String Models of Glueball and Regge Trajectories

The closed relativistic string carrying two point-like masses is considered as the model of a glueball with two constituent gluons. Here the gluon-gluon interaction is simulated by a pair of strings. For this system exact solutions of classical equations of motions are obtained. They describe rotational states of the string resulting in the set of quasilinear Regge trajectories with different behavior. Introduction In various string models of mesons and baryons [1] – [8] the Nambu-Goto string simulates strong interaction between quarks at large distances and the QCD confinement mechanism. This string has linearly growing energy (energy density is equal to the string tension γ) and accounts for the nonperturbative contribution of the gluon field. All cited string hadron models generate linear or quasilinear Regge trajectories J ≃ α0 + αM, (1) where J and M are the angular momentum and energy of a hadron state, the slope α ≃ 0.9 GeV for the simplest model of meson is α = 1/(2πγ). The string models describe excited hadron states on the leading Regge trajectories if we use the rotational states of these systems (planar uniform rotations) for this purpose. These properties of the string were used for describing glueballs (bound states of gluons) on the base of different string models [9] – [12], including combinations of string and potential approaches [13] – [16]. The glueballs are predicted in QCD and observed in lattice QCD simulations [17, 18, 19]. The QCD glueball may be identified with the pomeron that is the Regge pole determining an asymptotic behavior of high-energy diffractive amplitudes [20, 21]. The pomeron Regge trajectory [19, 20] J ≃ 1.08 + 0.25M (2) differs from hadronic ones (1), in particular, its slope is essentially lower. String models of glueballs describing trajectories of the type (2) or some exotic hadron states (glueball candidates) were suggested in the following variants [9] – [15]: (a) the open ∗Is supported by Russian foundation of basic research, grant 05-02-16722