The production of Z$^0$ bosons at large rapidities in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV is reported. Z$^0$ candidates are reconstructed in the dimuon decay channel (${\rm Z}^0 \rightarrow \mu^+\mu^-$), based on muons selected with pseudo-rapidity $-4.0<\eta<-2.5$ and $p_{\rm T}>20$ GeV/$c$. The invariant yield and the nuclear modification factor, $R_{\rm AA}$, are presented as a function of rapidity and collision centrality. The value of $R_{\rm AA}$ for the 0-20% central Pb-Pb collisions is $0.67 \pm 0.11 \, \mbox{(stat.)} \, \pm 0.03 \, \mbox{(syst.)} \, \pm 0.06 \, \mbox{(corr. syst.)}$, exhibiting a deviation of $2.6 \sigma$ from unity. The results are well-described by calculations that include nuclear modifications of the parton distribution functions, while the predictions using vacuum PDFs deviate from data by $2.3\sigma$ in the 0-90% centrality class and by $3\sigma$ in the 0-20% central collisions.
Invariant yield of Z$^{0}$ production in 2.5 < y < 4.0 divided by the average nuclear overlap function in the 0-90% centrality class. The first uncertainty is statistical, the second is systematic.
Nuclear modification factor of Z$^{0}$ production in 2.5 < y < 4.0 in the 0-90% centrality class. The first uncertainty is statistical, the second is systematic.
Invariant yield of Z$^{0}$ production in 2.5 < y < 4.0 divided by the average nuclear overlap function as a function of rapidity in the 0-90% centrality class. The first uncertainty is statistical, the second is the uncorrelated systematic and the third is the correlated systematic.
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