Re-Study on the wave functions of $Υ(nS)$ states in LFQM and the radiative decays of $Υ(nS)\to η_b+γ$

Details Re-Study on the wave functions of $Υ(nS)$ states in LFQM and the radiative decays of $Υ(nS)\to η_b+γ$ Re-Study on the wave functions of $Υ(nS)$ states in LFQM and the radiative decays of $Υ(nS)\to η_b+γ$

2010-06-06

arxiv.org/abs/1006.1091v3

Phys.Rev.D82:034023,2010

Physics

High Energy Physics

High Energy Physics - Phenomenology

10 pages, 2 figures, 1 table. Typos corrected and more discussions added. accepted for publication in Physical Review D

Scientific paper

10.1103/PhysRevD.82.034023

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.

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