X(3872) as a hybrid state of the charmonium and the hadronic molecule

Abstract

In order to understand the structure of the X(3872), the $c \bar c$ charmonium core state coupling to the $D^0 \bar D^{\ast 0}$ and $D^+ D^{\ast -}$ molecular states are studied. The strengths of the couplings between the charmonium state and the hadronic molecular states are determined so as to reproduce the observed mass of the the X(3872). The isospin symmetry breaking is introduced by the mass differences of the neutral and charged $D$ mesons. The obtained structure of the X(3872) is that about 7% is $\ccbar$ charmonium, 75% is the isoscalar $D \bar D^\ast$ molecule and 18% is the isovector $D \bar D^\ast$ molecule, which explains observed properties of the X(3872) well. The structure of the X(3872) we have obtained is not just a $D^0 \bar D^{ast 0}$ hadronic molecule nor the compact tetraquark state but the charmonium-hadronic molecule hybrid state.