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

TL;DR

This study revises the wave functions of $Upsilon(nS)$ states in the Light-front quark model to better match experimental decay constants and predicts radiative decay rates consistent with observed data.

Contribution

It introduces modified analytical wave functions for $Upsilon(nS)$ states in LFQM, improving decay constant predictions and decay rate calculations.

Findings

Modified wave functions yield decay constants close to experimental values.

Predicted radiative decay rates agree with experimental data within errors.

The approach maintains orthogonality among $Upsilon(nS)$ states.

Abstract

The Light-front quark model (LFQM) 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 LFQM given in literature, the theoretically determined decay constants of the $\Upsilon(nS)$ obviously contradict to the data. It 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 $\Upsilon(nS)$. Based on these wave functions and by analogy to the hydrogen atom, we suggest a modified analytical form for the $\Upsilon(nS)$ wave functions. By use of the modified wave functions, the obtained decay constants are close to the experimental data. Then we calculate the rates of radiative decays of $\Upsilon(nS)\to \eta_b+\gamma$. Our predictions are consistent with the experimental data on decays $\Upsilon(3S)\to \eta_b+\gamma$ within the theoretical and experimental errors.