Leptonic and Digamma decay Properties of S-wave quarkonia states

Abstract

Based on Martin like potential, the S-wave masses of quarkonia have been reviewed. Resultant wave functions at zero inter quark separation are employed to compute the hyperfine splitting of the nS states and the leptonic and digamma decay widths of $n{^3S_1}$ and $n{^1S_0}$ states of quarkonia respectively. Analysis on the level differences of S-wave excited states of quantum mechanical bound systems show a systematic behaviour as n-increases. In view of such systematic behaviour expected for quarkonia, we observe that Y(4263) and X(4630) $1^{--}$ states are closer to the 4S and 6S states while $\psi(4415)$ and Z(4430) are closer to the 5S state of $c\bar{c}$ systems. Similarly we find $\Upsilon (10865)$ is not fit to be the 5S state of $b\bar{b}$ system. while $Y_b (10880)$ observed by Belle or (10996) observed by Babar fit to be the 6S state of bottonia. Our predicted leptonic width, 0.242 keV of $\Upsilon (10579, 4S)$ is in good agreement with the experimental value of 0.272 $\pm$ 0.029 keV. We predict the leptonic widths of the pure 5S and 6S states of upsilon states as 0.191 keV and 0.157 keV respectively. In the case of charmonia, we predict the leptonic widths of the 4S, 5S and 6S states as 0.654 keV, 0.489 keV and 0.387 keV respectively.