  In the early stages of heavy-ion collisions, the hot QCD matter expands more
longitudinally than transversely. This imbalance causes the system to become
rapidly colder in the longitudinal direction and a local momentum anisotropy
appears. In this paper, we study the heavy-quarkonium spectrum in the presence
of a small plasma anisotropy. We work in the framework of pNRQCD at finite
temperature. We inspect arrangements of non-relativistic and thermal scales
complementary to those considered in the literature. In particular, we consider
temperatures larger and Debye masses smaller than the binding energy, which is
a temperature range relevant for presently running LHC experiments. In this
setting we compute the leading thermal corrections to the binding energy and
the thermal width induced by quarkonium gluo-dissociation.
