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Cross-Correlation of CFHTLenS Galaxy Number Density and Planck CMB Lensing

We measure the cross-power spectrum between galaxy density from Canada-France-Hawaii-Telescope Lensing Survey (CFHTLenS) catalogues and gravitational lensing convergence from Planck data release 1 (2013) and 2 (2015). We investigate three main galaxy samples: $18.0<i_{\rm AB}<22.0$, $18.0<i_{\rm AB}<23.0$, $18.0<i_{\rm AB}<24.0$ in the redshift range $0.2<z<1.3$ in each of the four CFHTLenS wide fields. By comparing the measured cross-spectrum with model predictions, linear galaxy-dark matter biases of $b=0.82^{+0.24}_{-0.23}, 0.83^{+0.19}_{-0.18}, 0.82^{+0.16}_{-0.14}$ are inferred at significances of $3.5, 4.5, 5.6σ$ using the Planck 2015 release. These measurements are marginally consistent with biases derived from galaxy-galaxy auto-correlations: $b=1.15^{+0.02}_{-0.01}, 1.08^{+0.01}_{-0.01}$ and $0.96^{+0.01}_{-0.01}$ respectively. Using the 2013 Planck release, we obtain biases of $b=1.33^{+0.29}_{-0.28}, 1.19^{+0.23}_{-0.23}, 1.16^{+0.19}_{-0.18}$, showing significant differences between the releases.