A ug 2 00 0 QCD Glueball Regge Trajectories and the Pomeron

We report glueball Regge trajectories 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 and reveal clear Regge trajectories for each L and S combination giving ~ J = ~ L + ~ S, where S is the total (sum) gluon spin. Significantly, all trajectories have the same 0.28 GeV −2 Regge slope, similar to the Pomeron value of 0.25 GeV −2. Recent lattice data further supports this result and yields an intercept close to the Pomeron. Preprint submitted to Elsevier Preprint 8 April 2008 A vintage problem in hadronic physics is to fundamentally explain the observed monotonously rising, to asymptotically flat cross section behavior with increasing Mandelstam variable s. Pre-QCD cross section theorems [1] involving t channel exchanges motivated Pomeranchuk’s assertion [2] that vacuum quantum number (J = 0) t channel exchanges would describe elastic cross section high energy dependence. Related, it was historically known that hadronic resonances with specific quantum numbers could be connected to a series or ”tower” of excited states. From this backdrop the successful Regge picture [3,4], with poles and trajectories linear in t (mass squared), α(t) = α(0) + b t, emerged which effectively described cross sections and resonances and therefore unified both scattering and bound state data. Of particular interest in this communication are analyses of high energy diffraction data [5,6] yielding a J = J Regge trajectory with the largest intercept α(0). This trajectory is called the Pomeron and from detailed fits is given by αP (t) = 1.08 + 0.25 t . Note that by definition, the Pomeron entirely governs and correctly reproduces the high energy scattering behavior since the cross section scales as s. The simplicity of this picture is very appealing and the Pomeron remains a contemporary tool for understanding high energy processes, both experimentally and theoretically [7] . In the discussion below we specialize to the soft non-perturbative Pomeron (for an account of the BFKL hard Pomeron in perturbative QCD see [8,9]). According to Regge theory, the trajectory describing scattering should also be consistent with physical hadron states, implying a J = J trajectory of mesons also having slope near 0.25 GeV . However, all known hadronic resonances (both mesons and baryons) fall on Chew-Frautschi [10] trajectories having very similar slopes close to 0.9 GeV −2 but different intercepts, (e.g. αρ(t) = . 55 + 0.9 GeV −2 t for the negative parity, positive G parity tower, ρ, ω, ω3, ρ3 · · ·). This incompatibility led to the conjecture that the Pomeron corresponded instead to a Regge trajectory for gluonic states, and most likely one describing the J glueballs. Accordingly, the gluonic nature of the Pomeron has been widely investigated (see [11] for a recent review) with several recent studies linking the Pomeron and glueball trajectories. From meson trajectories and Wilson loops, Kaidalov and Simonov [12] estimate that the glueball intercept is α(0) ≃ . 7, while Soloviev [13] computes α(0) = 1.07±0.03 using the quantized elliptic NambuGotto string model. Motivated by the Maldacena conjecture, and solving the dilaton wave equation, Brower, Mathur and Tan [14] obtained a glueball intercept of α(0) ≃ 1.2. Finally, using mass relations between the glueball and meson sectors, Brisudova, Burakovsky and Goldman [15] obtain a glueball Regge trajectory with slope ≃ 0.3 ± 0.1 GeV .