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Correlations in light nuclei and their relation to fine tuning and uncertainty quantifications of many body forces in low-energy nuclear physics

The large nucleon-nucleon scattering length, and the isospin approximate symmetry, are low energy properties of quantum chromodynamics (QCD). These entail correlations in the binding energies of light nuclei, e.g., the A=3 iso-multiplet, and Tjon's correlation between the binding energy of three and four body nuclei. Using a new representation of these, we establish that they translate into a correlation between different short-range contributions to three body forces in chiral effective field theory of low-energy nuclear physics. We demonstrate that these correlations should be taken into account in order to avoid fine-tuning in the calibration of three body forces. We relate this to the role of correlations in uncertainty quantification of non-renormalizable effective field theories of the nuclear regime. In addition, we show that correlations can be useful in assessing the importance of forces induced by renormalization group (RG) transformations. We give numerical evidence that such RG transformations can be represented effectively by adding a constant to the pure three nucleon contact low energy constant $c_E$.