The effect of strong electric field on the evolution of charmonium in quark gluon plasma

In ultra-relativistic heavy-ion collisions, the strong electric field can be produced by the colliding nuclei. The magnitude of the electric field $E$ is on the order of $eE\sim m_{\pi }^2$ at the early stage of the collision. In quark gluon plasma (QGP), such a strong electric field can have a significant impact on the evolution of charmonia. We employ the time-dependent Schr"odinger equation to study the evolution of charmonium states in the strong electric field generated by the moving charges. The electric field can result in transitions between charmonium states with different angular momenta. In order to see this effect, we make comparisons between the yields of $J\mathrm{/}\psi$, ${\psi }^{\mathrm{\prime }}$ and ${\chi }_c$ with and without the electric field. The results show that in the early stage of the collision the electric field induces significant dissociation of $J\mathrm{/}\psi$. In the meantime, ${\chi }_c$ is generated via the transition from $J\mathrm{/}\psi$ by the electric field.