  We here concentrate on available $\pi^\pm$ and $K^\pm$ ALICE preliminary
$R_{AA}$ data in central 2.76 TeV Pb+Pb collisions at LHC. These data show an
interesting fine resolution hierarchy, i.e. the measured $K^\pm$ data have
consistently lower suppression compared to $\pi^\pm$ measurements. We here ask
whether theoretical predictions based on energy loss in dynamical QCD medium
can quantitatively and qualitatively explain such fine resolution. While our
suppression calculations agree well with the data, we find that qualitatively
explaining the fine hierarchy critically depends on the choice of fragmentation
functions. While the most widely used fragmentation functions lead to the
reversal of the observed hierarchy, a more recent version correctly reproduce
the experimental data. We here point to the reasons behind such discrepancy in
the predictions. Our results argue that accuracy of the theoretical predictions
reached a point where comparison with fine resolution data at LHC can generate
useful understanding.
