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Cross-correlation between $Planck$ CMB lensing potential and galaxy catalogues from HELP

We present the study of cross-correlation between Cosmic Microwave Background (CMB) gravitational lensing potential map released by the \textit{Planck} collaboration and photometric redshift galaxy catalogues from the \textit{Herschel} Extragalactic Legacy Project (HELP), divided into four sky patches: NGP, \textit{Herschel} Stripe-82, and two halves of SGP field, covering in total $\sim 660$ deg$^{2}$ of the sky. We estimate the galaxy linear bias parameter, $b_{0}$, from joint analysis of cross-power spectrum and galaxy auto-power spectrum using Maximum Likelihood Estimation technique to obtain values ranging from $0.70 \pm 0.01$ for SGP Part-2 to $1.02 \pm 0.02$ for SGP Part-1 field. We also estimate the amplitude of cross-correlation and find the values spanning from $0.67 \pm 0.18$ for SGP Part-2 to $0.80 \pm 0.23$ for SGP Part-1 field, respectively. For NGP and SGP Part-1 fields the amplitude is consistent with the expected value for the standard cosmological model within $\sim 1\,σ$, while for \textit{Herschel} Stripe-82 and SGP Part-2 we find the amplitude to be smaller than expected with $\sim 1.5\,σ$ and $\sim 2\,σ$ deviation, respectively. We perform several tests on various systematic errors to study the reason for the deviation, however, value of the amplitude turns out to be robust with respect to these errors. The only significant change in the amplitude is observed when we replace the minimum-variance CMB lensing map, used in the baseline analysis, by the lensing map derived from the CMB temperature map with deprojected thermal Sunyaev-Zeldovich signal.