We report three additional SINFONI detections of H-alpha emission line from quasar absorbers, two of which are new identifications. These were targeted among a sample of systems with log N(HI)>19.0 and metallicities measured from high-resolution spectroscopy. The detected galaxies are at impact parameters ranging from 6 to 12 kpc from the quasars line-of-sight. We derive star formation rates (SFR) of a few solar masses per year for the two absorbers at z_abs~1 and SFR=17 solar masses per year for the DLA at z_abs~2. These three detections are found among a sample of 16 DLAs and sub-DLAs (5 at z_abs~1 and 7 at z_abs~2). For the remaining undetected galaxies, we derive flux limits corresponding to SFR<0.1--11.0 solar masses per year depending on redshift of the absorber and depth of the data. When combined with previous results from our survey for galaxy counterparts to HI-selected absorbers, we find a higher probability of detecting systems with higher metallicity as traced by dust-free [Zn/H] metallicity. We also report a higher detection rate with SINFONI for host galaxies at z_abs~1 than for systems at z_abs~2. Using the NII/H-alpha ratio, we can thus compare absorption and emission metallicities in the same high-redshift objects, more than doubling the number of systems for which such measures are possible.
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