  Single and pair top-quark production in proton-lead (p-Pb) and lead-lead
(Pb-Pb) collisions at the CERN Large Hadron Collider (LHC) and future circular
collider (FCC) energies, are studied with next-to-leading-order perturbative
QCD calculations including nuclear parton distribution functions. At the LHC,
the pair-production cross sections amount to sigma(t-tbar) = 3.4 mub in Pb-Pb
at sqrt(s) = 5.5 TeV, and sigma(t-tbar) = 60 nb in p-Pb at sqrt(s) = 8.8 TeV.
At the FCC energies of sqrt(s) = 39 and 63 TeV, the same cross sections are
factors of 90 and 55 times larger respectively. In the leptonic final-state
t-tbar --> W+b W-bbar --> b bbar l+l- nu+nu-, after typical acceptance and
efficiency cuts, one expects about 90 and 300 top-quarks per nominal LHC-year
and 4.7 10^4 and 10^5 per FCC-year in Pb-Pb and p-Pb collisions respectively.
The total t-tbar cross sections, dominated by gluon fusion processes, are
enhanced by 3--8% in nuclear compared to p-p collisions due to an overall net
gluon antishadowing, although different regions of their differential
distributions are depleted due to shadowing or EMC-effect corrections. The
rapidity distributions of the decay leptons in t-tbar processes can be used to
reduce the uncertainty on the Pb gluon density at high virtualities by up to
30% at the LHC (full heavy-ion programme), and by 70% per FCC-year. The cross
sections for single-top production in electroweak processes are also computed,
yielding about a factor of 30 smaller number of measurable top-quarks after
cuts, per system and per year.
