A Search for Molecular Gas toward a BzK-selected Star-forming Galaxy at z = 2.044

We present a search for CO(3-2) emission in SDF-26821, a BzK-selected star-forming galaxy (sBzK) at z = 2.044, using the 45-m telescope of the Nobeyama Radio Observatory and the Nobeyama Millimeter Array. We do not detect significant emission and derive 2 \sigma limits: the CO luminosity of L'CO < 3.1 x 10^10 K km s^{-1} pc^{-2}, the ratio of far-infrared luminosity to CO luminosity of L_FIR/L'CO > 57 Lsun (K km s^{-1} pc^{-2})^{-1}, and the molecular gas mass of M_H2 < 2.5 x 10^10 Msun, assuming a velocity width of 200 km s^{-1} and a CO-to-H2 conversion factor of alpha_CO=0.8 Msun (K km s^{-1} pc^{-2})^{-1}. The ratio of L_FIR/L'CO, a measure of star formation efficiency (SFE), is comparable to or higher than the two z ~ 1.5 sBzKs detected in CO(2-1) previously, suggesting that sBzKs can have a wide range of SFEs. Comparisons of far-infrared luminosity, gas mass, and stellar mass among the sBzKs suggest that SDF-26821 is at an earlier stage of forming stars with a similar SFE and/or more efficiently forming stars than the two z ~ 1.5 sBzKs. The higher SFEs and specific star formation rates of the sBzKs compared to local spirals are indicative of the difference in star formation modes between these systems, suggesting that sBzKs are not just scaled-up versions of local spirals.