  The central goal of jet quenching studies in high-energy nuclear collisions
is the characterization of those QCD medium properties that are accessible by
these probes. Most of the discussion in the last years has been focused on the
determination of the jet quenching parameter, $\hat q$. We present here an
extraction of this parameter using data of inclusive particle suppression at
RHIC and LHC energies for different centralities. Our approach consists of
fitting a $K$ factor that quantifies the departure of this parameter from an
ideal estimate, $K\equiv \hat q/(2\epsilon^{3/4})$, where $\hat q$ is
determined by the local medium quantities as provided by hydrodynamical
calculations. We find that this $K$ factor is larger at RHIC than at the LHC,
as obtained already in previous analyses, but, surprisingly, it is almost
independent of the centrality of the collision. Taken at face value, the $K$
factor would not depend on the local properties of the medium as energy density
or temperature, but on global collision quantities such as the center of mass
energy. This is a very intriguing, unexpected possibility for which we cannot
yet provide a clear interpretation. We also comment on the limitations of the
formalism that may affect this conclusion.
