  We present stacking analyses on our ALMA deep 1.1 mm imaging in the SXDF
using 1.6 {\mu}m and 3.6 {\mu}m selected galaxies in the CANDELS WFC3 catalog.
We detect a stacked flux of ~0.03-0.05 mJy, corresponding to LIR < 10^11 Lsun
and a star formation rate (SFR) of ~ 15 Msun/yr at z = 2. We find that galaxies
brighter in the rest-frame near-infrared tend to be also brighter at 1.1 mm,
and galaxies fainter than m[3.6um] = 23 do not produce detectable 1.1 mm
emission. This suggests a correlation between stellar mass and SFR, but
outliers to this correlation are also observed, suggesting strongly boosted
star formation or extremely large extinction. We also find tendencies that
redder galaxies and galaxies at higher redshifts are brighter at 1.1 mm. Our
field contains z ~ 2.5 H-alpha emitters and a bright single-dish source.
However, we do not find evidence of bias in our results caused by the bright
source. By combining the fluxes of sources detected by ALMA and fluxes of faint
sources detected with stacking, we recover a 1.1 mm surface brightness of up to
20.3 +/- 1.2 Jy/deg, comparable to the extragalactic background light measured
by COBE. Based on the fractions of optically faint sources in our and previous
ALMA studies and the COBE measurements, we find that approximately half of the
cosmic star formation may be obscured by dust and missed by deep optical
surveys, Much deeper and wider ALMA imaging is therefore needed to better
constrain the obscured cosmic star formation history.
