  We present deep SINFONI K band integral field spectra of two submillimeter
(SMG) galaxy systems: BR 1202-0725 and J1000+0234, at $z=4.69$ and $4.55$
respectively. Spectra extracted for each object in the two systems do not show
any signature of the [O II]$\lambda\lambda$3726,29\AA$\,$ emission-lines,
placing upper flux limits of $3.9$ and $2.5 \times 10^{-18}\,$${\rm
erg\,s^{-1}\,\,cm^{-2} \,}$ for BR 1202-0725 and J1000+0234, respectively.
Using the relation between the star formation rate (SFR) and the luminosity of
the [O II] doublet from Kennicutt (1998), we estimate unobscured SFR upper
limits of $\sim$ $10-15\,\rm M_\odot\,yr^{-1} \,$ and $\sim$ $30-40\,\rm
M_\odot\,yr^{-1} \,$ for the objects of the two systems, respectively. For the
SMGs, these values are at least two orders of magnitude lower than those
derived from SED and IR luminosities. The differences on the SFR values would
correspond to internal extinction of, at least, $3.4 - 4.9$ and $2.1 - 3.6$ mag
in the visual for BR 1202-0725 and J1000+0234 SMGs, respectively. The upper
limit for the [O II]-derived SFR in one of the LAEs (Ly$\alpha2$) in the
BR1202-0725 system is at least one order of magnitude lower than the previous
SFR derived from infrared tracers, while both estimates are in good agreement
for Ly$\alpha$1. The lower limits to the internal extinction in these two
Lyman-alpha emitters (LAEs) are $0.6$ mag and $1.3$ mag, respectively. No
evidence for the previously claimed (Ohta et al. 2000) [O II] emission
associated with Ly$\alpha$1 is identified in our data, implying that residuals
of the K-band sky emission lines after subtraction in medium-band imaging data
could provide the adequate flux.
