The exact interpretation of mass differences in upper part of the charmonium spectrum

Abstract

Mass differences of the charmonium mesons $\psi$(3770), $X$(3872), $\chi$(3929), $X$(3940), $\psi$(4040), $\psi$(4160), $X$(4259) and $\psi$(4415) have been studied. The analysis of data has shown, 5 of 7 mass differences with $\psi$(4415) are precisely interpreted by using of harmonic quarks and their complete oscillators. Upper part of the charmonium spectrum consists of two groups. Except for two particles ($\psi$(3770) and $\psi$(4040)) connected among themselves, the others 5 particles are connected with a meson $\psi$(4415). The levels are separated by elementary groups of harmonic quarks and completed oscillators. Experimental and calculated data are in the good consent. The masses of mesons $\psi$(4415), $X$(4260), $\psi$(4160), $X$(3943) and $\chi$(3929) were recalculated. The second group demonstrates that harmonic quarks can also well work below threshold $D\bar{D}$.