J--Glueballs and a Low Odderon Intercept

Abstract

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 ...

Coulomb gauge approach to qq̄g hybrid mesons

“…In this work, we study qqg hybrid states using a field theoretical, relativistic many-body approach based upon an effective QCD Hamiltonian, H eff , formulated in the Coulomb gauge. This model successfully describes the meson spectrum [28,29] and is also consistent [30] with lattice glueball (and oddball) predictions. Using standard bare current quark masses, it properly incorporates chiral symmetry, yet dynamically generates a constituent mass and spontaneous chiral symmetry breaking [31].…”

“…We also made predictions for three-body glueballs (oddballs) [30] and published [32] a brief study of the three-body hybrid meson using a variational treatment. We now extend the latter and also provide more complete details of the variational calculation.…”

“…In previous publications [28,29,30,31] we have used this model to study the two-body meson and glueball systems by diagonalizing H eff using the Tamm-Dancoff and Random Phase approximations. We also made predictions for three-body glueballs (oddballs) [30] and published [32] a brief study of the three-body hybrid meson using a variational treatment.…”

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The BES f0(1810): a new glueball candidate

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