Status of $\psi$ (3686), $\psi$ (4040), $\psi$ (4160), Y (4260), $\psi$ (4415) and X (4630) charmonia like states

Abstract

We examine the status of charmonia like states by looking into the behaviour of the energy level differences and regularity in the behaviour of the leptonic decay widths of the excited charmonia states. The spectroscopic states are studied using a phenomenological Martin-like confinement potential and their radial wave functions are employed to compute the di-leptonic decay widths. Their deviations from the expected behaviour provide a clue to consider them as admixtures of the nearby S and D states. The present analysis strongly favour \\backslash$psi \$ (3686) as admixture of $c \bar{c}$ (2S) and $c \bar{c}$g (4.1 GeV) hybrid, \\backslash$psi\$(4040)and\$$\backslash$psi\$(4160)asadmixturestatesofcharmonia(3S,3D)stateswithmixingangle\$$\backslash$theta\$=11$^\circ$and45$^\circ$respectively.WeidentifyY(4260)asapure$c \bar{c}$(4S)statewhoseleptonicdecayispredictedas0.65keV.WhileX(4630)isclosertothe$c \bar{c}$(6S)state.Thestatusof\$$\backslashpsi \ (4415) is still not clear as it does not fit to be pure or admixture state.