Analysis of the strong vertices \(\Lambda _cD^{(*)}N^*(1535)\) and \(\Lambda _bB^{(*)}N^*(1535)\) in QCD sum rules

Abstract

In this article, we firstly analyze the mass and pole residue of negative parity nucleon \(N^*(1535)\) within the two-point QCD sum rules. Basing on these results, we continuously study the strong coupling constants of vertices \(\Lambda _cDN^*\), \(\Lambda _cD^*N^*\), \(\Lambda _bBN^*\) and \(\Lambda _bB^*N^*\) 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 \(\langle \bar{q}q\rangle \), \(\langle g_s^2GG\rangle \), \(\langle \bar{q} g_s\sigma Gq\rangle \), \(\langle \bar{q}q\rangle ^2\) and \(g_s^2\langle \bar{q}q\rangle ^2\) are also considered. By setting the four momentum of \(D^{(*)}[B^{(*)}]\) mesons off-shell, the strong coupling constants in deep space-like regions (\(Q^2=-q^2\gg \Lambda _{QCD}^2\)) 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 \(Q^{2}=-m_{D^{(*)}[B^{(*)}]}^2\). The results are \(G_{\Lambda _cDN^*}(Q^2=-m_D^2)=4.06^{+0.96}_{-0.75}\), \(f_{\Lambda _cD^*N^*}(Q^2=-m_{D^*}^2)=3.73^{+0.68}_{-0.16}\), \(g_{\Lambda _cD^*N^*}(Q^2=-m_{D^*}^2)=9.22^{+3.16}_{-0.36}\), \(G_{\Lambda _bBN^*}(Q^2=-m_B^2)=9.11^{+1.54}_{-1.61}\), \(f_{\Lambda _bB^*N^*}(Q^2=-m_{B^*}^2)=8.55^{+2.69}_{-2.21}\) and \(g_{\Lambda _bB^*N^*}(Q^2=-m_{B^*}^2)=-\,0.25^{+0.16}_{-0.01}\).