  Recently the inclusive transverse momentum distributions of primary charged
particles were measured for different centralities in $Pb+Pb$ collisions. A
strong suppression of the nuclear modification factor in central collisions
around $p_T \sim 6-7$ GeV/c was seen. As a possible explanation, the
hydrodynamic description of the collision process was tentatively proposed.
However, such effect, (albeit much weaker) also exists in the ratio of
data/fits, both in nuclear $Pb+Pb$ collisions, and in the elementary $p+p$ data
in the same range of transverse momenta for which such an explanation is
doubtful. As shown recently, in this case, assuming that this effect is
genuine, it can be attributed to a specific modification of a quasi-power like
formula usually used to describe such $p_T$ data, namely the Tsallis
distribution. Following examples from other branches of physics, one simply has
to allow for the power index becoming a complex number. This results in
specific log-periodic oscillations dressing the usual power-like distribution,
which can fit the $p+p$ data. In this presentation we demonstrate that this
method can also describe $Pb+Pb$ data for different centralities. We compare it
also with a two component statistical model with two Tsallis distributions
recently proposed showing that data at still larger $p_T$ will be sufficient to
discriminate between these two approaches.
