We present a spectroscopic sample of z \approx 0.5 luminous red galaxies ( LRGs ) that are located within physical projected distances \rho \la 350 h ^ { -1 } ~ { } { kpc } ~ { } of a QSO sightline .
Of the 37 LRGs in our sample , eight have associated Mg II absorbers with rest-frame equivalent width W _ { r } ( 2796 ) > 0.3 Å and velocity separation | \Delta v| \la 350 km s ^ { -1 } and 29 do not have associated Mg II absorbers to a 2- \sigma limit of W _ { r } ( 2796 ) = 0.3 Å .
We perform a stellar population synthesis analysis using stacked spectra of the Mg II absorbing and non-absorbing LRG subsamples .
We find that LRGs with or without associated Mg II absorbers share similar star formation histories and are best described by old stellar population models ( \ga 1 Gyr ) .
Younger stellar populations ( \la 1 Gyr ) fail to reproduce their spectra .
These findings are consistent with the lack of [ O II ] emission features in the LRG spectra .
The primarily old stellar populations in the LRGs indicate that starburst driven outflows are unlikely to explain the observed Mg II absorbers at large distances from the LRGs .
In addition , the spectroscopic LRG sample allows us to derive a sensitive constraint for the cool gas covering fraction of \langle \kappa \rangle = 14 \pm 6 % in the LRG halos for absorbers of W _ { r } ( 2796 ) > 0.3 Å .
Finally , we speculate on the origin of the observed Mg II absorbers around the LRGs .