Predicting another doubly charmed molecular resonance $T_{cc}^{\prime+}(3876)$

The isospin breaking effect plays an essential role in generating hadronic molecular states with a very tiny binding energy. Very recently, the LHCb Collaboration observed a very narrow doubly charmed tetraquark $T_{cc}^+$ in the $D^0D^0\pi$ mass spectrum, which lies just below the $D^0D^{*+}$ threshold around 273 keV. In this work, we study the $D^0D^{*+}/D^+D^{*0}$ interactions with the one-boson-exchange effective potentials and consider the isospin breaking effect carefully. We not only reproduce the mass of the newly observed $T_{cc}^+$ very well in the doubly charmed molecular tetraquark scenario, but also predict the other doubly charmed partner resonance $T_{cc}^{\prime+}$ with $m=3876~\text{MeV}$, and $\Gamma= 412~\text{keV}$. The prime decay modes of the $T_{cc}^{\prime+}$ are $D^0D^+\gamma$ and $D^+D^0\pi^0$. The peculiar characteristic mass spectrum of the $D^0D^{*+}/D^+D^{*0}$ molecular systems can be applied to identify the doubly charmed molecular states.