Zero-energy neutron-triton and proton-Helium-3 scattering with EFT(π)

Model-independent constraints for the neutron-triton and proton-Helium-3 scattering lengths are calculated with a leading-order interaction derived from an effective field theory without explicit pions. Using the singlet neutron-proton scattering length, the deuteron-, and triton binding energy as input, the predictions a(s) (t-n) = 9.2 +/- 2.6 fm, a(t)(t-n) = 7.6 +/- 1.6 fm, a(s)(C)(He-3-p) = 3.6 +/- 0.32 fm, and a(t)(C)(He-3-p) = 3.1 +/- 0.23 fm are obtained. The calculations employ the resonating group method and include the Coulomb interaction when appropriate. The theoretical uncertainty is assessed via a variation of the regulator parameter of the short-distance interaction from 400 MeV to 1.6 GeV. The phase-shift and scattering-length results for the proton-Helium-3 system are consistent with a recent phase shift analysis and with model calculations. For neutron-triton, the results for the scattering lengths in both singlet and triplet channels are significantly smaller than suggested by R-matrix and partial-wave-analysis extractions from data. For a better understanding of this discrepancy, the sensitivity of the low-energy four-body scattering system to variations in the neutron-neutron and proton-proton two-nucleon scattering lengths is calculated. Induced by strong charge-symmetry-breaking contact interactions, this dependence is found insignificant. In contrast, a strong correlation between the neutron-triton scattering length and the triton binding energy analogous to the Phillips line is found. (C) 2013 Elsevier B.V. All rights reserved.