  We propose a new high-resolution neutrino experiment within a dipole magnetic
field, HiResM$\nu$. This experiment will run along with long-baseline neutrino
oscillation experiments (LBL$\nu$) such as NO$\nu$A, a large-cavity detector at
DUSEL, or a Liquid-Argon detector in the Medium-Energy (ME) configuration of
the NuMI-beam. Assuming the 120 GeV Main Injector proton intensities we
anticipate 140(50) million $\nu_\mu$ ($\overline{\nu}_\mu$) Charged-Current
(CC) events in the fiducial volume, for 3(4)-year run with the ME
(anti)neutrino beam. Alternatively, the same statistics could be collected in
just 1(1.5) year with the High Energy (HE) beam configuration. The goals of
HiResM$\nu$ are twofold. It will measure the relative abundance and the energy
spectrum of $\nu_\mu$, $\overline{\nu}_\mu$, $\nu_e$ and $\overline{\nu}_e$
CC-interactions, which are directly relevant to LBL$\nu$. It will serve as an
`Event-Generator' of real neutrino interactions to estimate backgrounds and
efficiencies in LBL$\nu$. As such, it will provide a quantitative determination
of the overall energy-scale of neutrino CC interactions and of hadronic
multiplicities for all CC and Neutral-Current (NC) event topologies. In
addition, it will perform precise measurements of electroweak parameters, of
(semi)exclusive processes such as quasi-elastic, resonance, $\pi^0$ / $K^0_S$ /
$\Lambda$/charm-hadron production, as well as of the hadronic structure of
nucleons and nuclei. We expect to reach a sensitivity of about 0.2% on the weak
mixing angle by combining different channels. The new experiment will also
perform searches for new physics beyond the Standard Model.
