Abstract
We study the charmonium dissociation in the hot medium with finite baryon chemical potential $\mu_B$. Charmonium bound states are dissociated in the medium by the color screening effect and the random scatterings with thermal partons, which are included in the real and imaginary parts of the potential respectively. $J/\psi$ fraction in the $c\bar c$ pair defined to be the quantum overlap between the wave package and the wave function of $J/\psi$ eigenstate decreases with time due to the complex potentials. When $\mu_B$ is large compared with the medium temperature, the Deybe mass is increased evidently. We consider $\mu_B$-dependent Deybe mass in both real and imaginary parts of the potential to calculate the $J/\psi$ survival probability in the static medium and the Bjorken medium. $J/\psi$ survival probability is reduced evidently by the $\mu_B$ effect at low temperatures available in the medium produced in Beam Energy Scan experiments, while this effect becomes not apparent at high temperatures.
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