Relativistic Quark Model Calculation of the l1, l2 Coefficients of the Chiral Lagrangian

We briefly report on a relativistic quark model scheme to calculate the O(P^4) pion-pion vertex in the planar approximation and in the chiral limit. The calculation is reduced to the solution of simple integral equations (Bethe-Salpeter like) by an effective use of chiral Ward Identities. Specific model computations are provided.Comment: Proc. V Intnal. Conf. on Quark Confinement and the Hadron Spectrum, Gargnano,Italy 200

Relativistic Many-Body Hamiltonian Approach to Mesons

We represent QCD at the hadronic scale by means of an effective Hamiltonian, $H$, formulated in the Coulomb gauge. As in the Nambu-Jona-Lasinio model, chiral symmetry is explicity broken, however our approach is renormalizable and also includes confinement through a linear potential with slope specified by lattice gauge theory. This interaction generates an infrared integrable singularity and we detail the computationally intensive procedure necessary for numerical solution. We focus upon applications for the $u, d, s$ and $c$ quark flavors and compute the mass spectrum for the pseudoscalar, scalar and vector mesons. We also perform a comparative study of alternative many-body techniques for approximately diagonalizing $H$: BCS for the vacuum ground state; TDA and RPA for the excited hadron states. The Dirac structure of the field theoretical Hamiltonian naturally generates spin-dependent interactions, including tensor, spin-orbit and hyperfine, and we clarify the degree of level splitting due to both spin and chiral symmetry effects. Significantly, we find that roughly two-thirds of the $\pi$-$\rho$ mass difference is due to chiral symmetry and that only the RPA preserves chiral symmetry. We also document how hadronic mass scales are generated by chiral symmetry breaking in the model vacuum. In addition to the vacuum condensates, we compute meson decay constants and detail the Nambu-Goldstone realization of chiral symmetry by numerically verifying the Gell-Mann-Oaks-Renner relation. Finally, by including D waves in our charmonium calculation we have resolved the anomalous overpopulation of $J/\Psi$ states relative to observation

Chiral symmetry breaking for fermions charged under large Lie groups

We reexamine the dynamical generation of mass for fermions charged under various Lie groups with equal charge and mass at a high Grand Unification scale, extending the Renormalization Group Equations in the perturbative regime to two-loops and matching to the Dyson-Schwinger Equations in the strong coupling regime.Comment: 8 pages, 12 plot

Soft interactions in jet quenching

We study the collisional aspects of jet quenching in a high energy nuclear collision, especially in the final state pion gas. The jet has a large energy, and acquires momentum transverse to its axis more effectively by multiple soft collisions than by few hard scatterings (as known from analogous systems such as J/\psi production at Hera). Such regime of large E and small momentum transfer corresponds to Regge kinematics and is characteristically dominated by the pomeron. From this insight we estimate the jet quenching parameter in the hadron medium (largely a pion gas) at the end of the collision, which is naturally small and increases with temperature in line with the gas density. The physics in the quark-gluon plasma/liquid phase is less obvious, and here we revisit a couple of simple estimates that suggest indeed that the pomeron-mediated interactions are very relevant and should be included in analysis of the jet quenching parameter. Finally, the ocasional hard collisions produce features characteristic of a L\`evy flight in the q_perp^2 plane perpendicular to the jet axis. We suggest one- and two-particle q_perp correlations as interesting experimental probes.Comment: 14 pages, 16 figure