The imprints of massive neutrinos on the three-point correlation function of large-scale structures

Free-streaming of cosmic neutrinos affects the distribution and growth of cosmic structures on small scales. This enables the sum of neutrino masses $M_\nu$ to be constrained from clustering studies. We investigate the possibility of disentangling massive neutrino cosmologies with the three-point correlation function (3PCF) for the first time. We measured the isotropic connected 3PCF $\zeta$ and the reduced 3PCF $Q$ of halo catalogs from the Quijote suite of $N$-body simulations, considering $M_\nu =0.0, 0.1, 0.2,$ and $0.4 \, \mathrm{eV}$ in different redshift bins. We developed a framework to quantify the detectability of massive neutrinos for different triangle configurations and shapes, and applied it to a case compatible with a stage-IV spectroscopic survey. We also compared our results with the analysis of simulations without neutrinos, but with different $\sigma_8$ values, to test whether the 3PCF can break the well-known degeneracy between the two parameters. We found that as a result of free-streaming, the strongest signal is found for quasi-isosceles and squeezed triangles; this signal increases for decreasing redshifts. Among these configurations, elongated triangles, tracing the filamentary structure of the cosmic web, are the most affected by massive neutrinos, with a 3PCF signal increasing with $M_\nu$. A complementary source of signal comes from right-angled triangles in $Q$. Importantly, we found that the signatures of a $\sigma_8$ variation appear to be significantly different on elongated triangles in $\zeta$ and right-angled triangles in $Q$, suggesting that the 3PCF can be used to effectively break the $M_\nu - \sigma_8$ degeneracy. These results open the possibility to use the 3PCF as a powerful complementary tool for constraining neutrino masses in current and future spectroscopic surveys such as DESI, Euclid, 4MOST, and the Nancy Grace Roman Space Telescope.