With the advent of a new generation of cosmological experiments that will provide high-precision measurements of the cosmic microwave background (CMB) and galaxies in the large-scale structure, it is pertinent to examine the potential of performing a joint analysis of multiple cosmological probes. In this paper, we study the cosmological information content contained in the one-loop power spectra and tree bispectra of galaxies cross-correlated with CMB lensing. We use the FFTLog method to compute angular correlations in spherical harmonic space, applicable for wide angles that can be accessed by forthcoming galaxy surveys. We find that adding the bispectra and cross-correlations with CMB lensing offers a significant improvement in parameter constraints, including those on the total neutrino mass, $M_ u$, and local non-Gaussianity amplitude, $f_{rm NL}$. In particular, our results suggest that the combination of the Vera C. Rubin Observatorys Legacy Survey of Space and Time (LSST) and CMB-S4 will be able to achieve $sigma(M_ u)=42$ meV from galaxy and CMB lensing correlations, and $sigma(M_ u)=12$ meV when further combined with the CMB temperature and polarization data, without any prior on the optical depth.
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