Analysis of 2S singly heavy baryons in HQET

Abstract

We have employed HQET to determine the masses of radially excited ($n=2$) S-wave charm and bottom baryons. The HQET Lagrangian containing the non-perturbative parameters is shown with heavy baryon fields. The non-perturbative parameters, couplings, and decay widths are also studied for the S-wave singly heavy baryons. The HQET parameters $\overline{\Lambda}$, $\lambda_1$ and $\lambda_2$ are calculated for the ground state ($n=1$) using the masses of S-wave baryons. The mass term ratios of $n=1$ and $n=2$ mesons and baryons containing parameters $\overline{\Lambda}$ and $\lambda_1$ are studied by varying the bottom quark mass. This analysis shows that heavy quark behaves the same inside mesons and baryons in both 1S and 2S states. The HQET symmetry of $\overline{\Lambda}$ is used to find the parameters and masses for $n=2$ S-wave baryons. The variation of mass of 2S baryons with the non-perturbative parameters $\lambda_1$ and $\lambda_2$ is discussed. The Regge trajectories are also plotted in the $(n,M^2)$ plane using masses of $n=1$ and 2 charm and bottom baryons. The Regge trajectories are parallel and equidistant lines in the $(n,M^2)$ plane. We have also studied the strong decays of charm and bottom baryons for both $n=1$ and $n=2$ states. We have estimated the coupling constants $g_1=0.913^{+0.010}_{-0.017}$ and $g_2=0.559^{+0.006}_{-0.010}$ for $n=1$, and $\frac{\widetilde{g}_1}{\widetilde{g}_2}=1.52$ for $n=2$. We have also shown the semi-electronic decays rates of charm baryons in the spectator heavy quark approximation for $1S\rightarrow 1S$, $2S\rightarrow 1S$ and $2S\rightarrow 2S$ transitions. The decay rates for $1S\rightarrow 1S$ transitions are of same order as $2S\rightarrow 1S$ transitions. This analysis gives a good agreement with available theoretical and experimental data.