Interpretation of the X(3872) as a charmonium state plus an extra component due to the coupling to the meson-meson continuum

Abstract

We present a quark model calculation of the charmonium spectrum with self energy corrections due to the coupling to the meson-meson continuum. The bare masses used in the calculation are computed within the relativized quark model by Godfrey and Isgur. The strong decay widths of 3S, 2P, 1D and 2D $c\bar{c}$ states are also calculated, in order to set the values of the ${}^3{P}_0$ pair-creation model's parameters we use to compute the vertex functions of the loop integrals. Finally, the nature of the X(3872) resonance is analyzed and the main possibilities ($c\bar{c}$ state or $D{\bar{D}}^{\ast }$ molecule) are discussed. According to our results, the X(3872) is compatible with the meson ${\chi }_{c1}(2P)$, with $J^{PC}=1^{++}$, and is thus interpreted as a $c\bar{c}$ core plus higher Fock components due to the coupling to the meson-meson continuum. These $J^{PC}=1^{++}$ quantum numbers are in agreement with the experimental results found by the LHCb collaboration. In our view, the X(3872)'s mass is lower than the quark model's predictions because of self energy shifts.