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Model-independent constraints for the neutron-triton and proton-Helium-3scattering lengths are calculated with a leading-order interaction derived froman effective field theory without explicit pions. Using the singletneutron-proton scattering length, the deuteron, and the triton binding energyas input, the predictions $\ants=9.2\pm2.6 $fm, $\antt=7.6\pm1.6 $fm,$\aphes=3.6\pm0.32 $fm, and $\aphet=3.1\pm 0.23 $fm are obtained. Thecalculations employ the resonating group method and include the Coulombinteraction when appropriate. The theoretical uncertainty is assessed via avariation of the regulator parameter of the short-distance interaction from$400 $MeV to $1.6 $GeV. The phase-shift and scattering-length results for theproton-Helium-3 system are consistent with a recent phase shift analysis andwith model calculations. For neutron-triton, the results for the scatteringlengths in both singlet and triplet channels are significantly smaller thansuggested by R-matrix and partial-wave-analysis extractions from data. For abetter understanding of this discrepancy, the sensitivity of the low-energyfour-body scattering system to variations in the neutron-neutron andproton-proton two-nucleon scattering lengths is calculated. Induced by strongcharge-symmetry-breaking contact interactions, this dependence is foundinsignificant. In contrast, a strong correlation between the neutron-tritonscattering length and the triton binding energy analogous to the Phillips lineis found.

Zero-energy neutron-triton and proton-Helium-3 scattering with \eftnopi