$J=3/2$ charmed hypertriton

By solving exact three-body equations, we study the three-baryon system with charm $+1$. We look for possible bound states using baryon-baryon interactions obtained from a chiral constituent quark model. The smaller effect of the ${\mathrm{\Lambda }}_c\leftrightarrow {\mathrm{\Sigma }}_c$ conversion reverses the order of the $(I,J)=(0,1/2)$ and $(I,J)=(0,3/2)$ states, rather close on the strange sector. The diminishing of the kinetic energy due to the large reduced mass gives rise to a bound state in the $(I,J)=(0,3/2)$ channel. After correcting for Coulomb effects, the binding energy would be between 140 and 715 keV.

Figure 1

Diagram to generate ${\mathrm{\Lambda }}_c^{+}$ by means of antiproton collisions on the deuteron.

Figure 2

(a) Fredholm determinant for the $J=1/2$ and $J=3/2I=0{\mathrm{\Lambda }}_{c}NN$ channels. (b) Fredholm determinant for the $J=1/2$ and $J=3/2I=1{\mathrm{\Lambda }}_{c}NN$ channels.

Figure 3

(a) Fredholm determinant for the $J=1/2$ and $J=3/2I=0{\mathrm{\Sigma }}_{c}NN$ channels. (b) Fredholm determinant for the $J=1/2$ and $J=3/2I=1{\mathrm{\Sigma }}_{c}NN$ channels. (c) Fredholm determinant for the $J=1/2$ and $J=3/2I=2{\mathrm{\Sigma }}_{c}NN$ channels.

Figure 4

Fredholm determinant for the $J=1/2$ and $J=3/2I=0{\mathrm{\Lambda }}_{c}NN$ channels. The solid line stands for the full calculation and the dashed line for when the ${\mathrm{\Lambda }}_c\leftrightarrow {\mathrm{\Sigma }}_c$ transition is taken to be zero.

Figure 5

Fredholm determinant for the $(I,J)=(0,3/2){\mathrm{\Lambda }}_{c}NN$ channel for the different values of the width parameter for the charmed quark wave function.