Search Results (24 total)

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.

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_⊥.

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 investigate the effect of dynamical fermions on the sphaleron transition rate at finite temperature for the Abelian Higgs model in one spatial dimension. The fermion degrees of freedom are included through bosonization. Using a numerical simulation, we find that massless fermions do not change the rate within the measurement accuracy. Surprisingly, the exponential dependence of the sphaleron energy on the Yukawa coupling is not borne out by the transition rate, which shows a very weak dependence on the fermion mass.

We study the Chern-Simons number diffusion rate in the (1+1)-dimensional lattice Abelian Higgs model at temperatures much higher than, as well as comparable to, the sphaleron energy. It is found that in the high-temperature limit the rate is likely to grow as a power of 2/3 of the temperature. In the intermediate-temperature regime, our numerical simulations show that the very weak temperature dependence of the rate, found in previous work, persists at smaller lattice spacings. We discuss possibilities of relating the observed behavior of the rate to static finite-temperature properties of the model.

As part of an ongoing effort to characterize the high temperature phase of QCD, in a numerical simulation using the staggered fermion scheme, we measure the quark baryon density in the vicinity of a fixed test quark at high temperature and compare it with similar measurements at low temperature and at the crossover temperature. We find an extremely weak correlation at high temperature, suggesting that small color singlet clusters are unimportant in the thermal ensemble. We also find that at T=0.75 T_c the total induced quark number shows a surprisingly large component attributable to baryonic screening. A companion simulation of a simple flux tube model produces similar results and also suggests a plausible phenomenological scenario: As the crossover temperature is approached from below, baryonic states proliferate. Above the crossover temperature the mean size of color singlet clusters grows explosively, resulting in an effective electrostatic deconfinement.

We have extended our previous study of the lattice QCD spectrum with two flavors of staggered dynamical quarks at 6 / g²=5.6 and am_q=0.025 and 0.01 to larger lattices, with better statistics and with additional sources for the propagators. The additional sources allowed us to estimate the Δ mass and to measure the masses of all mesons whose operators are local in time. These mesons show good evidence for flavor symmetry restoration, except for the masses of the Goldstone and non-Goldstone pions. PCAC is observed in that m_π²∝m_q, and f_π is estimated. Use of undoubled lattices removes the problems with the pion propagator found in our earlier work. Previously we found a large change in the nucleon mass at a quark mass of am_q=0.01 when we increased the spatial size from 12 to 16. No such effect is observed at the larger quark mass, am_q=0.025. Two kinds of wall source were used, and we have found difficulties in getting consistent results for the nucleon mass between the two sources.

We present results of a lattice simulation of quantum chromodynamics with two degenerate flavors of dynamic Wilson fermions at 6 / g²=5.3 at each of two dynamical fermion hopping parameters κ=0.1670 and 0.1675 corresponding to pion masses in lattice units of about 0.45 and 0.31. The simulations include three other values of valence quark mass, in addition to the dynamical quarks. We present calculations of masses and of the decay constants of vector mesons and of pseudoscalars, including the D-meson decay constant. The effects of sea quarks on matrix elements and spectroscopy are small.

We have carried out spectrum calculations with two flavors of dynamical Kogut-Susskind quarks on four lattice sizes from 8³×24 to 16³×24 at couplings that correspond to chiral symmetry restoration for a lattice with six time slices. We estimate that the linear spatial sizes of the lattices range from 1.8 to 3.6 fm. We find significant finite-size effects for all particles between the smallest and largest volume with the larger quark mass that we study, am_q=0.025, where a is the lattice spacing. The nucelon experiences the largest effect of about 6%. We also study a lighter quark mass, am_q=0.0125, on the two largest lattices. Effects of the dynamical and valence quark masses on the hadron spectrum are studied both directly, by comparing the two simulations, and by extracting mass derivatives from the correlation functions. We do not find much improvement in the nucleon to ρ mass ratio as we decrease the quark mass at this lattice spacing. Finally, we report on an unsuccessful attempt to see effects of the ρ→2π decay on the ρ mass, and on studies of Wilson and Kogut-Susskind hadron masses with large valence quark masses.

We have measured some simple matrix elements for pseudoscalar and vector mesons made of Wilson valance quarks and staggered sea quarks at β=5.6 at sea quark masses am_q=0.01 and 0.025. Our measurements include the decay constants of pseudoscalars (including f_D), the wave function at the origin (or decay constant) of vector mesons, and the calculation of quark masses from current algebra. The effects of sea quarks on the simulations are small. We make comparisons to quenched simulations at similar values of the lattice spacing (1 / a≃2 GeV).

We have carried out a numerical study of the high-temperature behavior of lattice QCD with two flavors of staggered quarks. Our simulations were performed on 16³×8 lattices with a quark mass m_q=0.0125, in units of the inverse lattice spacing. By monitoring the Wilson-Polyakov line, the chiral order parameter 〈ψ̅ ψ〉, and the average plaquette, we have determined that a crossover between the low-temperature state of ordinary hadronic matter and the high-temperature quark-gluon plasma occurs at a gauge coupling of 6 / g²=5.54(2). Thermodynamic quantities do not show a large jump, although the equilibration time becomes quite long in the vicinity of the crossover. We have measured the entropy densities in the neighborhood of the crossover and further into the plasma phase. Measurements of the hadronic screening lengths and the Debye screening lengths were made which cast light on the differences between the two regimes. Finally, we measured the topological susceptibilities to further explore the chiral properties of QCD.

We report on a study of hadron thermodynamics with two flavors of Wilson quarks on 12³×6 lattices. We have studied the crossover between the high- and low-temperature regimes for three values of the hopping parameter, κ=0.16, 0.17, and 0.18. At each of these values of κ we have carried out spectrum calculations on 12³×24 lattices for two values of the gauge coupling in the vicinity of the crossover in order to set an energy scale for our thermodynamics calculations and to determine the critical value of the gauge coupling for which the pion and quark masses vanish. For κ=0.17 and 0.18 we find coexistence between the high- and low-temperature regimes over 1000 simulation time units indicating either that the equilibration time is extremely long or that there is a possibility of a first-order phase transition. The pion mass is large at the crossover values of the gauge coupling, but the crossover curve has moved closer to the critical curve along which the pion and quark masses vanish, than it was on lattices with four time slices (N_t=4). In addition, values of the dimensionless quantity T_c/m_ρ are in closer agreement with those for staggered quarks than was the case at N_t=4.

We present an analysis of hadronic spectroscopy for Wilson valence quarks with dynamical staggered fermions at a lattice coupling 6 / g²=5.6 at a sea-quark mass of am_q=0.01 and 0.025, and of Wilson valence quarks in the quenched approximation at β=5.85 and 5.95, both on 16³ × 32 lattices. We make comparisons with our previous results with dynamical staggered fermions at the same parameter values but on 16⁴ lattices doubled in the temporal direction.

The first results of numerical simulations of quantum chromodynamics on the Intel iPSC/860 parallel processor are presented. We performed calculations with two flavors of Kogut-Susskind quarks at N_t=6 with masses of 0.15T and 0.075T (0.025 and 0.0125 in lattice units) in order to locate the crossover from the low-temperature regime of ordinary hadronic matter to the high-temperature chirally symmetric regime. As with other recent two-flavor simulations, these calculations are insufficient to distinguish between a rapid crossover and a true phase transition. The phase transition is either absent or feeble at this quark mass. An improved estimate of the crossover temperature in physical units is given and results are presented for the hadronic screening lengths in both the high- and low-temperature regimes.

We use numerical simulations to study the spatial structure of a quark and an antiquark in the imaginary-time excitations which mediate the Debye screening of color singlet sources in the high-temperature phase of QCD. We find that these correlation functions are very similar to the zero-temperature wave functions of the corresponding particles. This result contrasts with results on the ρ and nucleon screening lengths for these sources, which are well described by a gas of free or weakly interacting quarks.

We obtain estimates of the lightest glueball masses, the string tension, and the topological susceptibility in an exploratory study of QCD with two light flavors of quarks. Our calculations are performed at β=5.6 with staggered quark masses m_q=0.010 and 0.025 and on lattices ranging from 12⁴ to 16⁴. Our estimates suggest that, just as in the pure gauge theory, the 0⁺⁺ is the lightest glueball with the 2⁺⁺ about 50% heavier. Our m_q=0.01 results predict a 0⁺⁺ glueball mass of about 1.6 times the ρ mass and the square root of the string tension of about 0.48 times the ρ mass, which is surprisingly close to the usual phenomenologically motivated estimates of around 0.55. Our value of the topological susceptibility at m_q=0.01 is consistent with the prediction, to O(m_q) of the standard anomalous Ward identity. However, the variation of this susceptibility between m_q=0.01 and m_q=0.025 is weaker than the linear dependence one expects at small m_q in the broken-chiral-symmetry phase of QCD.

The effect of field configuration copying on both fermion and fermion-antifermion pair correlation functions is studied in detail in a simple quantum-mechanical model. It is found that, with very few exceptions, the copying procedure results in a large correction to the corresponding effective masses. In particular, this correction leads to an oscillatory behavior of the effective masses, similar to that observed for mesons in recent lattice QCD calculations. It is argued that the copying technique is unlikely to be useful as a spectroscopic tool.

We study hadron thermodynamics with Wilson quarks. The crossover curve between the high-and low-temperature phases is determined as a function of gauge coupling and hopping parameter on 8³×4 lattices. Screening lengths are calculated in the vicinity of the crossover region, and meson masses are calculated along the crossover curve on 8²×16×4 and 8³×16 lattices, respectively.

We have carried out a simulation of QCD using the hybrid-molecular-dynamics algorithm with two flavors of staggered quarks. The spectrum was calculated for 6 / g²=5.6 and dynamical quark masses am_q=0.025 and 0.01. Lattice sizes of 12⁴, 12³×24, and 16⁴ were used to generate the gauge configurations. Hadron propagators were calculated with both staggered and Wilson quarks on doubled or quadrupled latices. Finite-size effects are visible on the smaller lattices. Some improvement in the ρ-to-nucleon mass ratio and chiral symmetry is seen as compared to previous calculations, but, as in most lattice calculations, the proton-to-ρ mass ratio remains larger than in the real world and the proton-Δ splitting is too small.

We have carried out a simulation of quantum chromodynamics using the hybrid-molecular-dynamics algorithm with two flavors of Kogut-Susskind quarks. We have used Kogut-Susskind and Wilson valence quarks to calculate the hadron mass spectrum. Among our extensive results we discuss baryon hyperfine splitting, the nucleon-to-ρ mass ratio, the sclar-to-tensor-glueball mass ratio, and the quantization and susceptibility of the topological charge. We have used a gauge coupling of 6/g²=5.60, and quark masses am_q=0.025 and 0.01, in generating gauge configurations on 12⁴, 12³×24, and 16⁴ lattices.

A simple quantum-mechanical example is used to analyze the effect of field configuration copying on a fermion correlation function. It is shown that the copying procedure may result in a large correction to the fermion effective mass except for short-time correlations in the low-temperature regime. This correction possibly explains the oscillatory behavior of meson effective masses in a recent lattice QCD calculation.

The slightly doped Hubbard model at finite temperature is analyzed in the spin-wave expansion. It is found that in d=2 weak uniform magnetization perpendicular to the staggered magnetization is present for any finite doping fraction. In d=3 there is no net magnetization for doping fractions smaller than some critical one. We suggest that this mechanism can be responsible for recent experimental observations of in-plane spin canting in La₂CuO₄.

Perturbation theory is combined with spin-wave techniques to study the large-U one-band Hubbard model near half filling. It is shown that the antiferromagnetic order is preserved for finite doping fractions. A uniform magnetization perpendicular to the staggered one is predicted for doping fractions above some critical value. This critical value is zero for d=2 and nonzero for d>2.

A ground state of lattice SU(2) QCD with Kogut-Susskind fermions at finite chemical potential is studied. Strong-coupling perturbation theory yields an effective Hamiltonian analogous to that of the Heisenberg antiferromagnetic model. By use of this analogy a phase transition restoring both the U(1) symmetry of the baryon number and the axial symmetry is predicted. This result is then confirmed by a nonperturbative calculation.