The nature of the $X(3915)/X(3930)$ resonances from a coupled-channels approach

Abstract

The positive parity $\chi_{cJ}(2P)$ charmonium states are expected to lie around the 3.9 GeV/$c^2$ energy region, according to the predictions of quark models. However, a plethora of states with difficult assignment and unconventional properties have been discovered over the years, i.e., the $X(3872)$, $X(3940)$, $Y(3940)$, $X(3915)$, $X(3860)$ and the $X(3930)$ resonances, which complicates the description of this intriguing region. In this work we analyze the $0^{++}$ and $2^{++}$ sectors, employing a coupled-channels formalism successfully applied to the $1^{++}$ sector, where the $X(3872)$ was described as a $D\bar D^\ast+h.c.$ molecule with a sizable $c\bar c$ $(2^3P_1)$ component. This coupled-channels formalism is based on a widely-used Constituent Quark Model, which describes the quark-quark interactions, and the $^3P_0$ quark pair creation mechanism, used to couple the two and four quark sectors. The recent controversy about the quantum numbers of the $X(3915)$ state, the properties of the $X(3930)$ one and the nature of the new $X(3860)$ resonance are analyzed in a unified theoretical framework, being all the parameters completely constrained from previous calculations in the low-lying heavy quarkonium phenomenology.