Re-Study on the wave functions of $\Upsilon(nS)$ states in LFQM and the radiative decays of $\Upsilon(nS) o \eta_b+\gamma$

摘要

The Light-front quark model (LFQM) has been applied to calculate thetransition matrix elements of heavy hadron decays. However, it is noted thatusing the traditional wave functions of the LFQM given in literature, thetheoretically determined decay constants of the $\Upsilon(nS)$ obviouslycontradict to the data. It implies that the wave functions must be modified.Keeping the orthogonality among the $nS$ states and fitting their decayconstants we obtain a series of the wave functions for $\Upsilon(nS)$. Based onthese wave functions and by analogy to the hydrogen atom, we suggest a modifiedanalytical form for the $\Upsilon(nS)$ wave functions. By use of the modifiedwave functions, the obtained decay constants are close to the experimentaldata. Then we calculate the rates of radiative decays of $\Upsilon(nS)\to\eta_b+\gamma$. Our predictions are consistent with the experimental data ondecays $\Upsilon(3S)\to \eta_b+\gamma$ within the theoretical and experimentalerrors.