Production cross sections of muons from semi-leptonic decays of charm and beauty hadrons were measured at forward rapidity ($2.5<y<4$) in proton--proton (pp) collisions at a centre-of-mass energy $\sqrt{s}=5.02$ TeV with the ALICE detector at the CERN LHC. The results were obtained in an extended transverse momentum interval, $2 < p_{\rm T} < 20$ GeV/$c$, and with an improved precision compared to previous measurements performed in the same rapidity interval at centre-of-mass energies $\sqrt{s}= 2.76$ and 7 TeV. The $p_{\rm T}$- and $y$-differential production cross sections as well as the $p_{\rm T}$-differential production cross section ratios between different centre-of-mass energies and different rapidity intervals are described, within experimental and theoretical uncertainties, by predictions based on perturbative QCD.
$p_{\rm T}$-differential production cross section of muons from heavy-flavour hadron decays at forward rapidity in pp collisions at $\sqrt{s}=5.02$ TeV in the rapidity interval $2.5 < y < 4$.
Production cross section of muons from heavy-flavour hadron decays as a function of rapidity in pp collisions at $\sqrt{s} = 5.02$ TeV for the $p_{\rm T}$ interval $2 < p_{\rm T} < 7$ GeV/$c$.
Production cross section of muons from heavy-flavour hadron decays as a function of rapidity in pp collisions at $\sqrt{s} = 5.02$ TeV for the $p_{\rm T}$ interval $7 < p_{\rm T} < 20$ GeV/$c$.