In this article, the strong coupling constants of vertices $BB\Upsilon$, $BB^{ *}\Upsilon$, $B^{ *}B^{ *}\Upsilon$, $BB^{ *}\eta_{ b}$ and $B^{ *}B^{ *}\eta_{ b}$ are analyzed in the framework of QCD sum rules. In this work, all possible off-shell cases and the contributions of vacuum condensate terms including $\langle\overline{ q}q\rangle$, $\langle\overline{ q}g_{ s}\sigma Gq\rangle$, $\langle g_{ s}^{ 2}G^{ 2}\rangle$, $\langle f^{ 3}G^{ 3}\rangle$ and $\langle\overline{ q}q\rangle\langle g_{ s}^{ 2}G^{ 2}\rangle$ are considered. The momentum dependent strong coupling constants are first calculated and then are fitted into analytical functions $g(Q^{ 2})$ which are used to extrapolate into time-like regions to obtain the final values of strong coupling constants. The final results are $g_{ BB\Upsilon}=40.67^{ +7.55}_{ -4.20}$, $g_{ BB^{ *}\Upsilon}=11.58^{ +2.19}_{ -1.09}$ GeV$^{ -1}$, $g_{ B^{ *}B^{ *}\Upsilon}=57.02^{ +5.32}_{ -5.31}$, $g_{ BB^{ *}\eta_{ b}}=23.39^{ +4.74}_{ -2.30}$ and $g_{ B^{ *}B^{ *}\eta_{ b}}=12.49^{ +2.12}_{ -1.35}$ GeV$^{ -1}$. These strong coupling constants are important input parameters which reflect the dynamic properties of the interactions among the mesons and quarkonia.
Categories: hep-ph