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The one-point probability distribution function (PDF) is a powerful summarystatistic for non-Gaussian cosmological fields, such as the weak lensing (WL)convergence reconstructed from galaxy shapes or cosmic microwave background(CMB) maps. Thus far, no analytic model has been developed that successfullydescribes the high-convergence tail of the WL convergence PDF for smallsmoothing scales from first principles. Here, we present a halo-model formalismto compute the WL convergence PDF, building upon our previous results for thethermal Sunyaev-Zel'dovich field. Furthermore, we extend our formalism toanalytically compute the covariance matrix of the convergence PDF. Comparisonsto numerical simulations generally confirm the validity of our formalism in thenon-Gaussian, positive tail of the WL convergence PDF, but also reveal theconvergence PDF's strong sensitivity to small-scale systematic effects in thesimulations (e.g., due to finite resolution). Finally, we present a simpleFisher forecast for a Rubin-Observatory-like survey, based on our new analyticmodel. Considering the $\{A_s, \Omega_m, \Sigma m_\nu\}$ parameter space andassuming a Planck CMB prior on $A_s$ only, we forecast a marginalizedconstraint $\sigma(\Sigma m_\nu) \approx 0.08$ eV from the WL convergence PDFalone, even after marginalizing over parameters describing the haloconcentration-mass relation. This error bar on the neutrino mass sum iscomparable to the minimum value allowed in the normal hierarchy, illustratingthe strong constraining power of the WL convergence PDF. We make our codepublicly available at https://github.com/leanderthiele/hmpdf.

Accurate Analytic Model for the Weak Lensing Convergence One-Point Probability Distribution Function and its Auto-Covariance