  Using a spectral stacking technique we searched for the average \lya emission
from high-z Damped \lya (DLA) galaxies detected in the Sloan Digital Sky Survey
QSO spectra. We used a sample of 341 DLAs of mean redshift <z>= 2.86 and log
N(HI) > 20.62 to place a 3$\sigma$ upper limit of 3.0 \times 10^{-18} erg
s^{-1} cm^{-2} on the \lya flux emitted within $\sim$1.5 arcsec (or 12 kpc)
from the QSO line of sight. This corresponds to an average \lya luminosity of <
2 \times 10^{41} erg s^{-1} or 0.03 $L_\star$(\lya). This limit is deeper than
the limit of most surveys for faint \lya emitters. The lack of \lya emission in
DLAs is consistent with the in situ star formation, for a given N(HI), being
less efficient than what is seen in local galaxies. Thus, the overall DLA
population seems to originate from the low luminosity end of the high redshift
\lya emitting galaxies and/or to be located far away from the star forming
regions. The latter may well be true since we detect strong OVI absorption in
the stacked spectrum, indicating that DLAs are associated with a highly ionized
phase possibly the relics of galactic winds and/or originating from cold
accretion flows. We find the contribution of DLA galaxies to the global star
formation rate density to be comparatively lower than that of Lyman Break
Galaxies.
