Analysis of the strong vertices $\Lambda_cD^{(*)}N^*(1535)$ and $\Lambda_bB^{(*)}N^*(1535)$ in QCD sum rules

TL;DR

This paper calculates the strong coupling constants of certain baryon-meson-nucleon vertices involving $ ext{N}^*(1535)$ using QCD sum rules, providing numerical results for on-shell couplings.

Contribution

It introduces a comprehensive QCD sum rule analysis of the vertices involving $ ext{N}^*(1535)$, including mass, pole residues, and strong coupling constants, with detailed consideration of vacuum condensates.

Findings

Computed strong coupling constants for $ ext{N}^*(1535)$ related vertices.

Provided numerical values for on-shell coupling constants.

Used analytical continuation to obtain physical coupling values.

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 $g_{\Lambda_bB^*N^*}(Q^2=-m_{B^*}^2)=-0.25^{+0.16}_{-0.01}$.