Structure of charmed baryons studied by pionic decays

We investigate the decays of the charmed baryons aiming at the systematic understanding of hadron internal structures based on the quark model by paying attention to heavy quark symmetry. We evaluate the decay widths from the one-pion emission for the known excited states, ${\mathrm{\Lambda }}_c^{*}(2595)$, ${\mathrm{\Lambda }}_c^{*}(2625)$, ${\mathrm{\Lambda }}_c^{*}(2765)$, ${\mathrm{\Lambda }}_c^{*}(2880)$, and ${\mathrm{\Lambda }}_c^{*}(2940)$, as well as for the ground states ${\mathrm{\Sigma }}_c(2455)$ and ${\mathrm{\Sigma }}_c^{*}(2520)$. The decay properties of the lower excited charmed baryons are well explained, and several important predictions for higher excited baryons are given. We find that the axial-vector-type coupling of the pion to the light quarks is essential, which is expected from chiral symmetry, to reproduce the decay widths especially of the low-lying ${\mathrm{\Lambda }}_c^{*}$ baryons. We emphasize the importance of the branching ratios of $\mathrm{\Gamma }({\mathrm{\Sigma }}_c^{*}\pi )/\mathrm{\Gamma }({\mathrm{\Sigma }}_c\pi )$ for the study of the nature of higher excited ${\mathrm{\Lambda }}_c^{*}$ baryons.

Figure 1

Level structure of the charmed baryons with isospin $I=0$ and $I=1$ $Y_c(mass)J^P$ considered in this study. The hatched squares denote their total decay widths in Particle Data Group (PDG) [24]. The arrows indicate the possible decay paths with one-pion emission evaluated in this study.

Figure 2

Definitions of the Jacobi coordinates $\overrightarrow{\rho }$ and $\overrightarrow{\lambda }$. The quarks 1 and 2 are the light quarks, and 3 the heavy (charm) quark.

Figure 3

Decay amplitude of the charmed baryon $Y_c$ to $Y_c^{\prime }$ with one-pion emission.

Figure 4

Feynman diagram of the sequential decay of ${\mathrm{\Lambda }}_c^{*}\to {\mathrm{\Sigma }}_c\pi$ followed by ${\mathrm{\Sigma }}_c\to {\mathrm{\Lambda }}_c\pi$ supposed in Eq. (69).

Figure 5

Convoluted decay width of ${\mathrm{\Lambda }}_c^{*}(2595;\lambda \text{-mode})\to {\mathrm{\Sigma }}_c(2455)\pi$ as functions of total energy ($=$ the mass of the ${\mathrm{\Lambda }}_c^{*}$). The thin (blue) lines denote the ${\pi }^{-}$, ${\pi }^0$, and ${\pi }^{+}$ emission decay widths as indicated in the figure. The thick (red) solid line denotes the sum of the three charge states. The resulting Breit-Winger spectral functions of the ${\mathrm{\Lambda }}_c^{*}$ are also shown in arbitrary units.