  Fluctuations of conserved charges are sensitive to the QCD phase transition
and a possible critical endpoint in the phase diagram at finite density. In
this work, we compute the baryon number fluctuations up to tenth order at
finite temperature and density. This is done in a QCD-assisted effective theory
that accurately captures the quantum- and in-medium effects of QCD at low
energies. A direct computation at finite density allows us to assess the
applicability of expansions around vanishing density. By using different
freeze-out scenarios in heavy-ion collisions, we translate these results into
baryon number fluctuations as a function of collision energy. We show that a
non-monotonic energy dependence of baryon number fluctuations can arise in the
non-critical crossover region of the phase diagram. Our results compare well
with recent experimental measurements of the kurtosis and the sixth-order
cumulant of the net-proton distribution from the STAR collaboration. They
indicate that the experimentally observed non-monotonic energy dependence of
fourth-order net-proton fluctuations is highly non-trivial. It could be an
experimental signature of an increasingly sharp chiral crossover and may
indicate a QCD critical point. The physics implications and necessary upgrades
of our analysis are discussed in detail.
