Forecast of cross-correlation of Chinese Survey Space Telescope cosmic shear tomography with Ali CMB Polarization Telescope cosmic microwave background lensing

We present a forecast study on the cross-correlation between cosmic shear tomography from the Chinese Survey Space Telescope (CSST) and cosmic microwave background (CMB) lensing from Ali CMB Polarization Telescope (AliCPT-1) in Tibet. The correlated galaxy and CMB lensing signals were generated from Gaussian realizations based on inputted auto and crossspectra. To account for the error budget, we considered the CMB lensing reconstruction noise based on the AliCPT-1 lensing reconstruction pipeline; shape noise of the galaxy lensing measurement; CSST photo- z error; photo- z bias; intrinsic alignment (IA) effect; and multiplicative bias. The AliCPT-1 CMB lensing mock data were generated according to two experimental stages, namely the '4 modules*yr' and '48 modules*yr' cases. We estimate the cross-spectra in four tomographic bins according to the CSST photo- z distribution in the range of z is an element of [0, 4). After reconstructing the pseudo-cross-spectra from the realizations, we calculate the signal-to-noise ratio (SNR). By combining the four photo- z bins, the total cross-correlation SNR approximate to 15 (AliCPT-1 `4 modules*yr') and SNR approximate to 22 (AliCPT-1 '48 modules*yr'). Finally, we study the cosmological application of this cross-correlation signal. Excluding IA in the template fitting would lead to roughly a 0.6 sigma increment in sigma(8) due to the negative IA contribution to the galaxy lensing data. For AliCPT-1 first and second stages, the cross-correlation of CSST cosmic shear with CMB lensing gives errors on the clustering amplitude sigma(sigma 8) = (+0.043)(-0.038) or sigma(S8) = +/- 0.031 and sigma(S8) = (0.030)(-0.027+) or sigma(S8) = +/- 0.018, respectively.