First Observation of Coherent $pi^0$ Production in Neutrino Nucleus Interactions with $E_{ u}<$ 2 GeV

The MiniBooNE experiment at Fermilab has amassed the largest sample to date of $pi^0$s produced in neutral current (NC) neutrino-nucleus interactions at low energy. This paper reports a measurement of the momentum distribution of $pi^0$s produced in mineral oil (CH$_2$) and the first observation of coherent $pi^0$ production below 2 GeV. In the forward direction, the yield of events observed above the expectation for resonant production is attributed primarily to coherent production off carbon, but may also include a small contribution from diffractive production on hydrogen. Integrated over the MiniBooNE neutrino flux, the sum of the NC coherent and diffractive modes is found to be (19.5 $pm$1.1 (stat) $pm$2.5 (sys))% of all exclusive NC $pi^0$ production at MiniBooNE. These measurements are of immediate utility because they quantify an important background to MiniBooNEs search for $ u_{mu} to u_e$ oscillations.