Can we understand the decay width of the $T_{cc}^{+}$ state?

Abstract

Inspired by the recent discovery of a doubly charmed tetraquark state $T_{cc}^{+}$ by the LHCb Collaboration, we employ the effective Lagrangian approach to investigate the decay width of $T_{cc}^{+}\to D^{+}{D}^0\ddot{I}{€}^0/D^0{D}^0\ddot{I}{€}^{+}$ and $T_{cc}^{+}\to D^0{D}^{+}{\hat{I}}^3$ with the assumption that $T_{cc}^{+}$ is an isoscalar $D{D}^{\ast }$ molecule. We show that both the $T_{cc}\to DD\ddot{I}€$ and $T_{cc}\to DD{\hat{I}}^3$ modes contribute to the decay width of $T_{cc}$, with the former being dominant. The resulting total decay width of about $\hat{I}“=63$ keV is smaller than the experimental decay width obtained from the Breit-Wigner fit of the LHCb data, $\hat{I}“=410\pm 165\pm 43_{-38}^{+18}$ keV, while close to the number obtained from the alternative unitary analysis, $\hat{I}“=48\pm 2_{-14}^{+0}$ keV, which supports the molecular nature of $T_{cc}$.