  The process that quenched star formation in galaxies at intermediate and high
redshift is still the subject of considerable debate. One way to investigate
this puzzling issue is to study the number density of quiescent galaxies at
z~2, and its dependence on mass. Here we present the results of a new study
based on very deep Ks-band imaging (with the HAWK-I instrument on the VLT) of
two HST CANDELS fields (the UKIDSS Ultra-deep survey (UDS) field and
GOODS-South). The new HAWK-I data (taken as part of the HUGS VLT Large Program)
reach detection limits of Ks>26 (AB mag). We select a sample of
passively-evolving galaxies in the redshift range 1.4<z<2.5. Thanks to the
depth and large area coverage of our imaging, we have been able to extend the
selection of quiescent galaxies a magnitude fainter than previous analyses.
Through extensive simulations we demonstrate, for the first time, that the
observed turn-over in the number of quiescent galaxies at K>22 is real. This
has enabled us to establish unambiguously that the number counts of quiescent
galaxies at z~2 flatten and slightly decline at magnitudes fainter than
Ks~22(AB mag.). We show that this trend corresponds to a stellar mass threshold
$M_*10^{10.8}\,{\rm M_{\odot}}$ below which the mechanism that halts the star
formation in high-redshift galaxies seems to be inefficient. Finally we compare
the observed pBzK number counts with those of quiescent galaxies extracted from
four different semi-analytic models. We find that none of the models provides a
statistically acceptable description of the number density of quiescent
galaxies at these redshifts. We conclude that the mass function of quiescent
galaxies as a function of redshift continues to present a key and demanding
challenge for proposed models of galaxy formation and evolution.
