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

TL;DR

This paper investigates the molecular structure of the $P_{c}(4380)$ pentaquark using coupled channel analysis with one-pion exchange, revealing bound states with specific quark compositions and sizes around 1.5 fm.

Contribution

It introduces a coupled channel potential model with one-pion exchange to identify bound states and pentaquarks involving charm and bottom quarks, expanding understanding of exotic hadrons.

Findings

Existence of bound states with several MeV binding energy below thresholds.

Identification of pentaquarks with $c\bar{b}$, $b\bar{c}$, and $b\bar{b}$ compositions.

Bound states have sizes around 1.5 fm.

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.