I. INTRODUCTION Realistic nucleon-nucleon (NN) potentials reproduce the experimental NN scattering data up to energies of 350 MeV with a χ 2 per datum close to 1. However, the use of these potentials in the description of the three- and four-nucleon bound and scattering states gives a χ 2 per datum much larger than 1 (see for example Ref. [1]). In order to improve that situation, different three-nucleon force (TNF) models have been introduced so far. Widely used in the literature are the Tucson-Melbourne (TM) and the Urbana IX (URIX) models [2, 3]. These models are based on the exchange mechanism of two pions between three nucleons. The TM model has been revisited within a chiral symmetry approach [4], and it has been demonstrated that the contact term present in it should be dropped. This new TM potential, known as TM’, has been subsequently readjusted [5]. The final operatorial structure coincides with that one given in the TNF of Brazil already derived many years ago [6]. TNF models based on πρ and ρρ meson exchange mechanisms have also been derived [7] and their effects have been studied in the triton binding energy [8]. More recently, TNFs have been derived [9] using a chiral effective field theory at next-to-next-to-leading order. A local version of these interactions (hereafter referred as N2LOL) can be found in Ref. [10]. At this particular order, the TNF has two unknown constants that have to be determined. More in general, all the models contain a certain number of parameters that fix the strength of the different terms that compose the interaction. It is a common practice to determine these parameters from the three- and four-nucleon binding energies. In the chiral effective field theory there is a consistent derivation of the two- and three- nucleon interactions and some of the low energy constants entering in the TNF are fixed already from the NN data. On the other hand, the parametrization of the TM’ and URIX interactions have been determined in association with specific NN potentials. Therefore, their parametrizations could change when used with different NN potentials since different NN potentials predict different A = 3 , 4 binding energies. The n − d doublet scattering length $^{2}$a$_{nd}$ can give valuable information. In principle this quantity is correlated, to some extent, to the A = 3 binding energy through the so- called Phillips line [11, 12]. However the presence of TNFs of the type studied here breaks this correlation. Therefore $^{2}$a$_{nd}$ emerges as an independent observable that can be used to evaluate the capability of the interaction models to describe the low energy region. Due 2