Tests of two-body Dirac equation wave functions in the decays of quarkonium and positronium into two photons
Two-body Dirac equations of constraint dynamics provide a covariant framework to investigate the problem of highly relativistic quarks in meson bound states. This formalism eliminates automatically the problems of relative time and energy, leading to a covariant three dimensional formalism with the same number of degrees of freedom as appears in the corresponding nonrelativistic problem. It provides bound state wave equations with the simplicity of the nonrelativistic Schr\"odinger equation. Here we begin important tests of the relativistic 16 component wave function solutions obtained in a recent work on meson spectroscopy, extending a method developed previously for positronium decay into two photons. Preliminary to this we examine the positronium decay in the $^{3}P_{0,2}$ states as well as the $^{1}S_{0}$. The two-gamma quarkonium decays that we investigate are for the ${\ensuremath{\eta}}_{c}$, ${\ensuremath{\eta}}_{c}^{\ensuremath{'}}$, ${\ensuremath{\chi}}_{c0}$, ${\ensuremath{\chi}}_{c2}$, ${\ensuremath{\pi}}^{0}$, ${\ensuremath{\pi}}_{2}$, ${a}_{2}$, and ${f}_{2}^{\ensuremath{'}}$ mesons. Our results for the four charmonium states compare well with those from other quark models and show the particular importance of including all components of the wave function as well as strong and c.m. energy dependent potential effects on the norm and amplitude. The results for the ${\ensuremath{\pi}}^{0}$, although off the experimental rate by 13%, are much closer than the usual expectations from a potential model. We conclude that the two-body Dirac equations lead to wave functions which provide good descriptions of the two-gamma decay amplitude and can be used with some confidence for other purposes.

title: Lectures on the Near-Side Ridge, Landau Hydrodynamics, and Heavy Quarkonia in High Energy Heavy-Ion Collisions
abstract: 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: The Momentum Kick Model Description of the Near-Side Ridge and Jet Quenching
abstract: In central high-energy heavy-ion collisions, jets are produced in nucleon-nucleon collisions and they interact with the dense medium produced in the interacting region. Depending on the relative azimuthal angle relative to the trigger particle, observed high-pt jets can be classified as near-side jets or away-side jets. An away-side jet is associated with a broad cone of particles pointing azimuthally opposite to the trigger particle direction. The strong attenuation of the away-side jet in its passage through the produced dense matter is one of the many notable experimental observations in relativistic heavy-ion collisions and is a signature for the production of the strongly-coupled quark-gluon plasma [1, 2, 3, 4]. On the other hand, a near-side jet is characterized by the presence of associated particles within a narrow azimuthal angle along the trigger particle direction. It retains many of the characteristics of the associated fragmentation products as those of a jet in pp and peripheral heavy-ion collisions. The near-side jet occurs when the high-pt jet emerges near the surface of the produced parton medium.

title: Meson-meson scattering in relativistic constraint dynamics
abstract: Dirac's relativistic constraint dynamics have been successfully applied to obtain a covariant nonperturbative description of QED and QCD bound states. We use this formalism to describe a microscopic theory of meson-meson scattering as a relativistic generalization of the nonrelativistic quark-interchange model developed by Barnes and Swanson.

title: Wigner function of produced particles in string fragmentation
abstract: I show that quantum chromodynamics in four dimensions (QCD4) with transverse confinement can be approximately compactified into QCD2 with a transverse quark mass m{sub T} that is obtained by solving a set of coupled transverse eigenvalue equations. In the limits of a strong coupling and a large number of flavors, QCD2 further admits Schwinger QED2-type bosonized solutions. I therefore examine phenomenologically the space-time dynamics of particles produced in string fragmentation by studying the Wigner function of bosons produced in Schwinger QED2, which mimics many features of string fragmentation in quantum chromodynamics. I find that particles with momenta in different regions of the rapidity plateau are produced at the initial moment of string fragmentation as a quark pulls away from an antiquark at high energies, in contrast to classical depictions of string fragmentation with longitudinal space-momentum-time ordering.

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: Confining force and running coupling with twelve fundamental and two sextet fermions
abstract: We investigate two models of much recent interest in lattice Beyond Standard Model studies: N_f=2 fermions in the 2-index symmetric (sextet) representation, and N_f=12 fermions in the fundamental representation, both with SU(3) gauge symmetry. We present results at fixed lattice spacing for the static fermion potential and force as measured via lattice simulations. We show indications that both models are confining in the chiral limit and that neither theory is conformal. This is consistent with our findings for the mass spectrum, which indicate that chiral symmetry is spontaneously broken in both theories.

title: Excited isovector mesons using the stochastic LapH method
abstract: The spectrum of excited isovector mesons is studied using a 32^3 x 256 anisotropic lattice with u,d quark masses set to give a pion mass near 240 MeV. Results in the bosonic isovector nonstrange symmetry channels of zero total momentum are presented using correlation matrices of unprecedented size. In addition to spatially-extended single-meson operators, large numbers of two-meson operators are used, involving a wide variety of light isovector, isoscalar, and strange meson operators of varying relative momenta. All needed Wick contractions are efficiently evaluated using a stochastic method of treating the low-lying modes of quark propagation that exploits Laplacian Heaviside quark-field smearing. Level identification is discussed.

title: A Model for Neutrino Masses and Dark Matter with the Discrete Gauge Symmetry
abstract: A simple renormalizable U(1) gauge model is constructed to explain the smallness of the active neutrino masses and provide the stable cold dark matter candidate simultaneously. The local U(1) symmetry is assumed to be spontaneously broken by a scalar field around the TeV scale. The active neutrino masses are then generated at one-loop level. This model contains several cold dark matter candidates whose stability is guaranteed by a residue discrete gauge $Z_2$ symmetry a la the Krauss-Wilczek mechanism. Unlike the other dark matter models, no further global discrete or continuous symmetry is introduced. Moreover, all the new degrees of freedom beyond the Standard Model acquire their masses only after the spontaneous breaking of U(1) thus they could be probed at or below the TeV scale. The possible cosmological and phenomenological consequences are briefly discussed.

title: Can a light Higgs impostor hide in composite gauge models
abstract: The 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 is investigated. In previous studies  the chiral condensate and the mass spectrum were shown to be consistent with chiral symmetry breaking (χSB) at vanishing fermion mass. The recently reported β -function  is not inconsistent with this observation, suggesting that the model is very close to the conformal window and a light “Higgs impostor” could emerge as a composite state. In this work we describe the methodology and preliminary results of studying the emergence of the light composite scalar with 0++ quantum numbers.

title: A novel method for evaluating correlation functions in lattice hadron spectroscopy
abstract: We describe a new approach for evaluating hadronic correlation functions which combines Laplacian-Heaviside quark smearing with a stochastic estimator of quark propagators. This method utilizes noise dilution in a new way to reduce the variance in correlators. The efficacy of the new algorithm is demonstrated on a number of systems, including disconnected diagrams and multi-hadron correlators, on a small lattice where comparisons with the results obtained with exactly determined quark propagators are possible. On larger lattice volumes, the use of exact propagators becomes prohibitively expensive, while the stochastic method is still computationally feasible.