Effective field theory for the nucleon-quarkonium interaction

Abstract

We develop an effective field theory approach for the $S$-wave quarkonium-nucleon system. We adopt a natural power counting equivalent to Weinberg's power counting in nucleon-nucleon effective field theories and compute the quarkonium-nucleon potential, scattering length and effective range up to $\mathcal{O}(m_{\pi }^3/{\Lambda }_{\chi }^3)$ accuracy, including the full light-quark mass dependence. We compare our results with lattice QCD studies of quarkonium-nucleon system, obtain an estimation of the leading order quarkonium-nucleon contact term and determine the $J/\psi$ and ${\eta }_c$ chromopolarizabilities.

Journal version. 22 pages, 5 figures