Mass and width of $T_{c\bar{c}}(4020)$ in the developed Bethe-Salpeter theory

In experiments exotic meson resonance $T_{c\bar{c}}(4020)$ lies above the $D^{\ast }{\bar{D}}^{\ast }$ threshold, and in principle one can not explain $T_{c\bar{c}}(4020)$ as a meson-meson bound state because meson-meson bound state must lie below the $D^{\ast }{\bar{D}}^{\ast }$ threshold. In this work, exotic resonance $T_{c\bar{c}}(4020)$ is considered as an unstable meson-meson molecular state $D^{\ast }{\bar{D}}^{\ast }$, and the developed Bethe-Salpeter theory for dealing with unstable state is applied to investigate resonance $T_{c\bar{c}}(4020)$. We calculate the mass and width of unstable meson-meson molecular state $D^{\ast }{\bar{D}}^{\ast }$ in the framework of relativistic quantum field theory and find that this unstable meson-meson molecular state lies above the $D^{\ast }{\bar{D}}^{\ast }$ threshold, which is consistent with experimental values of resonance $T_{c\bar{c}}(4020)$.