One pion production in neutrino reactions: including non-resonant background

We investigate neutrino induced one pion production on nucleons. The elementary neutrino--nucleon cross section is calculated as the sum of the leading Delta pole diagram and several background diagrams obtained within the non-linear sigma model. This approach does not introduce any new adjustable parameters, which allows unambiguous predictions for the observables. Considering electroproduction experiments as benchmark, the model is shown to be applicable up to pion-nucleon invariant mass $W<1.4\GeV$ and provides a good accuracy. With respect to the total one pion cross section, the model predicts the background at the level of $=10% for the $p\pi^+$, 30% for $p\pi^0$ and 50% for $n\pi^+$ final states. The results are compared with experimental data for various differential cross sections. Distributions with respect to muon-nucleon and muon-pion invariant masses are presented for the first time. The model describes the data quite well, with the discrepancies being of the same order as those between different data sets.