Quantized relativistic flux tube

Abstract

We explore the dynamics of mesons composed of spinless quarks connected by a straight flux tube. The mesons are quantized and the constituent motion is relativistic. The methods developed are applied to mesons containing equal mass quarks and heavy-light quarks. For massless quarks a nearly straight leading Regge trajectory with Nambu slope is accompanied by nearly parallel equally spaced daughter trajectories. For heavy-light mesons an analogous structure is found but with double the usual Nambu slope. Comparison with six observed spin-averaged heavy-light meson states yields good agreement. PACS number(s): 12.38.Aw, 12.38.Lg

Hybrid mesons in the context of the relativistic equation

“…This is consistent with the corrections of Merlin and Paton [3] where the string rigid-rod moment of inertia is included in the centrifugal-barrier term of the effective radial Hamiltonian. However, the rigid-rod flux tube model developed by Olsson is difficult to solve [10][11][12][13], since the quantization of the meson is reduced to a transcendental algebraic matrix equation. Brambilla and Prosperi [14,15] have constructed the Hamiltonian of the relativistic rigid-rod explicitly in terms of canonical variables in the form of an expansion in the string tension σ constant.…”

“…However, almost all of the corrections may be incorporated into a redefinition of the potential surfaces to include the moment of inertia of the string [3]. Olsson and coworkers [7][8][9][10][11][12] have formulated a quantized relativistic rigid-rod flux tube model for mesons in which the flux tube terminates on fermionic quarks with arbitrary mass. In their model the string always lies in a straight line between the quarks and the quarks move freely so that both rotation and radial motion can occur.…”

“…In their model the string always lies in a straight line between the quarks and the quarks move freely so that both rotation and radial motion can occur. The entire system is quantized in orbital angular momentum and energy [10]. The formalism for fermionic quark confinement is unusual in that the string rigid-rod moment of inertia is introduced into the kinetic rather than the usual interaction term.…”

A comparative analysis of Mesonic, Baryonic and Glueball Regge trajectories

“…Also, using quantized flux tube concept, the effect of the quark mass on the RTs has been investigated [28] and the dimensionless slope comes out to be…”

“…The authors [27][28][29] have done a pioneering work in "String Model" to study the mesonic RTs. They deduced that at high J values, RTs are linear and parallel, while at low J, mesonic RTs essentially show non linearity.…”