A non-conventional neutrino beamline for the measurement of the electron neutrino cross section

Absolute neutrino cross section measurements at the GeV scale are ultimately limited by the knowledge of the initial $\nu$ flux. In order to evade such limitation and reach the accuracy that is needed for precision oscillation physics ($\sim 1$%), substantial advances in flux measurement techniques are requested. We discuss here the possibility of instrumenting the decay tunnel to identify large-angle positrons and monitor $\nu_e$ production from $K^+ \rightarrow e^+ \nu_e \pi^0$ decays. This non conventional technique opens up opportunities to measure the $\nu_e$ CC cross section at the per cent level in the energy range of interest for DUNE/HK. We discuss the progress in the simulation of the facility (beamline and instrumentation) and the ongoing R&D.