  We explore the scaling relation between the flux of the Sunyaev-Zel'dovich
(SZ) effect and the total mass of galaxy clusters using already reduced Chandra
X-ray data present in the ACCEPT (Archive of Chandra Cluster Entropy Profile
Tables) catalogue. The analysis is conducted over a sample of 226 objects,
examining the relatively small scale corresponding to a cluster overdensity
equal to 2500 times the critical density of the background universe, at which
the total masses have been calculated exploiting the hydrostatic equilibrium
hypothesis. Core entropy (K0) is strongly correlated with the central cooling
time, and is therefore used to identify cooling-core (CC) objects in our
sample. Our results confirm the self-similarity of the scaling relation between
the integrated Comptonization parameter (Y) and the cluster mass, for both CC
and NCC (non-cooling-core) clusters. The consistency of our calibration with
recent ones has been checked, with further support for Y as a good mass proxy.
We also investigate the robustness of the constant gas fraction assumption, for
fixed overdensity, and of the Yx proxy (Kravstov et al. 2007) considering CC
and NCC clusters, again sorted on K0 from our sample. We extend our study to
implement a K0-proxy, obtained by combining SZ and X-ray observables, which is
proposed to provide a CC indicator for higher redshift objects. Finally, we
suggest that an SZ-only CC indicator could benefit from the employment of
deprojected Comptonization radial profiles.
