The exact quantization of the CLEO and BELLE data for $D$ mass differences by the harmonic quarks and oscillators

Abstract

The harmonic quarks and their complete oscillators are successfully used for the exact quantitative results and an explanation of the $D$ meson mass differences. For the first time it is shown that the mass differences of the charmed mesons with the same flavors are strictly quantized by the rest masses of harmonic quarks in both "free" state and complete oscillator state. The $D^*(2007)^0$ $\to$ $D^0$ transition has the following neutral quark group: $d$-oscillator + $u^0$-quark with rest energy 142.124 MeV. It is argued that it is the unique model solution within the 4$σ$ experimental interval. The $D_s^{*+}$ - $D_s^+$ mass difference is quantized by the simplest quark reaction with the difference energy 143.756 MeV. The energy of the $D_{sJ}$(2460)$^+$ $\to$ $D_s^+$ transition explains by the decay of the one complete $s$-oscillator with the energy 491.33 MeV. The full agreement with experimental data of CLEO and BELLE is obtained. The problems of a quark shells and the quantization by quark rest masses are discussed.