of k. Other applications of the techniques developed here are discussed briefly.

We compute quark-antiquark pair production in the context of the color glass condensate model for central heavy-ion collisions. The calculation is performed analytically to leading order in the density of hard sources present in the projectiles, and is applicable to quarks with a mass large compared to the saturation momentum. The formulas derived in this paper are compared to expressions derived in the framework of collinearly factorized perturbative QCD and in k_⊥ factorization models. We comment on the breaking of k_⊥ factorization which occurs beyond leading order in our approach.

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.

We derive the hard thermal loop action for soft electromagnetic fields in the finite temperature world-line formulation at imaginary time by first integrating out the hard fermion modes from the microscopic QED action. Further, using the finite T world-line method, we calculate all static higher order terms in the soft electromagnetic field. At high T, the leading non-linear terms are independent of the temperature and, except for a term quartic in the time component of the vector potential, they cancel exactly against the vacuum contribution. The remaining T-dependent non-linear terms become more strongly suppressed by the temperature as the number of soft fields increases, thus making the expansion reliable.

The initial gluon multiplicity per unit area per unit rapidity, dN/L²/dη, in high energy nuclear collisions, is equal to f_N(g²μL) (g²μ)²/g², with μ² proportional to the gluon density per unit area of the colliding nuclei. For an SU(2) gauge theory, we compute f_N(g²μL)  =  0.14±0.01 for a wide range in g²μL. Extrapolating to SU(3), we predict dN/L²/dη for values of g²μL relevant to the Relativistic Heavy Ion Collider and the Large Hadron Collider. We compute the initial gluon transverse momentum distribution, dN/L²/d²k_⊥, and show it to be well behaved at low k_⊥.

The initial distribution of gluons at the very early times after a high-energy heavy ion collision is described by the bulk scale Q_s of gluon saturation in the nuclear wave function. The subsequent evolution of the system towards kinetic equilibrium is described by a nonlinear Landau equation for the single particle distributions [A. H. Mueller, Nucl. Phys. B572, 227 (2000); Phys. Lett. B 475, 220 (2000)]. In this paper, we solve this equation numerically for the idealized initial conditions proposed by Mueller, and study the evolution of the system to equilibrium. We discuss the sensitivity of our results on the dynamical screening of collinear divergences. In a particular model of dynamical screening, the convergence to the hydrodynamic limit is seen to be rapid relative to hydrodynamic time scales. The equilibration time, the initial temperature, and the chemical potential are shown to have a strong functional dependence on the initial gluon saturation scale Q_s.

We propose a new form for the small x effective action in QCD. This form of the effective action is motivated by Wong’s equations for classical, colored particles in non-Abelian background fields. We show that the BFKL equation, which sums leading logarithms in x, is efficiently reproduced with this form of the action. We argue that this form of the action may be particularly useful in computing next-to-leading-order results in QCD at small x.

The one loop effective action in quantum field theory can be expressed as a quantum mechanical path integral over world lines, with internal symmetries represented by Grassmanian variables. In this paper, we develop a real time, many body, world line formalism for the one loop effective action. In particular, we study hot QCD and obtain the classical transport equations which, as Litim and Manuel have shown, reduce in the appropriate limit to the non-Abelian Boltzmann-Langevin equation first obtained by Bödeker. In the Vlasov limit, the classical kinetic equations are those that correspond to the hard thermal loop effective action. We also discuss the imaginary time world line formalism for a hot φ⁴ theory, and elucidate its relation to classical transport theory.

In very-high-energy nuclear collisions, the initial energy of produced gluons per unit area per unit rapidity, (dE/L²)/dη, is equal to f(g²μL) (g²μ)³/g², where μ² is proportional to the gluon density per unit area of the colliding nuclei. For an SU(2) gauge theory, a nonperturbative computation of f(g²μL) shows that it varies rapidly for small g²μL but varies only by ∼25%, from 0.208±0.004 to 0.257±0.005, for a wide range 35.36– 296.98 in g²μL. 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/dη for Au-Au collisions in the central region at RHIC and LHC.

We compute quark structure functions and the intrinsic Fock space distribution of sea quarks in a hadron wave function at small x. The computation is performed in an effective theory at small x where the gluon field is treated classically. At Q² large compared to an intrinsic scale associated with the density of gluons μ², large compared to the QCD scale Λ_QCD², and large compared to the quark mass squared M², the Fock space distribution of quarks is identical to the distribution function measured in deep inelastic scattering. For Q²<~M² but Q²≫μ², the quark distribution is computed in terms of the gluon distribution function and explicit expressions are obtained. For Q²<~μ² but Q²≫Λ_QCD² we obtain formal expressions for the quark distribution functions in terms of the glue. An evaluation of these requires a renormalization group analysis of the gluon distribution function in the regime of high parton density. For light quarks at high Q², the DGLAP flavor singlet evolution equations for the parton distributions are recovered. Explicit expressions are given for heavy quark structure functions at small x.

We study relativistic S+Au collisions at 200A GeV/c using a hydrodynamical approach. We test various equations of state (EOS’s), which are used to describe the strongly interacting matter at densities attainable in the CERN-SPS heavy ion experiments. For each EOS, suitable initial conditions can be determined to reproduce the experimental hadron spectra; this emphasizes the ambiguity between the initial conditions and the EOS in such an approach. Simultaneously, we calculate the resulting thermal photon and dielectron spectra, and compare with experiments. If one allows the excitation of resonance states with increasing temperature, the electromagnetic signals from scenarios with and without phase transition are very similar and are not resolvable within the current experimental resolution. Only EOS’s with a few degrees of freedom up to very high temperatures can be ruled out presently. We deduce an upper bound of about 250 MeV for the initial temperature from the single photon spectra of WA80. With regard to the CERES dilepton data, none of the EOS’s considered, in conjunction with the standard leading order dilepton rates, succeed in reproducing the observed excess of dileptons below the ρ peak. Our work, however, suggests that an improved measurement of the photon and dilepton spectra has the potential to strongly constrain the EOS.

Using weak coupling methods McLerran and Venugopalan expressed the parton distributions in large nuclei as correlation functions of a two-dimensional Euclidean field theory. The theory has the dimensionful coupling g²μ, where μ²∼A^{1 / 3} is the valence quark color charge squared per unit area. We use a lattice regularization to investigate these correlation functions both analytically and numerically for the simplified case of SU(2) gauge theory. In weak coupling (g²μL≪5), where L is the transverse size of the nucleus, the numerical results agree with the analytic lattice weak coupling results. For g²μL≫5, no solutions exist at O(a⁴) where a is the lattice spacing. This suggests an ill-defined infrared behavior for the two-dimensional theory. A recent proposal of Jalilian-Marian, Kovner, McLerran, and Weigert for an analytic solution of the classical problem is discussed briefly.

We compute the quantum corrections to the gluon distribution function in the background of a non-Abelian Weizsäcker-Williams field. These corrections are valid to all orders in the effective coupling α_sμ, where μ² denotes the average valence quark color charge squared per unit area. We find ln(1/x) logarithmic corrections to the classical gluon distribution function. The one-loop corrections to the classical Weizsäcker-Williams field do not contribute to these singular terms in the distribution function. Their effect is to cause the running of α_s. © 1995 The American Physical Society.

We carefully compute the gluon propagator in the background of a non-Abelian Weizsäcker-Williams field. This background field is generated by the valence quarks in very large nuclei. We find contact terms in the small fluctuation equations of motion which induce corrections to a previously incorrect result for the gluon propagator in such a background field. The well-known problem of the Hermiticity of certain operators in the light cone gauge is resolved for the Weizsäcker-Williams background field. This is achieved by working in a gauge where singular terms in the equations of motion are absent and then gauge transforming the small fluctuation fields to the light cone gauge.

The energy densities achieved during central collisions of large nuclei at Brookhaven’s AGS may be high enough to allow the formation of quark-gluon plasma. Calculations based on relativistic nucleation theory suggest that rare events, perhaps one in every 10² or 10³, undergo the phase transition. Experimental ramifications may include an enhancement in the ratio of pions to baryons, a reduction in the ratio of deuterons to protons, and a larger source size as seen by hadron interferometry.

We compute the Green’s function for scalars, fermions, and vectors in the color field associated with the infinite momentum frame wave function of a large nucleus. Expectation values of this wave function can be computed by integrating over random orientations of the valence quark charge density. This relates the Green’s functions to correlation functions of a two-dimensional, ultraviolet finite, field theory. We show how one can compute the sea quark distribution functions and explicitly compute them in the kinematic range of transverse momenta, α_s²μ²≪k_t²≪μ², where μ² is the average color charge squared per unit area. When m_quark²≪μ²∼A^1/3, the sea quark contribution to the infinite momentum frame wave function saturates at a value that is the same as that for massless sea quarks.

We compute the dynamical prefactor in the nucleation rate of bubbles or droplets in first-order phase transitions for the case where both viscous damping and thermal dissipation are significant. This result, which generalizes previous work on nucleation, may be applied to study the growth of bubbles or droplets in condensed matter systems as well as in heavy ion collisions and in the expansion of the early universe.

We show that the gluon distribution function for very large nuclei may be computed for small transverse momentum as correlation functions of an ultraviolet finite two-dimensional Euclidean field theory. This computation is valid to all orders in the density of partons per unit area, but to lowest order in α_s. The gluon distribution function is proportional to 1 / x, and the effect of the finite density of partons is to modify the dependence on the transverse momentum for small transverse momenta.

We argue that the distribution functions for quarks and gluons are computable at small x for sufficiently large nuclei, perhaps larger than can be physically realized. For such nuclei, we argue that weak coupling methods may be used. We show that the computation of the distribution functions can be recast as a many-body problem with a modified propagator, a coupling constant which depends on the multiplicity of particles per unit rapidity per unit area, and for non-Abelian gauge theories, some extra media-dependent vertices. We explicitly compute the distribution function for gluons to lowest order, and argue how they may be computed in higher order.