Antineutrino induced Lambda(1405) production off the proton

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.