We report deep K-band (18-27GHz) observations with the 100-m Green Bank Telescope of HCN(1-0) line emission towards the two submillimeter-selected galaxies (SMGs) SMMJ02399-0136 (z=2.81) and SMMJ16359+6612 (z=2.52). For both sources we have obtained spectra with channel-to-channel rms noise of <=0.5mJy, resulting in velocity-integrated line fluxes better than < 0.1 Jy km/s, although we do not detect either source. Such sensitive observations -- aided by gravitational lensing of the sources -- permit us to put upper limits of L_HCN(1-0) < 2x10^10 K km/s pc^2 on the intrinsic HCN(1-0) line luminosities of the two SMGs. The far-infrared (FIR) luminosities for all three SMGs with sensitive HCN(1-0) observations to date are found to be consistent with the tight FIR-HCN luminosity correlation observed in Galactic molecular clouds, quiescent spirals and (ultra) luminous infrared galaxies in the local Universe. Thus, the observed HCN luminosities remain in accordance with what is expected from the universal star formation efficiency per dense molecular gas mass implied by the aforementioned correlation, and more sensitive observations with todays large aperture radio telescopes hold the promise of detecting HCN(1-0) emission in similar objects in the distant Universe.
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