A comprehensive, relativistic many-body approach to hadron structure is advanced based on the Coulomb gauge QCD Hamiltonian. Our method incorporates standard many-body techniques which render the approximations amenable to systematic improvement. Using BCS variational methods, dynamic chiral symmetry breaking naturally emerges and both quarks and gluons acquire constituent masses. Gluonia are studied both in the valence and in the collective, random phase approximations. Using representative values for the strong coupling constant and string tension, calculated quenched glueball masses are found to be in remarkable agreement with lattice gauge theory.Typeset using REVT E X 1 Our knowledge of the standard model cannot be considered complete until explicit gluonic degrees of freedom are found and understood [1]. In an effort to address this issue we advance a comprehensive framework for consistently describing and understanding hadron structure -including the glueball and hybrid sectors. The model is motivated in part by our previous studies of relativistic [4] The idea is to build on the known successes of the constituent quark model for heavy quarks by considering a many-body relativistic Hamiltonian in a quasiparticle basis where dynamical chiral symmetry breaking and massive gluon modes are explicit. Such a model incorporates an extensive Fock space but reduces to the simple quark model in the valence approximation. Furthermore, the simultaneous presence of quark and gluon degrees of freedom permits studying their mixture in hybrid and glueball states. This is especially important since glueball searches tend to occur in meson-rich regions of the hadron spectrum and also because it may be years before lattice gauge calculations provide significant insight. This letter focuses on the gluonic sector of the model Hamiltonian, presenting the glueball spectrum calculation and a discussion of the associated approximation schemes. In the summary we comment on other issues regarding applications to mesons, baryons and hybrids.There have been a variety of previous glueball studies: the Bag Model [6][7][8], QCD

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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.PACS numbers: 12.39. Pn, 11.10.St, 12.39.Ki, 12.39.Mk Common to the diverse areas of condensed matter, molecular, atomic, and nuclear physics is the routine implementation of many-body techniques such as the Bardeen, Cooper, Schrieffer (BCS), Tamm-Dancoff (TDA), and random phase approximation (RPA) methods. Particle physics, with an inherent few-body nature, has generally been devoid of such applications even though hadronic structure, requiring a relativistic QCD description, is an extremely challenging many-body problem. The purpose of the present Letter is to report a comparative study documenting the powerful utility of the above techniques for hadronic systems and to detail new, important meson structure results clarifying the nature of spin splittings and the role of chiral symmetry. The equations of motion, while numerically solvable, exhibit a richness and complexity beyond the simple two-body equations such as the generalized Schrödinger schemes. We find that both TDA and RPA solutions to an approximate QCD Hamiltonian with linear confinement reproduce the meson spectrum except for the pion, where only the RPA reasonably describes the mass and decay constant due to proper implementation of chiral symmetry.This work complements our previous many-body treatment [1] of the gluonic sector in which the lattice gauge "measurements" were reproduced. Our collaborative program seeks to develop a rigorous effective Hamiltonian from QCD and then to comprehensively investigate hadronic structure by systematic, accurate diagonalization utilizing controllable approximations. Reference [2] details our renormalization program, based upon a continuous cutoff regularization and similarity transformation. That work addressed only the gluon sector but a similar effort is currently in progress for the quark sector. Accordingly, this paper presents many-body solutions for only the unrenormalized effective Hamiltonian. The starting point is the approximate QCD quark Hamiltonian in the Coulomb gaugeinvolving the quark field C q ͑ x͒, current quark mass m q , and color density r a ͑ x͒ C y q ͑ x͒T a C q ͑ x͒. Coupling to the gluonic sector is omitted and the Faddeev-Popov determinant is replaced by its lowest order unit value. Consistent with our previous work [1], the confining potential is a linear interaction, V sj x 2 yj, rather than the harmonic oscillator [3,4] since lattice gauge theory generates this form ...

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 (k F a) → ∞ and (k F r) → 0, where k F 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.

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 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-Oaks-Renner relation. Finally, by including D waves in our charmonium calculation we have resolved the anomalous overpopulation of J/Ψ states relative to observation. PAC number(s): 12.39.Pn, 12.40.Yx Jona-Lasinio model. In Sec. III we detail our numerical, supercomputer solution of the gap equation along with the quark condensate and constituent mass values. Sections IV A and IV B describe the TDA and RPA, respectively, while Sec. IV C addresses weak decays and Sec IV D presents a derivation of the Gell-Mann-Oakes-Renner relation. The TDA and RPA meson spectra are compared and discussed in Sec. V. This section also includes results from a simple SU f (3) flavor mixing analysis for the η-η ′ system and our predictions for the charmed mesons. Conclusions and future work are summarized in Sec. VI. Finally, Appendix A provides further details regarding the BCS transformation and vacuum state while Appendix B presents the most general TDA equation for arbitrary angular momentum.

Weinberg's theorem for -scattering, including the Adler zero at threshold in the chiral limit, is analytically 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 -scattering amplitudes are calculated using the DysonSchwinger equations in the rainbow-ladder truncation, confirming the formal derivation.

We report an odderon Regge trajectory emerging from a field theoretical Coulomb gauge QCD model for the odd signature J PC (P C ÿ1) glueball states. The trajectory intercept is clearly smaller than the Pomeron and even the ! trajectory's 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. DOI: 10.1103/PhysRevLett.96.081601 PACS numbers: 11.55.Jy, 12.39.Mk, 12.39.Pn, 12.40.Yx Regge trajectories [1] have long been an effective phenomenological tool in hadronic physics. In Regge theory the scattering amplitude is governed by Regge poles, n s , in the complex J (angular momentum) plane. For integer J the amplitude has a pole in the complex s plane and, by crossing symmetry, for t < 0 at high s the cross section is dominated by the Regge trajectory, t bt 0 , with the largest intercept, 0 . This conjecture provides a unifying connection between hadron spectroscopy (Chew-Frautschi plot of J versus t M 2 J ) and the high energy behavior of the total cross section which scales as s 0 ÿ1 . For elastic scattering the energy dependence is well described by the leading Regge trajectory, the Pomeron, having P 0 1 and b P 0:2-0:3 GeV ÿ2 [for recent fits see Ref.[2] ]. Of course the Pomeron does not relate to conventional hadron spectra since meson trajectories typically have larger slopes, b M 0:9 GeV ÿ2 , and smaller intercepts, M 0 0:55. According to the glueball-Pomeron conjecture [3,4], supported by lattice [5] and other models [6], this trajectory is instead connected to glueball spectroscopy. The different Pomeron and meson trajectory slopes can be generated [4] by the gg and q q color factors, respectively, used in confining 2-body models. Because of the large gluon mass gap, which suppresses relativistic corrections and transverse gluon exchange [7], these models tend to be more robust for glueballs than mesons. They produce a Pomeron consisting of even signature J glueballs having maximum intrinsic spin S coupled to minimum possible orbital L.Of active interest is the odd signature, P C ÿ1 counterpart to the Pomeron, the odderon [8], for which there is no firm experimental evidence. Whereas the Pomeron predicts asymptotically equal pp and pp cross sections, the competitive presence of the odderon or any other C ÿ1 trajectory would produce a difference. However, high energy measurements reveal a minimal difference indicating that the odderon, if it exists, would have a smaller intercept probably at most comparable to the ! value, ! 0 0:5. Indeed, dedicated exclusive searches at HERA [9] exclude an odderon Regge trajectory with an intercept greater than 0.7. Although perturbative QCD calculations [10] based on the BKP equation predict an odderon intercept close to 1, they are only reliable for both s; ÿt QCD and thus suspect for t 0 . For example, the predicted ...

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-CooperSchrieffer, 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 -mass difference. A reasonable description of the observed meson spin splittings and chiral quantities, such as the quark condensate and the 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 b 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.