Statistical analysis of the nuclear three-body problem

The quantum three-nucleon problem represents a fundamental benchmark in nuclear few-body physics as it provides a direct test of how two-nucleon interactions propagate into three- body observables. In this thesis, the triton binding energy has been studied by solving the homogeneous Faddeev equations in momentum space, with the goal of understanding both numerical stability aspects and the sensitivity of the result to model choices and NN interaction parameters. The work is organized in two main parts. First, the numerical framework has been validated using the phenomenological Malfliet-Tjon potential, allowing an assessment of the the triton binding energy under variations of the potential parameters. In the explored region the binding energy varies smoothly and no numerical instabilities are observed, providing a reliable benchmark for the subsequent analysis. The study has been then extended to chiral effective field theory NN interactions at different chiral orders and regulator cutoffs. A Bayesian approach has been adopted to treat the cutoff in a quantitative way: posterior distributions have been constructed from the agreement with the experimental triton binding energy, and model averaging is used to estimate the residual regulator dependence. The analysis shows a strong cutoff dependence at leading order (LO), which progressively reduces at higher orders. An investigation of the local sensitivity of the triton binding energy to contact low energy constants (LECs) has been also performed. At NLO, the response of the triton energy is correlated with specific components of the NN interaction. The impact of LEC variations on NN partial waves and phase shifts has been analyzed, showing that the dominant variations mainly affect low momentum P-wave channels, while S-wave channels remain constrained. This analysis highlights the limited flexibility of NN only adjustments and supports the need for genuine three-nucleon forces for a fully consistent description.