We present an analytical expression that gives both the matter and tracer (halo or galaxy) power spectrum with 1-loop corrections that include the neutrino effects on the mode-coupling kernels. We use the FFTLog algorithm to accelerate calculating the higher-order corrections to the power spectrum. We then use our power spectrum and bispectrum models to pursue two main goals. First, we examine the impact of neutrino mass on cosmological parameter estimation from both the power spectrum and bispectrum in real space. We create 1-loop power spectrum and bispectrum templates in real-space and fit to the quijote simulation suite at redshift $z=0$, including the cross-covariance between the power spectrum and the bispectrum. We show the neutrino signature kernels estimate the same cosmological parameters as the model with the standard perturbation theory (SPT) kernels, even for DESI Year 5 volume, except for the galaxy bias parameters inferred from the bispectrum. Second, we investigate to what extent the bispectrum can improve parameter constraints. We perform a Fisher forecast using the power spectrum, the tree-level bispectrum, and a joint analysis that includes the cross-covariance between them. We show that including the bispectrum can substantially reduce the error bars on key parameters. For the neutrino mass in particular, the uncertainty is reduced by $\sim 20\%$. We notify that our forecast is very optimistic for DESI, as DESI is at a higher redshift.

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• Cosmological parameters
• Large scale structure of the Universe