  We investigate properties of the net baryon number fluctuations near chiral
crossover in a hot and dense medium of strongly interacting quarks. The
chirally invariant quark-antiquark interactions are modeled by an effective
quark-meson Lagrangian. To preserve remnants of criticality in the O(4)
universality class, we apply the functional renormalization group method to
describe thermodynamics near chiral crossover. Our studies are focused on the
influence of the momentum cuts on the critical behavior of different cumulants
of the net quark number fluctuations. We use the momentum scale dependence of
the flow equation to examine how the suppression of the momentum modes in the
infrared and ultraviolet regime modifies generic properties of fluctuations
expected in the O(4) universality class. We show, that the pion mass $m_\pi$ is
a natural soft momentum scale at which cumulants are saturated at their
critical values, whereas for scales larger than $2m_\pi$ the characteristic
O(4) structure of the higher order cumulants get lost. These results indicate,
that when measuring fluctuations of the net baryon number in heavy ion
collisions to search for a partial restoration of chiral symmetry or critical
point, a special care have to be made when introducing kinematical cuts on the
fluctuation measurements.
