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Abstract S 0proton-proton (p -p ) scattering length relies heavily on numerous and distinct theoretical techniques to remove the Coulomb contribution. Here, it has been determined from the half-off-the-energy-shellp -p scattering cross section measured at center-of-mass energies below 1 MeV using the quasi-freep +d →p +p +n reaction. A Bayesian data-fitting approach using the expression of the s-wave nucleon-nucleon scattering cross section returned ap -p scattering length fm and effective range$${a}_{pp}=-18.1{7}_{-0.58}^{+0.52}{| }_{stat}\pm 0.0{1}_{syst}$$ r 0 = 2.80 ± 0.05s t a t ± 0.001s y s t fm. A model based on universality concepts has been developed to interpret this result. It accounts for the short-range interaction as a whole, nuclear and residual electromagnetic, according to what the s-wave phase-shiftδ does in the description of low-energy nucleon-nucleon scattering data. We conclude that our parameters are representative of the short-range physics and propose to assess the charge symmetry breaking of the short-range interaction instead of just the nuclear interaction. This is consistent with the current understanding that the charge dependence of nuclear forces is due to different masses of up-down quarks and their electromagnetic interactions. This achievement suggests that these properties have a lesser than expected impact in the context of the charge symmetry breaking.