Measurement of Coherent Production of ${\pi }^{\pm }$ in Neutrino and Anti-Neutrino Beams on Carbon from $E_{\nu }$ of $1.5$ to $20$ GeV

Neutrino-induced coherent charged pion production on nuclei, ${}_{\mu }A\to {\mu }^{\pm }{\pi }^{\mp }A$ is a rare, inelastic interaction in which a small squared four-momentum $\mathrm{\mid }t\mathrm{\mid }$ is transferred to the recoil nucleus leaving it intact in the reaction. In the scintillator tracker of MINERvA, we remove events with evidence of particles from nuclear breakup and reconstruct $\mathrm{\mid }t\mathrm{\mid }$ from the final state pion and muon. We select low $\mathrm{\mid }t\mathrm{\mid }$ events to isolate a sample rich in coherent candidates. By selecting low $\mathrm{\mid }t\mathrm{\mid }$ events we produce a model-independent measurement of the differential cross section for coherent scattering of neutrinos and anti-neutrinos on carbon. We find poor agreement with the predicted kinematics in neutrino generators used by current oscillation experiments.