Information content in mean pairwise velocity and mean relative velocity between pairs in a triplet

Velocity field provides a complementary avenue to constrain cosmological information, either through the peculiar velocity surveys or kinetic Sunyaev Zel'dovich effect. One of commonly used statistics is mean radial pairwise velocity. Here, we consider three-point relative velocity, i.e. velocities between pairs in triplet. Using halo catalogs from Quijote suite N-body simulations, first showcase how analytical prediction for triplet achieve better than 4-5% accuracy using standard perturbation theory at leading order triangular configurations with minimum separation $r \geq 50\ h^{-1}$Mpc. Furthermore, present as novel probe neutrino mass estimation. We explore full information content velocities, and undertake this Fisher-matrix formalism 22,000 simulations suite, considering all maximum $20\ h^{-1}$Mpc $120\ h^{-1}$Mpc, respectively. find that allows 1$\sigma$ ($M_\nu$) constraint 0.065 eV, roughly 13 times (0.877 eV). This gain not limited only mass, but extends other parameters: $\Omega_{\mathrm{m}}$, $\Omega_{\mathrm{b}}$, $h$, $n_{\mathrm{s}}$ $\sigma_{8}$ achieving 8.9, 11.8, 15.5, 20.9 10.9 These results illustrate possibility exploiting constraining parameters accurately future cosmic microwave background experiments surveys.