Constraining neutrino mass with the tomographic weak lensing one-point probability distribution function and power spectrum

We study the constraints on neutrino mass sum (M_nu) from the one-point probability distribution function (PDF) and power spectrum of weak lensing measurements for an LSST-like survey, using the MassiveNuS simulations. The PDF provides access to non-Gaussian information beyond the power spectrum. It is particularly sensitive to nonlinear growth on small scales, where massive neutrinos also have the largest effect. We find that tomography helps improve the constraint on M_nu by 14% and 32% for the power spectrum and the PDF, respectively, compared to a single redshift bin. The PDF alone outperforms the power spectrum in constraining M_nu. When the two statistics are combined, the constraint is further tightened by 35%. We conclude that weak lensing PDF is complementary to the power spectrum and has the potential to become a powerful tool for constraining neutrino mass.