Three-Body Decay of ${\Lambda }_c^{*}(2595)$ and ${\Lambda }_c^{*}(2625)$ with consideration of ${\Sigma }_c(2455)\pi$ and ${\Sigma }_c^{*}(2520)\pi$ in intermediate States

Three-body decay of charmed baryons ${\Lambda }_c^{*}(2595)$ and ${\Lambda }_c^{*}(2625)$ into ${\Lambda }_c\pi \pi$ are studied with effective Lagrangians in which the coupling constants are extracted from the nonrelativistic quark model. We take into account sequential processes going through ${\Sigma }_c(2455)$ and ${\Sigma }_c^{*}(2520)$ in intermediate states. The total decay widths are sensitive to the coupling of ${\Lambda }_c^{*}$ with ${\Sigma }_c\pi$ open channel and to ${\Sigma }_c^{*}\pi$ closed channel. We find that ${\Lambda }_c^{*}(2595)$ and ${\Lambda }_c^{*}(2625)$ with $\lambda$ mode assignment can explain the experimental data nicely. We also show invariant mass distributions of ${\Lambda }_c^{*}(2595)$ and ${\Lambda }_c^{*}(2625)$ decays, which are significantly different for various quark configurations.

Figure 1

The level structure of low lying charmed baryons and their strong decays through pion emission. Black arrows indicate kinematically allowed decays, while red arrows are for kinematically forbidden ones to the closed channel.

Figure 2

All possible Feynman diagrams describing sequential decay of ${\mathrm{\Lambda }}_c^{*}\to {\mathrm{\Lambda }}_c{\pi }^{+}{\pi }^{-}$. ${\mathrm{\Lambda }}_c^{*}$ is either ${\mathrm{\Lambda }}_c^{*}(2595)$ or ${\mathrm{\Lambda }}_c^{*}(2625)$. The diagrams consist of the process going through ${\mathrm{\Sigma }}_c^{*}(2520)$ and ${\mathrm{\Sigma }}_c(2455)$ and their different charged states.

Figure 3

Initial particle rest frame is considered in which the four momentum of the initial particle is $P=(m_i,\mathbf{0})$. We define mass of ${\pi }^{+}$, ${\pi }^{-}$, and ${\mathrm{\Lambda }}_c$ as $m_1$, $m_2$, and $m_3$ respectively.

Figure 4

The resonance rest frame is defined as the rest frame of the subsystem of particle 2 and 3.

Figure 5

Dalitz plot and invariant mass distribution of ${\mathrm{\Lambda }}_c^{*}(2595)\to {\mathrm{\Lambda }}_c{\pi }^{+}{\pi }^{-}$ with ${\mathrm{\Sigma }}_c^{(*)0}{\pi }^{+}$ and ${\mathrm{\Sigma }}_c^{(*)++}{\pi }^{-}$ channels in an intermediate state. ${\mathrm{\Lambda }}_c^{*}(2595)$ is assumed to be $\lambda$ mode.

Figure 6

Dalitz plot and invariant mass distribution of ${\mathrm{\Lambda }}_c^{*}(2595)\to {\mathrm{\Lambda }}_c{\pi }^0{\pi }^0$ with ${\mathrm{\Sigma }}_c^{(*)+}{\pi }^0$ channels in intermediate state. ${\mathrm{\Lambda }}_c^{*}(2595)$ is assumed to be $\lambda$ mode.

Figure 7

A Dalitz plot and invariant mass distribution of ${\mathrm{\Lambda }}_c^{*}(2625)(\lambda -\text{mode})\to {\mathrm{\Lambda }}_c{\pi }^{+}{\pi }^{-}$.

Figure 8

A Dalitz plot and invariant mass distribution of ${\mathrm{\Lambda }}_c^{*}(2625)$ $(\rho -\mathrm{mode},j=1)\to {\mathrm{\Lambda }}_c{\pi }^{+}{\pi }^{-}$.

Figure 9

A Dalitz plot and invariant mass distribution of ${\mathrm{\Lambda }}_c^{*}(2625)(\rho -\text{mode},j=2)\to {\mathrm{\Lambda }}_c{\pi }^{+}{\pi }^{-}$.