The Physical Foundation of the Quark Model: the Quark Model as an approximation of the BCC Model

Abstract

From the Dirac sea concept, the BCC model infers that the quarks u and d constitute a body center cubic quark lattice in the vacuum; when a quark $q^*$ is excited from the vacuum, the nearest primitive cell u' and d' is accompanying excited by the quark $q^*$. Using the energy band theory, the model deduces the quantum numbers (I, S, C, b, and Q) and the masses of all quarks using a united mass formula. Then, it shows that the system of} 3 excited quarks ($q^*u'd'$$) is a baryon, and it deduces the baryon spectrum in terms of the sum laws. This theoretical baryon spectrum is in accordance with the experimental results. It also shows that there are only two elementary quarks (u and d), while the other quarks (s, c, b, ...) are the excited states of the elementary quarks, hence the SU(3) (u, d, and s), the SU(4) (u, d, s, and c), and the SU(5) (u, d, s, c, and b) are the natural extensions of the SU(2) (u and d). The BCC model provides the physical foundation (quarks, SU(N) groups, and that a baryon is made of 3 quarks) for the Quark Model. The Quark Model is the SU(N) approximation of the BCC model. The confinement concept is not needed in the BCC model, because it is replaced by the accompanying excitation concept. The SU(N)} groups are also not} necessary, as they are replaced by the body center cubic groups. We also predict some new baryons: }$Λ(2560)$, $Σ_{C}(2280)$, $Ω^{-}(3720)$, $Λ_{C}^{+}(6600)$, $Λ_{b}^{0}(9960)$...