Photometric redshifts and selection of high redshift galaxies in the NTT and Hubble Deep Fields

We present and compare in this paper new photometric redshift catalogs of the galaxies in three public fields: the NTT Deep Field, the HDF-N and the HDF-S. Photometric redshifts have been obtained for thewhole sample, by adopting a $\chi^2$ minimization technique on a spectral library drawn from the Bruzual and Charlot synthesis models, with the addition of dust and intergalactic absorption. The accuracy, determined from 125 galaxies with known spectroscopic redshifts, is $\sigma_z\sim 0.08 (0.3)$ in the redshift intervals $z=0-1.5 (1.5-3.5)$. The global redshift distribution of I-selected galaxies shows a distinct peak at intermediate redshifts, z~0.6 at I_{AB}<26 and z~0.8 at I_{AB}<27.5 followed by a tail extending to z~6. We also present for the first time the redshift distribution of the total IR-selected sample to faint limits ($Ks \leq 21$ and $J\leq22$). It is found that the number density of galaxies at 1.25<z<1.5 is ~ 0.1 /arcmin^22 at J<=21 and ~1./arcmin^2} at J<22, and drops to 0.3/arcmin^2 (at J<22) at 1.5<z<2. The HDFs data sets are used to compare the different results from color selection criteria and photometric redshifts in detecting galaxies in the redshift range 3.55$ in the HDF-S are indeed most likely M stars. (ABRIDGED)