  We exploit deep observations of the GOODS-N field taken with PACS, on board
of Herschel, as part of the PEP guaranteed time, to study the link between star
formation and stellar mass in galaxies to z~2. Starting from a stellar
mass-selected sample of ~4500 galaxies with mag[4.5mu]<23 (AB), we identify
~350 objects with a PACS detection at 100 or 160mu and ~1500 with only Spitzer
24 mu counterpart. Stellar masses and total IR luminosities (LIR) are estimated
by fitting the SEDs. Consistently with other Herschel results, we find that LIR
based only on 24 mu data is overestimated by a median factor ~1.8 at z~2,
whereas it is underestimated (with our approach) up to a factor ~1.6 at
0.5<z<1.0. We then exploit this calibration to correct LIR based on the MIPS
fluxes. These results clearly show how Herschel is fundamental to constrain
LIR, and hence the SFR, of high redshift galaxies. Using the galaxies detected
with PACS (and/or MIPS), we investigate the existence and evolution of the
relations between the star formation rate (SFR), the specific star formation
rate (SSFR=SFR/mass) and the stellar mass. Moreover, in order to avoid
selection effects, we also repeat this study through a stacking analysis on the
PACS images to fully exploit the far-IR information also for the Herschel and
Spitzer undetected subsamples. We find that the SSFR-mass relation steepens
with redshift, being almost flat at z<1.0 and reaching a slope of
alpha=-0.50^(+0.13)_(-0.16) at z~2, at odds with recent works based on
radio-stacking analysis at the same redshift. The mean SSFR of galaxies
increases with redshift, by a factor ~15 for massive M>10^(11) (M_sun) galaxies
from z=0 to z=2, and seems to flatten at z>1.5 in this mass range. Moreover,
the most massive galaxies have the lowest SSFR at any z, implying that they
have formed their stars earlier and more rapidly than their low mass
counterparts.
