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In this paper, the centrality dependent $\Zn$ and $\Wpm$ production and theisospin effect in $\Wpm$ production are investigated with a parton and hadroncascade model PACIAE in Pb--Pb collisions at $\sNN=5.02$~TeV. ALICE data of$\Zn$ production in Pb--Pb collisions at $\sNN=5.02$~TeV are found to bereproduced fairly well. The prediction on $\Wpm$ production in the samecollision system is given as well. An interesting isospin effect is observed inexploring the charge asymmetry between $\Wp$ and $\Wm$ as a function of theasymmetry between number of valence $u$- and $d$-quarks varied from small tolarge collision systems at center-of-mass energy 5.02 TeV. The results serve asa important benchmarks for understanding the initial conditions of heavy-ioncollisions.

Centrality dependence and isospin effect on $\Wpm$ and $\Zn$ productions in nucleus-nucleus collisions at $\sNN=5.02$~TeV