Stephen R. Cotanch

Glueball spectroscopy in a relativistic many-body approach to hadronic structure.

A comprehensive, relativistic many-body approach to hadron structure is advanced based on the Coulomb gauge QCD Hamiltonian. Dynamical chiral symmetry breaking naturally emerges, and both quarks and gluons acquire constituent masses when standard many-body techniques are employed. Gluonia are studied both in the valence and in the collective, random phase approximations. Calculated quenched glueball masses are found to be in remarkable agreement with lattice gauge theory when using representative values for the strong coupling constant and string tension. {copyright} {ital 1996 The American Physical Society.}

Chirally symmetric quark description of low-energy pi pi scattering

Weinberg’s theorem for π-π scattering, including the Adler zero at threshold in the chiral limit, is analyticall proved for microscopic quark models that preserve chiral symmetry. Implementing Ward-Takahashi identities, the isospin 0 and 2 scattering lengths are derived in exact agreement with Weinberg’s low energy results. Our proof applies to alternative quark formulations including the Hamiltonian and Euclidean space Dyson-Schwinger approaches. Finally, the threshold π-π scattering amplitudes are calculated using the Dyson- Schwinger equations in the rainbow-ladder truncation, confirming the formal derivation.

Meson Structure in a Relativistic Many-Body Approach

Results from an extensive relativistic many-body analysis utilizing a realistic effective QCD Hamiltonian are presented for the meson spectrum. A comparative numerical study of the BCS, Tamm-Dancoff (TDA), and RPA treatments provides new, significant insight into the condensate structure of the vacuum, the chiral symmetry governance of the pion, and the meson spin, orbital, and flavor mass splitting contributions. In contrast to a previous glueball application, substantial quantitative differences are computed between TDA and RPA for the light quark sector with the pion emerging as a Goldstone boson only in the RPA.

Relativistic many body Hamiltonian approach to mesons

Abstract 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 explicitly 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 π – ρ 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–Oakes–Renner relation.

QCD based quark description of pi pi scattering up to the sigma and rho region

We study forward and backward pi-pi scattering within a QCD model based on the Dyson--Schwinger, Bethe--Salpeter equations truncated to the rainbow-ladder level. Our microscopic relativistic quark formulation preserves chiral symmetry and reproduces the observed scattering lengths for total isospin zero, one and two. At higher energies both scalar and vector meson resonances naturally occur in the scattering amplitudes. We also report a comparative study with phenomenological meson-exchange models and find such approaches are reasonable especially near pi-pi resonances.

Many body methods and effective field theory

In the framework of pionless nucleon–nucleon effective field theory we study different approximation schemes for the nuclear many body problem. We consider, in particular, ladder diagrams constructed from particle–particle, hole–hole, and particle–hole pairs. We focus on the problem of finding a suitable starting point for perturbative calculations near the unitary limit (kFa)→∞ and (kFr)→0, where kF is the Fermi momentum, a is the scattering length and r is the effective range. We try to clarify the relationship between different classes of diagrams and the large g and large D approximations, where g is the fermion degeneracy and D is the number of space–time dimensions. In the large D limit we find that the energy per particle in the strongly interacting system is 1/2 the result for free fermions.

J(--) glueballs and a low odderon intercept

We report an odderon Regge trajectory emerging from a field theoretical Coulomb gauge QCD model for the odd signature J(PC) (P = C = -1) glueball states. The trajectory intercept is clearly smaller than the Pomeron and even the omega trajectorys intercept which provides an explanation for the nonobservation of the odderon in high energy scattering data. To further support this result we compare to glueball lattice data and also perform calculations with an alternative model based upon an exact Hamiltonian diagonalization for three constituent gluons.

QCD glueball Regge trajectory and the pomeron

We report a glueball Regge trajectory emerging from diagonalizing a confining Coulomb gauge Hamiltonian for constituent gluons. Using a BCS vacuum ansatz and gap equation, the dressed gluons acquire a mass, of order 800 MeV , providing the quasiparticle degrees of freedom for a TDA glueball formulation. The TDA eigenstates for two constituent gluons have orbital, L, excitations with a characteristic energy of 400 MeV revealing a clear Regge trajectory for ~ J = ~ L+ ~ S, where S is the total (sum) gluon spin. Significantly, the S = 2 glueball spectrum coincides with the Pomeron given by αP(t) = 1.08+0.25 t. Finally, we also ascertain that lattice data supports our result, yielding an average intercept of 1.1 in good agreement with the Pomeron.

Hyperfine meson splittings: chiral symmetry versus transverse gluon exchange

Meson spin splittings are examined within an effective Coulomb gauge QCD Hamiltonian incorporating chiral symmetry and a transverse hyperfine interaction necessary for heavy quarks. For light and heavy quarkonium systems the pseudoscalar-vector meson spectrum is generated by approximate Bardeen-Cooper- Schrieffer, random-phase approximation diagonalizations. This relativistic formulation includes both S and D waves for the vector mesons which generates a set of coupled integral equations. A smooth transition from the heavy to the light quark regime is found with chiral symmetry dominating the p-r mass difference. A reasonable description of the observed meson spin splittings and chiral quantities, such as the quark condensate and the p mass, is obtained. Similar comparisons with Tamm-Dancoff diagonalizations, which violate chiral symmetry, are deficient for light pseudoscalar mesons, indicating the need to simultaneously include both chiral symmetry and a hyperfine interaction. The hb mass is predicted to be around 9400 MeV, consistent with other theoretical expectations and above the unconfirmed 9300 MeV candidate. Finally, for comparison with lattice results, the J reliability parameter is also evaluated.

Ladder Dyson-Schwinger calculation of the anomalous gamma-3pi form-factor

The anomalous processes, \gamma \to 3 \pi and \gamma \pi \to \pi\pi, are investigated within the Dyson-Schwinger framework using the rainbow-ladder approximation. Calculations reveal that a complete set of ladder diagrams beyond the impulse approximation are necessary to reproduce the fundamental low-energy theorem for the anomalous form factor. Higher momentum calculations also agree with the limited form factor data and exhibit the same resonance behavior as the phenomenological vector meson dominance model.