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We investigated the relationship between two massive star‐forming galaxy populations at redshift   z ∼ 2 , namely submillimetre galaxies (SMGs) and BzK‐selected galaxies (BzKs). Out of 60 SMGs found in the Subaru/ XMM–Newton  deep field, we collected optical–near‐infrared photometry of 28 radio counterparts for 24 SMGs, based on refined sky positions with a radio map for 35 SMGs. We found a correlation between their  K ‐band magnitudes and  BzK  [≡( z − K ) − ( B − z )]  colours: almost all of the  K ‐faint  ( K  AB  &gt; 21.3)  radio‐detected SMGs have   BzK  &gt; −0.2 , and are therefore BzKs. This result strongly supports the idea of performing direct optical identification of SMGs by searching for BzKs around SMGs. We calculated the formal significance ( P ′ value) for each of the BzK associations around radio‐undetected SMGs, and found six new robust identifications, including one double identification. From this analysis, we obtained the current best estimate of the surface density of BzK‐selected SMGs, which indicates that only ∼1 per cent of BzKs are SMGs. If BzKs are normal disc‐like galaxies at   z ∼ 2 , as indicated by the correlation between their star formation rate and stellar mass and also by dynamical properties, SMGs are likely to be merging BzKs. In this case, a typical enhancement of the star formation rate as a result of merging is a factor of only ∼3, which is an order of magnitude lower than that of local ultraluminous infrared galaxies (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  (which will at least be higher than the fraction at   z ≲ 1  of ∼10 per cent), it is puzzling to find such a low fraction of SMGs in the progenitor population (BzKs).

A close relationship at z ∼ 2: submillimetre galaxies and BzK‐selected galaxies