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.

5 pages, 3 figures; v2: matching with Lattice data explained in greater detail, additional minor modifications

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