Lectures on the Near-Side Ridge, Landau Hydrodynamics, and Heavy Quarkonia in High Energy Heavy-Ion Collisions
We give an introduction to three diﬀerent topics that are of current interest in heavy-ion collisions. Particles associated with the near-side jet are found to exhibit a Δφ-Δη correlation in the form of a ridge in the Δη direction but a peak at Δφ ~ 0. The experimental data support the description that the ridge particles are medium partons kicked by the jet. The measurement of the characteristics of the ridge provides a unique tool to probe the nature of the (jet parton)-(medium parton) collision and the momentum distribution of dense matter formed in the early stage of the heavy-ion collision. We ﬁnd that the magnitude of the longitudinal momentum kick along the jet direction acquired by a medium parton in collision with the jet is about 1 GeV, and the early parton momentum distribution is in the form of a rapidity plateau with a thermal-type transverse momentum distribution. In the second lecture, we re-examine the validity of Landau hydrodynamics which provides a reasonable description of the space-time dynamics of the hot matter produced in high-energy heavy-ion collisions. We ﬁnd that the rapidity distribution of produced particles should be more appropriately modiﬁed from Landau’s result. Past successes of the Gaussian distribution in explaining experimental rapidity data can be understood, not because it is an approximation of the original Landau distribution, but because it is in fact a close representation of the modiﬁed distribution. In the ﬁnal lecture, we give an introduction to the development of the potential model for quarkonia, using thermodynamical quantities obtained in lattice gauge calculations. We ﬁnd that the potential model is consistent with the lattice gauge spectral function analysis, if the color-singlet heavy quark-antiquark potential is a linear combination of the color-singlet free energy F 1 and internal energy U 1 , with coeﬃcients that depend on the equation of state. We ﬁnd that the eﬀects of dynamical quark modiﬁes only slightly the stability of J/ψ and the quark drip line limits possible quarkonium states with light quarks to temperatures close to, and slightly greater than, the critical phase transition temperature.

title: Relativistic Hard-Scattering and Tsallis Fits to p T Spectra in pp Collisions at the LHC ∗
abstract: Motivated by the good Tsallis fits to the high-p T spectra in pp collisions at the LHC, we study the relativistic hard-scattering model and obtain an approximate analytical expression for the differential hard-scattering cross section at � � 0. The power-law behavior of the transverse spectra, in the form of d�/dp 2/1/p n, gives a power index n in the range of 4.5-5.5 for jet production as predicted by pQCD, after the dependencies of the structure functions and the running coupling constant are properly taken into account. The power indices for hadron production n are slightly greater than those for jet production.

title: Extended Glauber Model of Antiproton-Nucleus Annihilation for All Energies and Mass Numbers
abstract: Previous analytical formulas in the Glauber model for high-energy nucleus-nucleus collisions developed by Wong are utilized and extended to study Antiproton-nucleus annihilations for both high and low energies, after taking into account the effects of Coulomb and nuclear interactions, and the change of the antiproton momentum inside a nucleus. The extended analytical formulas capture the main features of the experimental antiproton-nucleus annihilation cross sections for all energies and mass numbers. At high antiproton energies, they exhibit the granular property for the lightest nuclei and the black-disk limit for the heavy nuclei. At low antiproton energies, they display the effect of the antiproton momentum increase due to the nuclear interaction for the light nuclei, and the effect of the magnification due to the attractive Coulomb interaction for the heavy nuclei.

title: Singularity structures in Coulomb-type potentials in two-body Dirac equations of constraint dynamics
abstract: Two-body Dirac equations (TBDE) of Dirac's relativistic constraint dynamics have been successfully applied to obtain a covariant nonperturbative description of QED and QCD bound states. Coulomb-type potentials in these applications lead naively in other approaches to singular relativistic corrections at short distances that require the introduction of either perturbative treatments or smoothing parameters. We examine the corresponding singular structures in the effective potentials of the relativistic Schroedinger equation obtained from the Pauli reduction of the TBDE. We find that the relativistic Schroedinger equation leads in fact to well-behaved wave function solutions when the full potential and couplings of the system are taken into account. The most unusual case is the coupled triplet system with S=1 and L={l_brace}(J-1),(J+1){r_brace}. Without the inclusion of the tensor coupling, the effective S-state potential would become attractively singular. We show how including the tensor coupling is essential in order that the wave functions be well-behaved at short distances. For example, the S-state wave function becomes simply proportional to the D-state wave function and dips sharply to zero at the origin, unlike the usual S-state wave functions. Furthermore, this behavior is similar in both QED and QCD, independent of the asymptotic freedom behavior of the assumed QCDmore » vector potential. Light- and heavy-quark meson states can be described well by using a simplified linear-plus-Coulomb-type QCD potential apportioned appropriately between world scalar and vector potentials. We use this potential to exhibit explicitly the origin of the large pi-rho splitting and effective chiral symmetry breaking. The TBDE formalism developed here may be used to study quarkonia in quark-gluon plasma environments.« less

title: Potential Models and Lattice Gauge Current-Current Correlators
abstract: We compare current-current correlators in lattice gauge calculations with correlators in different potential models for a pseudoscalar charmonium in the quark-gluon plasma. An important ingredient in the evaluation of the current-current correlator in the potential model is the basic principle that, out of the set of continuum states, only resonance states and Gamow states with lifetimes of sufficient magnitudes can propagate as composite objects and can contribute to the current-current correlator. When the contributions from the bound states and continuum states are properly treated, the potential model current-current correlators obtained with the potential proposed by Wong [ (2005)] are consistent with the lattice gauge correlators. The proposed potential model thus gains support to be a useful tool to complement lattice gauge calculations for the study of QQ{bar} states at high temperatures.

title: Quantum Treatment of the Multiple Scattering and Collective Flow in Intensity Interferometry
abstract: We apply the path‐integral method to study the multiple scattering and collective flow in intensity interferometry in high‐energy heavy‐ion collisions. We show that the Glauber model and eikonal approximation in an earlier quantum treatment are special examples of the more general path‐integral method. The multiple scattering and collective flow lead essentially to an initial source at a shifted momentum, with a multiple collision absorption factor that depends on the pion absorption cross section and a phase factor that depends on the deviations of the in‐medium particle momenta from their asymptotic values.

title: Twelve fundamental and two sextet fermion flavors
abstract: We report extended simulation results and their new analysis in two important gauge theories with twelve fermion flavors in the fundamental SU(3) color representation and two fermions in the sextet representation. We probe the $N_f=12$ model with respect to the conformal window using mass deformed finite size scaling (FSS) theory driven by the fermion mass anomalous dimension. Our results at fixed gauge coupling show problems with the conformal scenario of the $N_f=12$ model. In the sextet model with two flavors, under the conformal hypothesis, we determine large values for the anomalous fermion mass dimension with $\gamma\geq 1$. Since our sextet analysis favors the chiral symmetry breaking hypothesis without conformality, the large exponent $\gamma$ could play an important role in understanding the composite Higgs mechanism. The new results discussed here include our extended data sets and exceed what was presented at the conference.

title: Can the nearly conformal sextet gauge model hide the Higgs impostor
abstract: New results are reported from large scale lattice simulations of a frequently discussed strongly interacting gauge theory with a fermion flavor doublet in the two-index symmetric (sextet) representation of the SU(3) color gauge group. We find that the chiral condensate and the mass spectrum of the sextet model are consistent with chiral symmetry breaking in the limit of vanishing fermion mass. In contrast, sextet fermion mass deformations of spectral properties are not consistent with leading conformal scaling behavior near the critical surface of a conformal theory. A recent paper could not resolve the conformal fixed point of the gauge coupling from the slowly walking scenario of a very small nearly vanishing β -function (DeGrand et al.  ). It is argued that overall consistency with our new results is resolved if the sextet model is close to the conformal window, staying outside with a very small non-vanishing β -function. The model would exhibit then the simplest composite Higgs mechanism leaving open the possibility of a light scalar state with quantum numbers of the Higgs impostor. It would emerge as the pseudo-Goldstone dilaton state from spontaneous symmetry breaking of scale invariance. We will argue that even without association with the dilaton, the scalar Higgs-like state can be light very close to the conformal window. A new Higgs project of sextet lattice simulations is outlined to resolve these important questions.

title: The excited hadron spectrum in lattice QCD using a new method of estimating quark propagation
abstract: Progress in determining the spectrum of excited baryons and mesons in lattice QCD is described. Large sets of carefully‐designed hadron operators have been studied and their effectiveness in facilitating the extraction of excited‐state energies is demonstrated. A new method of stochastically estimating the low‐lying effects of quark propagation is proposed which will allow reliable determinations of temporal correlations of single‐hadron and multi‐hadron operators.

title: Extended hadron and two-hadron operators of definite momentum for spectrum calculations in lattice QCD
abstract: Multi-hadron operators are crucial for reliably extracting the masses of excited states lying above multi-hadron thresholds in lattice QCD Monte Carlo calculations. The construction of multi-hadron operators with significant coupling to the lowest-lying multi-hadron states of interest involves combining single hadron operators of various momenta. The design and implementation of large sets of spatially-extended single-hadron operators of definite momentum and their combinations into two-hadron operators are described. The single hadron operators are all assemblages of gauge-covariantly-displaced, smeared quark fields. Group-theoretical projections onto the irreducible representations of the symmetry group of a cubic spatial lattice are used in all isospin channels. Tests of these operators on 24^3 x 128 and 32^3 x 256 anisotropic lattices using a stochastic method of treating the low-lying modes of quark propagation which exploits Laplacian Heaviside quark-field smearing are presented. The method provides reliable estimates of all needed correlations, even those that are particularly difficult to compute, such as eta eta -> eta eta in the scalar channel, which involves the subtraction of a large vacuum expectation value. A new glueball operator is introduced, and the evaluation of the mixing of this glueball operator with a quark-antiquark operator, pi-pi, and eta-eta operators is shown to be feasible.

title: Conformal finite size scaling of twelve fermion flavors
abstract: Extended simulation results and their analysis are reported in a strongly coupled gauge theory with twelve fermion flavors in the fundamental SU(3) color representation. The conformality of the model is probed using mass deformed conformal finite size scaling (FSS) theory driven by the fermion mass anomalous dimension. Two independent conformal FSS fitting procedures are used in the analysis. The first one deploys physics motivated scaling functions, complemented by a second fitting procedure with spline based general B-forms for the scaling functions. The results at fixed gauge coupling show unresolved problems with the conformal hypothesis.