Pentaquark ${\Theta }^{+}$ in nuclear matter and ${\Theta }^{+}$ hypernuclei

We study the properties of the ${\Theta }^{+}$ in nuclear matter and ${\Theta }^{+}$ hypernuclei within the quark mean-field model, which has been successfully used for the description of ordinary nuclei and Λ hypernuclei. With the assumption that the nonstrange mesons couple only to the u and d quarks inside baryons, a sizable attractive potential of the ${\Theta }^{+}$ in nuclear matter is achieved as a consequence of the cancellation between the attractive scalar potential and the repulsive vector potential. We investigate the ${\Theta }^{+}$ single-particle energies in light, medium, and heavy nuclei. More bound states are obtained in ${\Theta }^{+}$ hypernuclei in comparison with those in Λ hypernuclei.

Figure 1

Variations of the baryon effective masses, $\delta M_i^{*}=M_i^{*}-M_i$ ($i=N,\Lambda ,{\Theta }^{+}$), as functions of the quark mass correction, $\delta m_q=m_q-m_q^{*}=-g_{\sigma }^q\sigma$.

Figure 2

Ratios of the baryon radii in nuclear matter $R_i$ to that in free space $R_i^0$ as functions of the nuclear matter density ρ.

Figure 3

Scalar and vector potentials $U_S$ and $U_V$ as functions of the nuclear matter density ρ.

Figure 4

${\Theta }^{+}$ single-particle energies in ${}_{\Theta }^{17}O,{}_{\Theta }^{41}\mathrm{Ca}$, and ${}_{\Theta }^{209}\mathrm{Pb}$.

Figure 5

Scalar potential $U_S^i$, vector potential $U_V^i$, and Coulomb potential $U_C$ for the nucleon ($i=N$) and the ${\Theta }^{+}$ ($i=\Theta$) in ${}_{\Theta }^{41}\mathrm{Ca}$ with a ${\Theta }^{+}$ bound at $1s_{1/2}$ state.