Redshift-space galaxy bispectrum in presence of massive neutrinos: A multipole expansion approach for Euclid

Massive neutrinos imprint distinctive signatures on the evolution of cosmic structures, notably suppressing small-scale clustering. We investigate the impact of massive neutrinos on the galaxy bispectrum in redshift-space, adopting a spherical harmonic multipole decomposition $B_L^m(k_1,\mu ,t)$, that captures the full angular dependence. We develop an analytical and numerical framework incorporating neutrino-corrected perturbation theory kernels and redshift-space distortions. Our results demonstrate that the linear triangle configurations are particularly sensitive to massive neutrinos, with deviations reaching up to $\sim 2\mathrm{\%}$ for a total mass $\sum m_{\nu }=0.12\mathrm{e}\mathrm{V}$. To assess detection prospects in galaxy surveys like $\mathit{\text{Euclid}}$, we compute the signal-to-noise ratio (SNR) for individual multipoles, including the effects of Finger-of-God damping and shot noise. The neutrino-induced signatures in $B_0^0$ and $B_2^0$ are found to be detectable with SNR $\gtrsim 5$ across a range of configurations, even after accounting for small-scale suppression. Higher-order multipoles such as $B_2^1$ and $B_2^2$ are moderately sensitive, with SNR $\gtrsim$ ($2-3$) in squeezed limits, while hexadecapole moments are more suppressed but still exhibit measurable signals at high $k_1$. Additionally, the SNR generally increases with wave number $k_1$, particularly for squeezed and stretched triangles, suggesting that access to smaller scales significantly enhances detection prospects. Our study highlights the potential of the redshift-space bispectrum multipoles as sensitive probes of massive neutrinos, complementing traditional power spectrum analyses, and underscores the importance of angular information and higher-order statistics for galaxy surveys.