Charmonium spectrum in an unquenched quark model

Abstract: The effects of virtual light quark pairs on the charmonium spectrum are studied. Pair creation is modelled with a ``$^{3}P_{0}$" vertex and intermediate states are summed up to 2S excitations. Quark model parameters are obtained by fitting to 12 well-known charmonium states, allowing for feedback between the decaying particle and the induced mass shifts. Both of these technical steps are new and improve agreement with the experimental spectrum. In general, the masses receive small shifts once model parameters are refit. This is true in almost cases except the $\chi_{cJ}(2P)$ multiplet, which experiences upwards mass shifts of order 150 MeV, has the ordering of the multiplet rearranged, and pushes the erstwhile $c\bar{c}$ ${2}^3P_1$ state well above $D^*\bar{D}$ threshold--observations that clarify the nature of the enigmatic $X(3872)$