  We present a detailed study of scaling relations between total cluster mass
and three mass proxies based on X-ray observables: temperature of the
intra-cluster medium, gas mass and the product of the two, Y_X. Our analysis is
based on two sets of high-resolution hydrodynamical simulations performed with
the TreePM-SPH GADGET code. The first set includes about 140 clusters with
masses above 5x10^13 M_sun/h (30 having mass above 10^15 M_sun/h), that have
been simulated with (i) non-radiative physics and including (ii) cooling, star
formation, chemical enrichment and the effect of supernova feedback triggering
galactic ejecta. This large statistics is used to quantify the robustness of
the scaling relations, to determine their redshift evolution and to calibrate
their intrinsic scatter and its distribution. We use a smaller set of clusters
including 18 halos with masses above 5x10^13 M_sun/h to test the robustness of
mass proxies against changing the physical processes included in simulations
(thermal conduction, artificial viscosity, cooling and star formation, galactic
winds and AGN feedback). We find the M-Y_X scaling relation to be the least
sensitive one to variations of the ICM physics, with its slope and redshift
evolution close to the self-similar model predictions. The distribution of the
scatter around the best-fitting relations is close to a log-normal one. M_gas
has the smallest scatter in mass, with values of sigma_lnM = 0.04-0.06,
depending on the physics included in the simulation, and with a mild dependence
on redshift. The M-T relation is the one with the largest scatter, with
sigma_lnM > 0.1 at z=0, increasing to > 0.15 at z=1. The intrinsic scatter in
the M-Y_X relation is slightly larger than in the M-M_gas relation. These
results confirm that both Y_X and M_gas mass proxies are well suited for
cosmological applications of future large X-ray surveys. [abridged]
