Three-body decay of ${\mathrm{\Lambda }}_c^{*}(2595)$ and ${\mathrm{\Lambda }}_c^{*}(2625)$ with the inclusion of a direct two-pion coupling

We investigate the three-body decays of ${\mathrm{\Lambda }}_c^{*}(2595)$ and ${\mathrm{\Lambda }}_c^{*}(2625)$ into ${\mathrm{\Lambda }}_c\pi \pi$ by including a direct process going through the two-pion coupling of ${\mathrm{\Lambda }}_c^{*}{\mathrm{\Lambda }}_c\pi \pi$ in addition to the sequential processes going through ${\mathrm{\Sigma }}_c(2455)$ and ${\mathrm{\Sigma }}_c^{*}(2520)$. The strength of the direct coupling is related to that of the Yukawa coupling by the chiral partner structure between ${\mathrm{\Lambda }}_c$’s and ${\mathrm{\Sigma }}_c$’s, while the strength of the Yukawa coupling is estimated by the quark model. It is found that the direct process gives a considerable contribution especially in the decay of ${\mathrm{\Lambda }}_c^{*}(2625)$. A clear indication of the direct process is seen in an asymmetric pattern in the angular correlation between the two pions. We discuss the usefulness of the detailed analysis of the decays for the study of the structure of ${\mathrm{\Lambda }}_c^{*}$.

Figure 1

Direct decay processes (red dashed lines) and sequential decay processes (blue dashed lines) of ${\mathrm{\Lambda }}_c^{*}(2595)$ and ${\mathrm{\Lambda }}_c^{*}(2625)$.

Figure 2

Chiral and heavy quark symmetry (HQS) partner classification between ${\mathrm{\Lambda }}_c$’s and ${\mathrm{\Sigma }}_c$’s.

Figure 3

Feynman diagrams of three-body decay of ${\mathrm{\Lambda }}_c^{*}(2595)$ into ${\mathrm{\Lambda }}_c^{+}{\pi }^{+}{\pi }^{-}$. The first two diagrams represent sequential processes going through ${\mathrm{\Sigma }}_c(2455{)}^0$ and ${\mathrm{\Sigma }}_c(2455{)}^{++}$. The last diagram corresponds to the direct process. For ${\mathrm{\Lambda }}_c^{*}(2625)$ decay, there are additional sequential processes going through ${\mathrm{\Sigma }}_c^{*}(2520)$.

Figure 4

The angle between the two pions in the rest frame of the intermediate resonance. In this rest frame, ${\mathrm{\Lambda }}_c^{+}$ and ${\pi }^{-}$ are going back to back.

Figure 5

The Dalitz plots of ${\mathrm{\Lambda }}_c^{*}(2595)$ $[\lambda \text{mode}]\to {\mathrm{\Lambda }}_c^{+}{\pi }^{+}{\pi }^{-}$ in $(m_{23}^2,m_{13}^2)$ plane and the invariant mass distribution of $m_{23}^2$ $({\mathrm{\Lambda }}_c^{+}{\pi }^{-})$. The upper Dalitz plot is without the direct process and in the middle one the direct process has been included.

Figure 6

The Dalitz plots of ${\mathrm{\Lambda }}_c^{*}(2595)$ $[\lambda \text{mode}]\to {\mathrm{\Lambda }}_c^{+}{\pi }^{+}{\pi }^{-}$ in $(m_{12}^2,m_{13}^2)$ plane and the invariant mass distribution of $m_{12}^2$ $({\pi }^{+}{\pi }^{-})$. The upper Dalitz plot is without the direct process and in the middle one the direct process has been included.

Figure 7

The angular correlation between the two pions in the rest frame of particle 2 and 3 for the decay of ${\mathrm{\Lambda }}_c^{*}(2595)$.

Figure 8

The Dalitz plots of ${\mathrm{\Lambda }}_c^{*}(2625)$ $[\lambda \text{mode}]\to {\mathrm{\Lambda }}_c^{+}{\pi }^{+}{\pi }^{-}$ in $(m_{23}^2,m_{13}^2)$ plane and the invariant mass distribution of $m_{23}^2$ $({\mathrm{\Lambda }}_c^{+}{\pi }^{-})$. The upper Dalitz plot is without the direct process and in the middle one the direct process has been included.

Figure 9

The Dalitz plots of ${\mathrm{\Lambda }}_c^{*}(2625)$ $[\lambda \text{mode}]\to {\mathrm{\Lambda }}_c^{+}{\pi }^{+}{\pi }^{-}$ in $(m_{12}^2,m_{13}^2)$ plane and the invariant mass distribution of $m_{12}^2$ $({\pi }^{+}{\pi }^{-})$. The upper Dalitz plot is without the direct process, and in the lower one, the direct process has been included.

Figure 10

The Dalitz plots of ${\mathrm{\Lambda }}_c^{*}(2625)[\lambda \text{mode}]\to {\mathrm{\Lambda }}_c^{+}{\pi }^{+}{\pi }^{-}$ in $(m_{12}^2,m_{13}^2)$ plane. The direct process is exclusively shown and the lower plot is the interference between the direct process and the sequential processes.

Figure 11

The angular correlation between the two pions in the rest frame of particle 2 and 3 for the decay of ${\mathrm{\Lambda }}_c^{*}(2625)$.

Figure 12

The Dalitz plots of ${\mathrm{\Lambda }}_c^{*}(2625)$ $[\rho \text{mode},j=1]\to {\mathrm{\Lambda }}_c^{+}{\pi }^{+}{\pi }^{-}$ in $(m_{23}^2,m_{13}^2)$ plane and the invariant mass distribution of $m_{23}^2$ $({\mathrm{\Lambda }}_c^{+}{\pi }^{-})$. The upper Dalitz plot is without the direct process and in the middle one the direct process has been included.

Figure 13

The angular correlation between the two pions in the rest frame of particle 2 and 3 for the decay of ${\mathrm{\Lambda }}_c^{*}(2625)$ with $\rho$ mode ($j=1$).

Figure 14

The Dalitz plots of ${\mathrm{\Lambda }}_c^{*}(2625)$ $[\rho \text{mode},j=2]\to {\mathrm{\Lambda }}_c^{+}{\pi }^{+}{\pi }^{-}$ in $(m_{23}^2,m_{13}^2)$ plane and the invariant mass distribution of $m_{23}^2$ $({\mathrm{\Lambda }}_c^{+}{\pi }^{-})$. The upper Dalitz plot is without the direct process and in the middle one the direct process has been included.

Figure 15

The angular correlation between the two pions in the rest frame of particle 2 and 3 for the decay of ${\mathrm{\Lambda }}_c^{*}(2625)$ with $\rho$ mode ($j=2$).