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We have applied the extended factorization scheme to investigate theelectroweak pion production on nuclei. The ANL-Osaka model, which was obtainedby analyzing the data of $\pi N$, $\gamma N$, $N(e,e'\pi)$ and $N(\nu,\mu\,\pi)$ reactions up to invariant mass $W=$ 2 GeV, is used to generate the matrixelements of current operators relevant to pion-production off the nucleon.Medium effects on the $\Delta$ (1232) component of meson-exchange current areincluded by using a $\Delta$-nucleus potential determined from the previous$\Delta$-hole model studies of pion-nucleus reactions. Nuclear correlations inthe initial target state and in the spectator system(s) are modeled usingrealistic hole spectral functions. As a first step, we show that the data of$^{12}$C$(e,e')$ up to the $\Delta$ (1232) region can be described reasonablywell. The interplay between the pion production and two-body meson-exchangemechanisms is shown to be essential in improving the agreement with the data inthe ``dip'' region, between the quasielastic and the $\Delta$ (1232) peaks.Predictions for $^{12}$C$(\nu,\mu\,\pi)$ have also been made. They can be usedto estimate pion-emission rates in neutrino-nucleus cross section, whichconstitutes an important systematic uncertainty to the reconstructed neutrinoenergy. With further improvements of the Metropolis Monte-Carlo techniques toaccount for final states comprised of more than two particles, our approach canbe employed up to $W=$ 2 GeV, where two-pion production and higher mass nucleonresonances must be included for analyzing the data from accelerator-basedneutrino-oscillation experiments.

Electroweak pion-production on nuclei within the extended factorization scheme