Is $\chi_{c1}(3872)$ generated from string breaking?

Abstract

We show, from a diabatic analysis of Lattice results for string breaking, that mixing of $Q\bar{Q}$ with open-flavor meson-meson configurations may be expressed through a mixing potential which is order $1 / m_{Q}$. A relation between the minimum string breaking energy gap and the string tension comes out naturally. Using this relation, and matching the energy gap for $b\bar{b}$ with Lattice QCD data, we study the mixing in the $c\bar{c}$ case without any additional parameter. A $1^{++}$ bound state very close below the ${D}^{0}\bar{D}^{\ast 0}$ threshold, in perfect correspondence with $\chi_{c1}(3872)$, is predicted.