  We have studied the strangeness changing antineutrino induced reactions
$\bar{\nu}_{l} p \rightarrow l^+ \phi B $, with $\phi B = K^-p$, $\bar{K}^0n$,
$\pi^0\Lambda$, $\pi^0\Sigma^0$, $\eta\Lambda$, $\eta\Sigma^0$,
$\pi^+\Sigma^-$, $\pi^-\Sigma^+$, $K^+\Xi^-$ and $K^0\Xi^0$, using a chiral
unitary approach. These ten coupled channels are allowed to interact strongly,
using a kernel derived from the chiral Lagrangians. This interaction generates
two $\Lambda(1405)$ poles, leading to a clear single peak in the $\pi \Sigma$
invariant mass distributions. At backward scattering angles in the center of
mass frame, $\bar{\nu}_{\mu} p \rightarrow \mu^+ \pi^0 \Sigma^0$ is dominated
by the $\Lambda(1405)$ state at around 1420~MeV while the lighter state becomes
relevant as the angle decreases, leading to an asymmetric line shape. In
addition, there are substantial differences in the shape of $\pi \Sigma$
invariant mass distributions for the three charge channels. If observed, these
differences would provide valuable information on a claimed isospin I=1,
strangeness S=-1 baryonic state around 1400 MeV. Integrated cross sections have
been obtained for the $\pi \Sigma$ and $\bar K N$ channels, investigating the
impact of unitarization in the results. The number of events with
$\Lambda(1405)$ excitation in $\bar\nu_\mu p$ collisions in the recent
antineutrino run at the MINERvA experiment has also been obtained. We find that
this reaction channel is relevant enough to be investigated experimentally and
to be taken into account in the simulation models of future experiments with
antineutrino beams.
