Coupled channel analysis of molecule picture of $P_{c}(4380)$

We construct a potential obtained by one-pion exchange for the coupled channel $Σ_c^\ast$$\bar{D}$-$Σ_c$$\bar{D}^\ast$, and solve the coupled Schrödinger equations to determine the binding energy. We find that there exists one or two bound states with the binding energy of several MeV below the threshold of $Σ_c^\ast$ and $\bar{D}$, dominantly made from a $Σ_c^\ast$ baryon and a $\bar{D}$ meson, with the size of about $1.5$fm for wide parameter region. We also study the pentaquark states including a $b$ quark and/or an anti-$b$ quark. We show that there exist pentaquarks including $c\bar{b}$, $b\bar{c}$ and $b\bar{b}$, all of which lie at about $10$MeV below the corresponding threshold and have size of about $1.5$fm.

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