Residues of $\Lambda_Q$-type and $\Sigma_Q$-type Baryons in the Bethe-Salpeter Equation Approach

Abstract

We study the residues of $\Lambda_Q$-type baryons ($\Lambda_Q$ and $\Xi_Q^A$) $(Q=b,c)$ and $\Sigma_Q$-type baryons ($\Sigma_Q^{(\ast)}$, $\Xi_Q^{S(\ast)}$ and $\Omega_Q^{(\ast)}$) in the quark-diquark model within the Bethe-Salpeter (BS) formalism. These residues can be used, for example, in the calculations of the amplitudes in the scattering processes. After constructing the baryonic currents in the BS formalism, we derive the relations between the BS wave functions and the residues for these baryons. The BS equations are solved numerically with the kernel including the scalar confinement and the one gluon exchange terms and with the covariant instantaneous approximation being employed in the calculations. Finally, we obtain the numerical values of the residues $0.103\,\rm GeV\sim0.224\,\rm GeV$ for $\Lambda_Q$, $0.143\,\rm GeV\sim0.215\,\rm GeV$ for $\Xi_Q^A$, $0.262\,\rm GeV\sim0.361\,\rm GeV$ for $\Sigma_Q^{(\ast)}$, $0.313\,\rm GeV\sim0.460\,\rm GeV$ for $\Xi_Q^{S(\ast)}$ and $0.473\,\rm GeV\sim0.571\,\rm GeV$ for $\Omega_Q^{(\ast)}$ in the ranges of the parameters in our model.