Best-fit models of the cross-power spectrum ﹩{C}_{{\ell }}^{\kappa y}﹩ and auto-power spectrum ﹩{C}_{{\ell }}^{{yy}}﹩ are plotted in red. They are compared to the measured cross-power spectrum from the skew spectrum analysis, the direct cross-power spectrum of the Planck lensing map with the y-parameter map, as well as the auto-power spectrum of the Planck y-parameter maps. The results from Hill & Spergel (2014), as well as Planck Collaboration et al. (2016b), are shown as a comparison, being the direct two-point lensing–SZ cross-correlation and the y-map auto-spectrum from the generated maps therein. The error bars for Planck Collaboration et al. (2016b) are smaller than the symbols used in the plot.