# Production of muons from heavy-flavour hadron decays at high transverse momentum in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ and 2.76 TeV

Measurements of the production of muons from heavy-flavour hadron decays in Pb$-$Pb collisions at $\sqrt{s_{\rm NN}}$ = $5.02$ and $2.76$ TeV using the ALICE detector at the LHC are reported. The nuclear modification factor $R_{\rm AA}$ at $\sqrt{s_{\rm NN}}$ = 5.02 TeV is measured at forward rapidity ($2.5 <~ y <~4$) as a function of transverse momentum $p_{\rm T}$ in central, semi-central, and peripheral collisions over a wide $p_{\rm T}$ interval, $3 <~ p_{\rm T} <~ 20$ GeV/$c$, in which a significant contribution of muons from beauty-hadron decays is expected at high $p_{\rm T}$. With a significantly improved precision compared to the measurements at lower collision energy, the $R_{\rm AA}$ shows an increase of the suppression of the yields of muons from heavy-flavour hadron decays with increasing centrality. A suppression by a factor of about three is observed in the $10\%$ most central collisions. The $R_{\rm AA}$ at $\sqrt{s_{\rm NN}}$ = 5.02 is similar to that reported at 2.76 TeV in a broader $p_{\rm T}$ interval and with an improved accuracy with respect to previously published measurements. The precise $R_{\rm AA}$ results have the potential to distinguish between model predictions implementing different mechanisms of parton energy loss in the high-density medium formed in heavy-ion collisions. The results place stringent constraints on the relative energy loss between charm and beauty quarks.