The light-front quark model has been applied to calculate the transition matrix elements of heavy hadron decays. However, it is noted that using the traditional wave functions of the light-front quark model given in the literature, the theoretically determined decay constants of the ${\rm Y}(nS)$ obviously contradict the data. This implies that the wave functions must be modified. Keeping the orthogonality among the $nS$ states and fitting their decay constants, we obtain a series of the wave functions for ${\rm Y}(nS)$. Based on these wave functions and by analogy with the hydrogen atom, we suggest a modified analytical form for the ${\rm Y}(nS)$ wave functions. Using the modified wave functions, the obtained decay constants are close to the experimental data. Then we calculate the rates of radiative decays of ${\rm Y}(nS)\to {\eta }_b+\gamma$. Our predictions are consistent with the experimental data on decays ${\rm Y}(3S)\to {\eta }_b+\gamma$ within the theoretical and experimental errors.

• Received 7 June 2010

DOI:https://doi.org/10.1103/PhysRevD.82.034023