"Quark Confinement" and Evolution of Covariant Hadron-Classification   Scheme
  The extension of Non-Relativistic-to-Covariant classification scheme seems to be an urgent problem in the Hadron Spectroscopy. Here are given the recent results of our research. 1) Brief history of our way of the extension on Kinematical Frameworks: from SU(2)_{sigma} $\otimes$ O(3)_{L} to U (4)_{DS,m} (Tensor-space of Dirac Spinor with the static unitary symm. SU(2)_{m}, which is new Mass-Reversal symm. reflecting the situation of Q.C.) $\otimes O(2)_{r\perp v}$ (2-dim. internal spatial-vector r vertical to Boost-velocity v, embedded in the O(3,1)_{Lorentz}). Also is brought in Cov. scheme the thus far Overlooked Chirality Symm. of QCD/Stand. Gauge Model. 2) Propertime tau-Quantum Mechanics for Conf. Q. System and Quantization of Comp. Hadron field is developed. The similar to conventional procedures are performed in Lorentz-Inv. Particle Frame (Galilean Inertial Frame with v=const) which becomes Lorentz-Cov. Observer F., when v=0. The one notable feature of the tau-Q.M. is concerned only future-development, inducing the Crossing Rule; the other also inducing Existence of the Chiral-Quark (JP=(1/2)-) in addition to Pauli-Quark (JP=(1/2)+), which is Origin of SU(2)_m-symm., leading to Existence of New-Exotics. 3) Evolved framework of hadron spectroscopy guided by tau-Q.M. is summarized: Especially, "Regge Trajectories", in qqbar meson system are given by $M^2$ vs. $\hat{N}(n,l)$; $M^2=M_{0}^2+N \Omega$ (N=2n+l), Intrinsic spin of Comp. Hadrons J=S, where Orbital l contributes only to N. 4) New Classif. scheme is applied to Phenomenology of Bottomonium System.As a result is shown Remarkable Fact, including a serious Problem in the N.R. scheme, concerned on Spin-Flip Mechanism of Heavy Quarks, seems to disappear in our scheme. This seems to suggest that the phenomenological knowledge,thus far obtained resorting on N.R.scheme, should be reexamined from the covariant one. 
Shin Ishida
hep-ph