The quasi-fission phenomeonon of double charm $T_{cc}^+$ induced by nucleon

In this work, we study the reaction of a nucleon and a doubly charmed state $T_{cc}$. Under the assumption of the $T_{cc}$ as a molecular state of $D^{*}D$, the reaction of the nucleon and $T_{cc}$ is mediated by exchanges of $\pi$, $\eta$, $\rho$, and $\omega$ meson, which results in split of $T_{cc}$ state with two $D$ mesons in final state. With the help of the effective Lagrangians, the cross section of $p+T^+_{cc}\to p+D^++D^0$ process is calculated, and a very large cross section can be obtained with very small incoming momentum of proton. It decrease rapidly with the increase of the momentum to about 10 mb at momenta of order of GeV. Such large cross section suggests that induced by a proton the $T_{cc}^+$ state is very easy to decay and transit to two $D$ mesons. In the rest frame of the $T_{cc}^+$ state, an obvious accumulation of final $D$ meson at small momentum region can be observed in predicted Dalitz plot, which is due to the molecular state interpretation of $T_{cc}$ state. This novel quasi-fission phenomenon of double charm molecular $T_{cc}^+$ state induced by a proton can be accessible at the forthcoming PANDA experiment.