Abstract
We study the residues of ${\mathrm{\ensuremath{\Lambda}}}_{Q}$-type baryons (${\mathrm{\ensuremath{\Lambda}}}_{Q}$ and ${\mathrm{\ensuremath{\Xi}}}_{Q}^{A}$) $(Q=b,c)$ and ${\mathrm{\ensuremath{\Sigma}}}_{Q}$-type baryons (${\mathrm{\ensuremath{\Sigma}}}_{Q}^{(*)}$, ${\mathrm{\ensuremath{\Xi}}}_{Q}^{S(*)}$ and ${\mathrm{\ensuremath{\Omega}}}_{Q}^{(*)}$) in the quark-diquark model within the Bethe-Salpeter (BS) formalism. These residues can be used, e.g., 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 $0.103\text{ }\text{ }\mathrm{GeV}\ensuremath{\sim}0.224\text{ }\text{ }\mathrm{GeV}$ for ${\mathrm{\ensuremath{\Lambda}}}_{Q}$, $0.143\text{ }\text{ }\mathrm{GeV}\ensuremath{\sim}0.215\text{ }\text{ }\mathrm{GeV}$ for ${\mathrm{\ensuremath{\Xi}}}_{Q}^{A}$, $0.262\text{ }\text{ }\mathrm{GeV}\ensuremath{\sim}0.361\text{ }\text{ }\mathrm{GeV}$ for ${\mathrm{\ensuremath{\Sigma}}}_{Q}^{(*)}$, $0.313\text{ }\text{ }\mathrm{GeV}\ensuremath{\sim}0.460\text{ }\text{ }\mathrm{GeV}$ for ${\mathrm{\ensuremath{\Xi}}}_{Q}^{S(*)}$ and $0.473\text{ }\text{ }\mathrm{GeV}\ensuremath{\sim}0.571\text{ }\text{ }\mathrm{GeV}$ for ${\mathrm{\ensuremath{\Omega}}}_{Q}^{(*)}$ in the ranges of the parameters in our model.
Highlights
The residues of baryons are important parameters in studying their hadronic properties; e.g., in QCD sum rules, the residues are needed as one of the main inputs for further calculating decay constants and coupling constants of baryons [1,2,3]
We study the residues of ΛQ-type baryons (ΛQ and ΞAQ) ðQ 1⁄4 b; cÞ and ΣQ-type baryons (ΣðQÃÞ, ΞSQðÃÞ and ΩðQÃÞ) in the quark-diquark model within the Bethe-Salpeter (BS) formalism
We present the solutions of the BS wave functions for ΣQ-type baryon in Figs. 5–7, where we give the numerical results of BS wave functions for ΣðQÃÞ, ΞSQðÃÞ and ΩðQÃÞ, with κ in the range 0.02–0.08 GeV3 for all of the ΣQ-type baryons in this work
Summary
The residues of baryons are important parameters in studying their hadronic properties; e.g., in QCD sum rules, the residues are needed as one of the main inputs for further calculating decay constants and coupling constants of baryons [1,2,3]. The BS equations for the ΛQ-type and the ΣQ-type baryons have been established in the quark-diquark picture in the leading order of the 1=mQ expansion [4,5] They were applied to study the properties of the ΛQ-type and the ΣQ-type baryons, and theoretical predictions were found to be consistent with the available experimental data [10,17]. The BS equations will be solved using the covariant instantaneous approximation [18,22,23,24], which is appropriate since the energy exchange between constituents inside the heavy baryons is expected to be small when we use the constituent quark masses in the BS equation We employ this approximation in this work for the purpose of simplifying our calculations.
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