The strong vertices of bottom mesons $B$, $B^{\ast }$ and bottomonia $\hat{I}\yen$, $\hat{I}{\cdot }_b$

Abstract

In this article, the strong coupling constants of vertices $BB\hat{I}\yen$, $B{B}^{\ast }\hat{I}\yen$, $B^{\ast }{B}^{\ast }\hat{I}\yen$, $B{B}^{\ast }\hat{I}{\cdot }_b$ and $B^{\ast }{B}^{\ast }\hat{I}{\cdot }_b$ 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 $⟨\overline{q}q⟩$, $⟨\overline{q}{g}_s\ddot{I}ƒGq⟩$, $⟨g_s^2{G}^2⟩$, $⟨f^3{G}^3⟩$ and $⟨\overline{q}q⟩⟨g_s^2{G}^2⟩$ 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 $g_{BB\hat{I}\yen }=40.67_{-4.20}^{+7.55}$, $g_{B{B}^{\ast }\hat{I}\yen }=11.58_{-1.09}^{+2.19}$ GeV${}^{-1}$, $g_{B^{\ast }{B}^{\ast }\hat{I}\yen }=57.02_{-5.31}^{+5.32}$, $g_{B{B}^{\ast }\hat{I}{\cdot }_b}=23.39_{-2.30}^{+4.74}$ and $g_{B^{\ast }{B}^{\ast }\hat{I}{\cdot }_b}=12.49_{-1.35}^{+2.12}$ GeV${}^{-1}$. These strong coupling constants are important input parameters which reflect the dynamic properties of the interactions among the mesons and quarkonia.

arXiv admin note: text overlap with arXiv:2304.13969