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We present an improved and extended analysis of the cross-correlation betweenthe map of the Cosmic Microwave Background (CMB) lensing potential derived fromthe \emph{Planck} mission data and the high-redshift galaxies detected by the\emph{Herschel} Astrophysical Terahertz Large Area Survey (H-ATLAS) in thephotometric redshift range $z_{\rm ph} \ge 1.5$. We compare the results basedon the 2013 and 2015 \textit{Planck} datasets, and investigate the impact ofdifferent selections of the H-ATLAS galaxy samples. Significant improvementsover our previous analysis have been achieved thanks to the highersignal-to-noise ratio of the new CMB lensing map recently released by the\textit{Planck} collaboration. The effective galaxy bias parameter, $b$, forthe full galaxy sample, derived from a joint analysis of the cross-powerspectrum and of the galaxy auto-power spectrum is found to be $b =3.54^{+0.15}_{-0.14}$. Furthermore, a first tomographic analysis of thecross-correlation signal is implemented, by splitting the galaxy sample intotwo redshift intervals: $1.5 \le z_{\rm ph} < 2.1$ and $z_{\rm ph}\ge 2.1$. Astatistically significant signal was found for both bins, indicating asubstantial increase with redshift of the bias parameter: $b=2.89\pm0.23$ forthe lower and $b=4.75^{+0.24}_{-0.25}$ for the higher redshift bin.Consistently with our previous analysis we find that the amplitude of the crosscorrelation signal is a factor of $1.45^{+0.14}_{-0.13}$ higher than expectedfrom the standard $\Lambda$CDM model for the assumed redshift distribution. Therobustness of our results against possible systematic effects has beenextensively discussed although the tension is mitigated by passing from 4 to3$\sigma$.

Toward a tomographic analysis of the cross-correlation between Planck CMB lensing and H-ATLAS galaxies