Single ${\Lambda }_c^{+}$ hypernuclei within quark mean-field model

Abstract

The quark mean-field (QMF) model is applied to study the single ${\Lambda }_c^{+}$ hypernuclei. The charm baryon, ${\Lambda }_c^{+}$, is constructed by three constituent quarks, $u,d$, and $c$, confined by central harmonic oscillator potentials. The confinement potential strength of charm quark is determined by fitting the experimental masses of charm baryons, ${\Lambda }_c^{+},{\Sigma }_c^{+}$, and ${\Xi }_{cc}^{++}$. The effects of pions and gluons are also considered to describe the baryons at the quark level. The baryons in ${\Lambda }_c^{+}$ hypernuclei interact with each other through exchanging the $\sigma ,\omega$, and $\rho$ mesons between the quarks confined in different baryons. The ${\Lambda }_c^{+}N$ potential in the QMF model is strongly dependent on the coupling constant between $\omega$ meson and ${\Lambda }_c^{+}$, $g_{\omega {\Lambda }_c^{+}}$. When the conventional quark counting rule is used, i. e., $g_{\omega {\Lambda }_c^{+}}=2/3g_{\omega N}$, the massive ${\Lambda }_c^{+}$ hypernucleus can exist, whose single ${\Lambda }_c^{+}$ binding energy is smaller with the mass number increasing due to the strong Coulomb repulsion between ${\Lambda }_c^{+}$ and protons. When $g_{\omega {\Lambda }_c^{+}}$ is fixed by the latest lattice ${\Lambda }_c^{+}N$ potential, the ${\Lambda }_c^{+}$ hypernuclei only can exist up to $A\sim 50$.

26 pages, 6 figures, 7 tables, accepted to Phys. Rev. C

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