  We investigate the relationship between two massive star-forming galaxy
populations at redshift z~ 2; i.e. submillimetre galaxies (SMGs) and
BzK-selected galaxies (BzKs). Out of 60 SMGs found in the Subaru/XMM-Newton
deep field, we collect optical--NIR photometry of 28 radio counterparts for 24
SMGs, based on refined sky positions with a radio map for 35 SMGs (Ivison et
al. 2007). We find a correlation between their K-band magnitudes and BzK [=
(z-K)-(B-z)] colours: almost all of the K-faint (K_AB > 21.3) radio-detected
SMGs have BzK>-0.2, and therefore BzKs. This result gives strong support to
perform direct optical identification of SMGs by searching for BzKs around
SMGs. We calculate the formal significance (P' value) for each of the BzK
associations around radio-undetected SMGs, and find 6 new robust
identifications, including one double identification. From this analysis, we
obtain the current best estimate on the surface density of BzK-selected SMGs,
which indicates that only ~1 per cent of BzKs are SMGs. If BzKs are normal
disk-like galaxies at z~ 2 as indicated by the correlation between their star
formation rate (SFR) and stellar mass and also by dynamical properties, SMGs
are likely to be merging BzKs. In this case, a typical enhancement of SFR due
to merging is only a factor of ~ 3, which is an order of magnitude lower than
that of local ULIRGs. This may indicate that most of the merging BzKs could be
observed as SMGs. Considering a possible high fraction of mergers at z~ 2 (at
least it would be higher than the fraction at z> 1 of ~ 10 per cent), it is
rather puzzling to find such a low fraction of SMGs in the progenitor
population, i.e. BzKs.
