Test of the Charge Symmetry Hypothesis of NN Interaction from the Coulomb-Free p–p Scattering Cross Section and Its Relation to Universality

We examine the results on the determination of the Coulomb-free 1S0 proton–proton (p–p) scattering length by analyzing the cross section of the quasi-free p + d → p + p + n reaction at center-of-mass energies below 1 MeV. This was achieved using a Bayesian data-fitting approach, yielding a p–p scattering length app=-18.17-0.58+0.52|stat±0.01syst fm and effective range r0=2.80±0.05stat±0.001syst fm. We test the stability of the results against the upper energy cutoff and fitting data sets separately. A model based on the Eckart potential is introduced for an effective description in the universal window. In this model, the short-range interaction is considered as a whole, similar to how the s-wave phase-shift δ functions in describing low-energy nucleon–nucleon scattering data. Based on our analysis, we confirm that the obtained parameters accurately represent the characteristics of the short-range physics and the influence of the up-down quark mass difference on the charge symmetry breaking is less significant as initially anticipated. Additionally, we suggest evaluating the charge symmetry breaking of the short-range interaction rather than solely focusing on the nuclear interaction.