Eur. Phys. J. C (2025) 85: 1061
https://doi.org/10.1140/epjc/s10052-025-14754-1

Regular Article - Theoretical Physics

Analysis of the strong vertices ${\mathrm{\Lambda }}_{c}D_{}^{(\ast )}{N}^{\ast }(1535)$ and ${\mathrm{\Lambda }}_{b}B_{}^{(\ast )}{N}^{\ast }(1535)$ in QCD sum rules

¹ School of Physics, Southeast University, 210094, Nanjing, People’s Republic of China
² Department of Mathematics and Physics, North China Electric Power University, 071003, Baoding, People’s Republic of China
³ Lanzhou Center for Theoretical Physics, Lanzhou University, 730000, Lanzhou, People’s Republic of China

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Received: 14 July 2025
Accepted: 9 September 2025
Published online: 24 September 2025

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 ${\mathrm{\Lambda }}_{c}D{N}^{\ast }$, ${\mathrm{\Lambda }}_c{D}^{\ast }{N}^{\ast }$, ${\mathrm{\Lambda }}_{b}B{N}^{\ast }$ and ${\mathrm{\Lambda }}_b{B}^{\ast }{N}^{\ast }$ 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 $⟨\overline{q}q⟩$, $⟨g_s^{2}GG⟩$, $⟨\overline{q}{g}_s\sigma Gq⟩$, ${⟨\overline{q}q⟩}^2$ and $g_s^2{⟨\overline{q}q⟩}^2$ 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 ($Q^2=-q^2\gg {\mathrm{\Lambda }}_{\mathit{QCD}}^2$) 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 $G_{{\mathrm{\Lambda }}_{c}D{N}^{\ast }}(Q^2=-m_D^2)=4.{06}_{-0.75}^{+0.96}$, $f_{{\mathrm{\Lambda }}_c{D}^{\ast }{N}^{\ast }}(Q^2=-m_{D^{\ast }}^2)=3.{73}_{-0.16}^{+0.68}$, $g_{{\mathrm{\Lambda }}_c{D}^{\ast }{N}^{\ast }}(Q^2=-m_{D^{\ast }}^2)=9.{22}_{-0.36}^{+3.16}$, $G_{{\mathrm{\Lambda }}_{b}B{N}^{\ast }}(Q^2=-m_B^2)=9.{11}_{-1.61}^{+1.54}$, $f_{{\mathrm{\Lambda }}_b{B}^{\ast }{N}^{\ast }}(Q^2=-m_{B^{\ast }}^2)=8.{55}_{-2.21}^{+2.69}$ and $g_{{\mathrm{\Lambda }}_b{B}^{\ast }{N}^{\ast }}(Q^2=-m_{B^{\ast }}^2)=-0.{25}_{-0.01}^{+0.16}$.