doublet n − d scattering length for some values of the parameters. The a -term gives a very small contribution to these quantities, therefore, in the following analysis we maintain it fixed at the value a = − 0 . 87 m − 1 π . The analysis is shown in Fig. 2. In the left panel, the doublet n − d scattering length, $^{2}$a$_{nd}$ , is given as a function of the parameter b (in units of its original value b 0 = − 2 . 58 m − 3 π ) for different values of the cutoff Λ (in units of m$_{π}$ ). The box in the figure includes those values of $^{2}$a$_{nd}$ compatible with the experimental results. On each point of the curves, the value of the constant d has been varied to reproduce the triton binding energy. Its corresponding values (in units of its original value d 0 = − 0 . 753 m − 3 π ) are given in the right panel as a function of b . Therefore, each point of the curves in both panels corresponds to a set of parameters that, in connection with the AV18 potential, reproduces the triton binding energy. The variations of the parameters given in Fig. 2 do not exhaust all the possibilities. The analysis has been done maintaining the attractive character of the b - and d -terms and, therefore, the lines in the left panels of the figure stop when one of the two parameters, b or d changes sign. We can observe that, with the AV18+TM’ potential, there is a very small region in the parameters’ phase space available for a simultaneous description of the triton binding energy and the doublet scattering length. This small region corresponds to a value of b around four times bigger than the original value b 0 and d results to be almost zero. Moreover, the value of the cutoff Λ around 3 . 8 m$_{π}$ is smaller than the values usually used with the TM’ potential (Λ ≈ 5 m$_{π}$ ). 

To be noticed that, for negative values of the parameters a , b and d , the TM’ potential is attractive and it does not include explicitly a repulsive term. Added to a specific NN potential that underestimates the three-nucleon binding energy, it supplies the extra binding by fixing appropriately its strength. As mentioned in Sec. I, the scattering length is sensitive to the balance between the attractive part and the repulsive part of the complete interaction. Therefore, in the case of the TM’ potential, it seems that introducing only attractive terms, fixed to reproduce the triton binding energy, it is difficult to reproduce correctly this balance. 

As discussed before, the TM’ potential is a modification of the original TM potential compatible with chiral symmetry. At next-to-next-to-leading order in the chiral effective field theory the D - and E -terms appear (see Ref. [9] and references therein) as given in Eq.(2). Here we introduce the following additional term to the TM’ potential based on a 

