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In chiral effective field theory the leading order (LO) nucleon-nucleonpotential includes two contact terms, in the two spin channels $S=0,1$, and theone-pion-exchange potential. When the pion degrees of freedom are integratedout, as in the pionless effective field theory, the LO potential includes twocontact terms only. In the three-nucleon system, the pionless theory includes athree-nucleon contact term interaction at LO whereas the chiral effectivetheory does not. Accordingly arbitrary differences could be observed in the LOdescription of three- and four-nucleon binding energies. We analyze the twotheories at LO and conclude that a three-nucleon contact term is necessary atthis order in both theories. In turn this implies that subleading three-nucleoncontact terms should be promoted to lower orders. Furthermore this analysisshows that one single low energy constant might be sufficient to explain thelarge values of the singlet and triplet scattering lengths.

Implications of Efimov physics for the description of three and four nucleons in chiral effective field theory