A Universal Spring and Meson Trajectories
S. Ishida, M. Oda
Progress of theoretical physics
1033 In the covariant oscillator quark model (COQM) the squared·mass spectra of confined meson systems are described by harmonic oscillators. On the basis of a "proto-type" classical Lagrangian for the confined particle system, which leads to the basic equation in the COQM, we propose, in this work, a hypothesis of universal spring, which predicts the respective values of oscillator quanta in terms of constituent quark masses and a spring constant. This prediction is compared systematically
... experiments by examining various kinds of meson-mass trajectories versus number of oscillator quanta in all possible cases of flavor-configurations. It seems to us that our universality is realized experimentally, although much more confirmation is necessary. § 1. Introduction Recently there seems to be a strong belief among theoretical physicists that quantum chromo dynamics (QCD) is the final theory for describing the strong interaction of hadrons. However, it is to be noted that QCD is the dynamics on the world of quarks and gluons which are all confined, while the strong interaction is concerned with the observable hadrons themselves. Since we have no established rigorous method of treating the relativistic bound state or confinement problem and the corresponding numerical lattice calculation approach is still in a primitive stage, the direct way to the strong interaction from QCD seems to be almost closed. In this situation to make any quantitative analyses we must anyhow resort to an indirect way, that is, a model which simulates QCD. Actually the non-relativistic quark models (NRQM) guided· by QCD have been very successful in treating the static problems of hadrons. However, they are obviously inapplicable to non-staticproblems such as hadron reactions, where a covariant treatment is required. The difficulty is most seriously seen in treating the electromagnetic (EM) processes of hadrons, where it is indispensable to get the conserved effective currents described in terms of "observable" hadrons themselves, and in doing so the covariant description of the center-of-mass motion of hadrons is necessary. This difficulty still remains in the semi-relativistic attempts l ) and even in the covariant approaches, 2) based upon the constraint dynamics, which can, by taking into account the effect of relativistic motion properly, describe the spectra of light-and heavy-quark systems in a unified way. A similar remark is also applicable to the heavy quark effective theory3) which are receiving much attention recently. This point has been one of the most important motives for the covariant oscillator quark model (COQM), where hadrons are defined as Fierz components of multilocal fields which satisfy a covariant equation heuristically derived.