Analysis of the strong vertices $\hat{I}{›}_c{D}^{(\ast )}{N}^{\ast }(1535)$ and $\hat{I}{›}_b{B}^{(\ast )}{N}^{\ast }(1535)$ in QCD sum rules

Abstract

In this article, we firstly analyze the mass and pole residue of negative parity nucleon $N^{\ast }(1535)$ within the two-point QCD sum rules. Basing on these results, we continuously study the strong coupling constants of vertices $\hat{I}{›}_{c}D{N}^{\ast }$, $\hat{I}{›}_c{D}^{\ast }{N}^{\ast }$, $\hat{I}{›}_{b}B{N}^{\ast }$ and $\hat{I}{›}_b{B}^{\ast }{N}^{\ast }$ in the framework of three-point QCD sum rules. At hadron side, all possible couplings of interpolating current to hadronic states are considered. At QCD side, the contributions of vacuum condensate terms $⟨\bar{q}q⟩$, $⟨g_s^{2}GG⟩$, $⟨\bar{q}{g}_s\ddot{I}ƒGq⟩$, $⟨\bar{q}q{⟩}^2$ and $g_s^2⟨\bar{q}q{⟩}^2$ are also considered. By setting the four momentum of $D^{(\ast )}[B^{(\ast )}]$ mesons off-shell, the strong coupling constants in deep space-like regions ($Q^2=-q^2\gg \hat{I}{›}_{QCD}^2$) are obtained. Then, the momentum dependent coupling constants in space-like regions are fitted into analytical function $G(Q^2)$ and are extrapolated into time-like regions ($Q^2<0$). Finally, the on-shell values of strong coupling constants are obtained by taking $Q^2=-m_{D^{(\ast )}[B^{(\ast )}]}^2$. The results are $G_{\hat{I}{›}_{c}D{N}^{\ast }}(Q^2=-m_D^2)=4.06_{-0.75}^{+0.96}$, $f_{\hat{I}{›}_c{D}^{\ast }{N}^{\ast }}(Q^2=-m_{D^{\ast }}^2)=3.73_{-0.16}^{+0.68}$, $g_{\hat{I}{›}_c{D}^{\ast }{N}^{\ast }}(Q^2=-m_{D^{\ast }}^2)=9.22_{-0.36}^{+3.16}$, $G_{\hat{I}{›}_{b}B{N}^{\ast }}(Q^2=-m_B^2)=9.11_{-1.61}^{+1.54}$, $f_{\hat{I}{›}_b{B}^{\ast }{N}^{\ast }}(Q^2=-m_{B^{\ast }}^2)=8.55_{-2.21}^{+2.69}$ and $g_{\hat{I}{›}_b{B}^{\ast }{N}^{\ast }}(Q^2=-m_{B^{\ast }}^2)=-0.25_{-0.01}^{+0.16}$.