  The $n+{}^3$H, $p+{}^3$He, $p+{}^3$H, and $n+{}^3$He elastic and charge
exchange reactions at low energies are studied by means of the hyperspherical
harmonic method. The considered nuclear Hamiltonians include modern two- and
three-nucleon interactions, in particular results are reported in case of
chiral two-nucleon potentials, with and without the inclusion of chiral
three-nucleon (3N) interactions. A detailed study of the convergence and
numerical stability of the method is presented. We have found that the effect
the 3N force is in general tiny except for $p+{}^3$H scattering below the
opening of the $n+{}^3$He channel. In such a case, the effect of 3N forces is
appreciable and a clear dependence on the cutoff used to regularize the
high-momentum tail of the interactions is observed. Such a dependence is
related to the presence of the poorly known sharp $0^+$ resonance, considered
to be the first excited state of ${}^4$He.
