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

TL;DR

This paper calculates the residues of various heavy baryons using the Bethe-Salpeter formalism within a quark-diquark model, providing numerical values useful for scattering amplitude computations.

Contribution

It introduces a method to compute baryon residues in the Bethe-Salpeter framework, including the derivation of relations between wave functions and residues, with numerical results for multiple baryons.

Findings

Numerical residues for $ ext{Lambda}_Q$, $ ext{Xi}_Q^A$, $ ext{Sigma}_Q^{(*)}$, $ ext{Xi}_Q^{S(*)}$, and $ ext{Omega}_Q^{(*)}$ baryons obtained.

Relations between Bethe-Salpeter wave functions and residues established.

Residue values range from 0.103 GeV to 0.571 GeV across different baryons.

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.