  QCD matrix elements of axial and vector currents between nucleons are
required for the Monte Carlo reconstruction of the energy of neutrinos that are
detected in long baseline oscillation experiments in the quasi-elastic regime.
The cleanest approach for determining the axial matrix elements is lattice QCD.
However, the extraction of these from the corresponding correlation functions
is complicated by very large excited state contributions, that are related to
transitions from the nucleon to a nucleon-pion pair. In this pilot study with a
pion mass $m_\pi = 429~ \mathrm{MeV}$, we demonstrate for the first time that
these contributions can be removed by including five-(anti)quark operators into
the basis of interpolators used to create the nucleon. The same techniques will
be needed to compute transition matrix elements between the nucleon and
nucleon-pion scattering states that are relevant in the resonance production
regime.
