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

Abstract

We construct a potential obtained by one-pion exchange for the coupled channel $\Sigma_c^\ast$$\bar{D}$-$\Sigma_c$$\bar{D}^\ast$, and solve the coupled Schr\"{o}dinger 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 $\Sigma_c^\ast$ and $\bar{D}$, dominantly made from a $\Sigma_c^\ast$ 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.