A Brief Overview of Hard-Thermal-Loop Perturbation Theory

The poor convergence of quantum field theory at finite temperature has been one of the main obstacles in the practical applications of thermal QCD for decades.Here we briefly review the progress of hard-thermal-loop perturbation theory (HTLpt) in reorganizing the perturbative expansion in order to improve the convergence.The quantum mechanical anharmonic oscillator is used as a simple example to show the breakdown of weak-coupling expansion,and variational perturbation theory is introduced as an effective resummation scheme for divergent weak-coupling expansions.We discuss HTLpt thermodynamic calculations for QED,pure-glue QCD,and QCD with N f=3 up to three-loop order.The results suggest that HTLpt provides a systematic framework that can be used to calculate both static and dynamic quantities for temperatures relevant at LHC.     

Dimensional Crossover of Magnetic Transition in Diluted Ising Spin Nets Probed by Muon Spin Relaxation

The magnetic ordering process of Ising spins on diluted square lattice was studied by muon spin relaxation using model compounds Rb₂Co _c Mg_1−c F₄. Muon relaxation shows an anomaly at a remarkably higher temperature T _N ^μSR than the transition temperature determined by neutron Bragg scattering T _N ^ND near the percolation threshold for square lattice (c _p=0.593). The difference between the two temperatures amounts to 50% of T _N ^ND just above c _p. The field cooling effect of DC magnetic susceptibility is appreciable below T _N ^ND while the temperature of the anomaly in AC susceptibility approaches to T _N ^μSR as the frequency is increased. It was concluded that there is a crossover from two-dimensional ordering at T _N ^μSR to three-dimensional ordering at T _N ^ND but the two-dimensional order between T _N ^μSR and T _N ^ND has slow fluctuations due to the fractal structure with a plenty of weak links. This revised version was published online in September 2006 with corrections to the Cover Date.     

Properties of quark gluon plasma from lattice calculations

I discuss lattice QCD calculations of the properties of strongly interacting matter at finite temperature, including the determination of the transition temperature T_c, equation of state, different static screening lengths and quarkonium spectral functions. The lattice data suggest that at temperatures above 2.0T_c many properties of the quark gluon plasma can be understood using weak coupling approach, although non-perturbative effects due to static magnetic fields are significant in some quantities.     

Crystallographic characteristics and phase transitions in the [N(C<Subscript>2</Subscript>H<Subscript>5</Subscript>)<Subscript>4</Subscript>]<Subscript>2</Subscript>CdBr<Subscript>4</Subscript> crystal in the low-temperature range

The results of x-ray structural studies of the [N(C₂H₅)₄]₂CdBr₄ crystal at low temperatures are presented. The unit cell parameters and the thermal expansion coefficients along the main crystallographic directions are measured at temperatures in the range from 90 to 320 K. The integrated intensities of the diffraction reflections are investigated as a function of the temperature. It is shown that the curves a = f(T), c = f(T), I ₅₀₀ = f(T), and I ₀₀₆ = f(T) at temperatures T ₁ ≈ 174 K and T ₂ ≈ 226 K exhibit anomalies in the form of abrupt changes in the lattice parameters and the diffraction reflection intensities. This indicates that the [N(C₂H₅)₄]₂CdBr₄ crystal undergo phase transitions at these temperatures. Moreover, there is an anomaly in the form of a small maximum at the temperature T ₃ = 293 K.     

Nonperturbative phenomena in QCD at finite temperature

The main objective of the present study is to analyze various nonperturbative phenomena in QCD both at low, T < T _c , and at high, T > T _c , temperatures. New methods are developed that make it possible, on one hand, to describe data obtained by numerically simulating QCD on a lattice and, on the other hand, to study new physical phenomena in QCD at finite temperature.     

QCD equation of state for heavy ion collisions

In this work, we calculate the equation of state(EoS) of quark gluon-plasma(QGP) using the CornwallJackiw-Tomboulis(CJT) effective action. We get the quark propagator by using the rank-1 separable model within the framework of the Dyson-Schwinger equations(DSEs). The results from CJT effective action are compared with lattice QCD data. We find that, when μ is small, our results generally fit the lattice QCD data when TT_c,but show deviations at and below T_c. It can be concluded that the EoS of CJT is reliable when TT_c. Then,by adopting the hydrodynamic code UVH2+1, we compare the CJT results of the multiplicity and elliptic flow v2 with the PHENIX data and the results from the original EoS in UVH2+1. While the CJT results of multiplicities generally match the original UVH2+1 results and fit the experimental data, the CJT results of v2 are slightly larger than the original UVH2+1 results for centralities smaller than 40% and smaller than the original UVH2+1 results for higher centralities.     

Quarkonia at Finite T: An Approach Based On QCD Sum Rules and the Maximum Entropy Method

Quarkonium spectral functions at finite temperature are studied, making use of a recently developed method of analyzing QCD sum rules by the maximum entropy method. This approach enables us to directly obtain the spectral function from the sum rules, without having to introduce any specific assumption about its functional form. QCD sum rules for heavy quarkonia incorporate finite temperature effects in form of changing values of the various gluonic condensates that appear in the operator product expansion. These changes depend on the energy density and pressure at finite temperature, which we extract from quenched lattice QCD calculations. As a result, it is found that the charmonium ground states of both S-wave and P-wave channels dissolve into the continuum already at temperatures around or slightly above the critical temperature T _c , while the bottomonium states are less influenced by temperature effects, surviving up to about 2.5 T _c or higher for S-wave and about 2.0 T _c for P-wave states.     

Comments on a Minimal Quasiparticle Approach for the QGP and Its Large-N c Limits

A minimal quasiparticle approach for describing QGP at temperatures much higher than the critical one is discussed. It involves an ideal-gas framework in which quark and gluon masses depend on temperature. This model is able to reproduce the recent equations of state computed in lattice QCD for temperatures typically higher than 2 T _c , in a range in which it is reasonable to neglect interactions between quasiparticles. In addition, the equations of state for a generic gauge theory with gauge groups SU(N _c ) and quarks in an arbitrary representation are studied. The gauge independence in the pure glue sector and the large-N _c equivalence between the gauge groups SU(N _c ) and SO(2N _c ) in a full plasma is finally shown for normalized thermodynamic quantities.     

The spectrum of hot hadronic matter and finite-temperature QCD sum rules

The sum rules method, which is widely used for the investigation of the resonance physics within the QCD framework, is generalized to the case of finite temperatures and densities. Conditions are formulated under which this method is quite efficient for the determination of the spectrum of hadronic matter at T ≠ 0. The finite-temperature QCD sum rules are analysed in the vector channel J^PC = 1⁻⁻. Sharp and qualitative changes in the spectrum are found in the temperature interval T = 130–150 MeV. It is naturally explained as a consequence of the disappearance of confinement at the temperature T_c = 140±10 MeV. The finite-temperature QCD sum rules also show that the restoration of chiral symmetry at some temperature T_F cannot precede deconfinement. In the case T_F⪢T_c the sum rules indicate that the intermediate phase at T_c<T<T_F is dominated by quasi-free quarks with nonzero dynamical mass m_q^T ≈ 300 MeV.     

Perturbative versus lattice QCD energy density correlators at high temperatures

Correlators of magnetic and electric field energy density are investigated for SU(N_c) gauge theory at high temperatures T. A separations z ⩽ 2/T the correlators are shown to be dominated by a power-law behavior even for finite gluon screening masses. This continuum behavior is well approximated on current 4 × 16³-lattices in the perturbative limit and leads to a considerable overestimate of screening masses deduced from fitting the lattice correlators with conventional exponential forms. The use of extended sources and sinks to enhance the signal improves the situation for screening masses m ⪢ T but leads to a largely uncontrolled error for masses less than T. In fact, we show that recent lattice QCD data of Grossmann et al., from which a magnetic screening mass m_M ∼ 2.9T was deduced, may even be consistent with a vanishing actual magnetic screening mass.     

Meson screening masses from lattice QCD with two light quarks and one strange quark

We present results for screening masses of mesons built from light and strange quarks in the temperature range of approximately between 140 MeV to 800 MeV. The lattice computations were performed with 2+1 dynamical light and strange flavors of improved (p4) staggered fermions along a line of constant physics defined by a pion mass of about 220 MeV and a kaon mass of 500 MeV. The lattices had temporal extents N _τ =4, 6 and 8 and aspect ratios of N _s /N _τ ≥4. At least up to a temperature of 140 MeV the pseudo-scalar screening mass remains almost equal to the corresponding zero temperature pseudo-scalar (pole) mass. At temperatures around 3T _c (T _c being the transition temperature) the continuum extrapolated pseudo-scalar screening mass approaches very close to the free continuum result of 2πT from below. On the other hand, at high temperatures the vector screening mass turns out to be larger than the free continuum value of 2πT. The pseudo-scalar and the vector screening masses do not become degenerate even for a temperature as high as 4T _c . Using these mesonic spatial correlation functions we have also investigated the restoration of chiral symmetry and the effective restoration of the axial symmetry. We have found that the vector and the axial-vector screening correlators become degenerate, indicating chiral symmetry restoration, at a temperature which is consistent with the QCD transition temperature obtained in previous studies. On the other hand, the pseudo-scalar and the scalar screening correlators become degenerate only at temperatures larger than 1.3T _c , indicating that the effective restoration of the axial symmetry takes place at a temperature larger than the QCD transition temperature.     

QCD sum rules and the Skyrme model at large Nc

We study the large-N_c behaviour of the baryon spectrum using QCD duality sum rules. A comparison of our results with the ones of the Skyrme model gives a determination of the Skyrme parameter e and a relation between the pion decay constant f_π and the quark condensate. As a consequence, we show that f_π is the only scale which controls the hadron dynamics. An extrapolation of our large-N_c results into the real world N_c = 3 yields a good agreement with phenomenological estimates.     

Absolute γ-decay rates of the fc(3.55) from tensor meson dominance and QCD-potentials

We compute the coupling gf_c of the 2⁺⁺ cc? meson f_c(3.55) to the energy-2-momentum tensor, 〈0|T_μν|f_c〉·√ = gf_c?μν, from the QCD-potential of Barbieri, Gatto, Kögerler and Kunszt. Vector meson and tensor dominance then imply, including color, Γ(Ψ' → γf_c) = 20 keV in good agreement with experiment. Other potentials available in the literature yield widths which are larger by up to a factor 2. A naive formulation of vector meson dominance for both γ's in f_c → γγ yields A width which is an order of magnitude above the experimental limit.     

New spectral representation and evaluation of f π and the quark condensate \left\langle {\bar qq} \right\rangle in the terms of string tension

New spectral representations for f _π and chiral condensate are derived in QCD and used for calculations in the large-N _c limit. Both quantities are expressed in this limit through string tension σ and gluon correlation length T _g without fitting parameters. As a result, one obtains $\left\langle {\bar qq} \right\rangle = - N_c \sigma ^2 T_g a_1 $ , $f_\pi = \sqrt {N_c } \sigma T_g a_2 $ , with a ₁=0.0823, a ₂=0.30. Taking σ=0.18 GeV² and T _g=1 GeV^?1, as known from analytic and lattice calculations, this yields $\left\langle {\bar qq} \right\rangle $ (μ=2 GeV)=?(0.225 GeV)³, f _π=0.094 GeV, which is close to the standard values.     

Few-Baryon Interactions from Lattice QCD

We report the recent progress on the determination of three-nucleon forces (3NF) in lattice Quantum Chromodynamics (QCD). We utilize the Nambu–Bethe–Salpeter wave function to define the potential in quantum field theory, and extract two-nucleon forces and 3NF on equal footing. The enormous computational cost for calculating multi-baryon correlators on the lattice is drastically reduced by developing a novel contraction algorithm (the unified contraction algorithm). Quantum numbers of the three-nucleon system are chosen to be (I, J ^P ) = (1/2, 1/2⁺) (the triton channel), and we extract 3NF in which three nucleons are aligned linearly with an equal spacing. Lattice QCD simulations are performed using N _f = 2 dynamical clover fermion configurations at the lattice spacing of a = 0.156fm on a 16³ × 32 lattice with a large quark mass corresponding to m _π = 1.13 GeV. Repulsive 3NF is found at short distance.     

NNLO hard-thermal-loop thermodynamics for QCD

We calculate the thermodynamic functions of a quark–gluon plasma for general Nc$N_c$ and Nf$N_f$ to three-loop order using hard-thermal-loop perturbation theory. At this order, all the ultraviolet divergences can be absorbed into renormalizations of the vacuum, the HTL mass parameters, and the strong coupling constant. We show that at three loops, the results for the pressure and trace anomaly are in very good agreement with recent lattice data down to temperatures T∼2Tc$T\sim 2T_c$.     

Magnetic and related properties of GdCu5.1In6.9

Magnetic measurements performed between 1.7 and 300K show that GdCu_5.1In_6.9 is an antiferromagnet below T _N = 13.4(1) K. At temperatures 17–300K the Curie-Weiss law is followed with p _eff = 7.57 μ _B and θ = -33.8K. Electrical resistivity measurements do not show any pronounced anomaly, but the resistivity is rather low with RRR ≈ 59. The EPR experiment shows that the resonance exists between 10 and 300 K. A temperature independent g-shift (Δg = -0.036(10)) and a Korringa.type linewidth broadening of 2.6 G/K was observed at temperatures higher than 55 K. The linewith increase found at high temperature well above T _N can suggest a significant amount of short. range order. ¹⁵⁵Gd Mössbauer effect examinations show that H _hf is perpendicular to the c-axis and therefore magnetic moments of Gd are located within the ab-plane.     

Charmonium states in quark-gluon plasma

We discuss how the spectral changes of quarkonia at T _c can reflect the ‘critical’ behaviour of QCD phase transition. Starting from the temperature dependencies of the energy density and pressure from lattice QCD calculation, we extract the temperature dependencies of the scalar and spin-2 gluon condensates near T _c. We also parametrize these changes into the electric and magnetic condensate near T _c. While the magnetic condensate hardly changes across T _c, we find that the electric condensate increases abruptly above T _c. Similar abrupt change is also seen in the scalar condensate. Using the QCD second-order Stark effect and QCD sum rules, we show that these sudden changes induce equally abrupt changes in the mass and width of J/ψ, both of which are larger than 100 MeV at slightly above T _c.