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Charmonium states can decay into pairs of $D$ and $\overline{D}$ mesons iftheir masses are above the allowed decay thresholds. In general $c\bar{c}$states near threshold will also undergo mixing with $D\overline{D}$ molecular(or tetraquark) states, by creation and annihilation of light quark-antiquarkpairs. The investigation of such effects sheds light on the higher Fock statecontributions to charmonium wavefunctions and on mass shifts, relative to ascenario where such mixing effects are neglected. A variational approach isapplied to a mixing matrix between operators of both sectors, of $c\bar{c}$ andof $D\overline{D}$ molecular type. The efficient calculation of severaldiagrams appearing in this matrix requires all-to-all propagators, which arerealized by sophisticated stochastic estimator techniques. The runs areperformed on $n_F=2$ $24^3\times 48$ lattice volumes with $m_{\pi} \approx 280$MeV, using the non-perturbatively improved clover Wilson action, both forvalence and for sea quarks.

Mixing of S-Wave Charmonia with $\mathrm{D}\overline{\mathrm{D}}$ Molecule States