Upper panel: scaling relation between the HCN(4-3) luminosity (converted from 5-4, see Sect. 3.1) and the total infrared luminosity. The black squares are the individual values found in our high-z sample (after correcting for the lensing magnification). The red star shows the average intrinsic and L_IR of our sample. The gray diamond is the mean position of the SPT SMG sample derived from the stacking of the ALMA cycle-0 data by Spilker et al. (2014). The orange downwards triangles are two H-ATLAS sources provided in Yang et al. (priv. comm.). The blue filled circles are from the local sample of Zhang et al. (2014). The black solid line is the best-fit relation of Zhang et al. (2014) and the dotted lines indicate the 1σ intrinsic scatter around it. Lower panel: same figure but for HCO⁺.