Evidence for Color-by-Color Disengagement from the Process of Lepton Production Associated with the Ψ-Series and Υ-Series Mesons - White, D. (Communications in Mathematics and Applications, 2010)
Form factors associated with the Ψ(1S) and (2S) are calculated directly from relevant experimental data in order to verify that they are given by f_1 = (1-q_s^2) = (8/9) in the case of the Ψ-Series mesons and f_2 = (1-q_c^2) = (5/9) in the case of the Υ-series mesons, where q_s = -1/3 represents the charge of the strange (s) quark and q_c= 2/3 represents the charge of the charm (c) quark. In two recent articles by the author form factors have been shown to represent the fraction of the originally produced quark/anti-quark (QQ^*) state which makes a transition to a QQ^* state of the next lowest mass … ss^* in the case of the Ψ-Series mesons and cc^* in the case of the Υ-series mesons … and thus figure prominently into the calculation of the hadronic and leptonic widths of a given meson via the constructs of the Gluon Emission Model (GEM). We undertake to calculate the form factors of the Ψ(2S), the Ψ(4040), the Ψ(4160), and the Ψ(4415) in order to show that f_1 = (8/9) is representative of all Ψ-states listed above, if and only if, it is assumed that one quark color (in the case of the Ψ(2S)) or two quark colors (in all other cases) become disengaged from lepton production. A similar set of calculations is performed as to the Υ-series mesons, such illustrating that all three quark colors are functional in lepton production in Υ(2S) decay, fewer than three functional in Υ(3S) and Υ(4S) decay, with likely only one color functioning in Υ(10860) and Υ(11020) decay. For each meson series, then, lepton decay is characterized by the phenomenon of sequential disengagement of quark color from lepton production as a function of increasing mass. In the Υ(3S) and Υ(4S) decay … and in the Ψ(3770) decay … it is observed that half-integer color contributions are in force … possibly leading to a heretofore unobserved quark property: "shade" of color ("light" and "dark").