Neutrino-induced coherent $\pi^{+}$ production in C, CH, Fe and Pb at $\langle E_{\nu}\rangle \sim 6$ GeV

MINERvA has measured the $\nu_{\mu}$-induced coherent $\pi^{+}$ cross section simultaneously in hydrocarbon (CH), graphite (C), iron (Fe) and lead (Pb) targets using neutrinos from 2 to 20 GeV. The measurements exceed the predictions of the Rein-Sehgal and Berger-Sehgal PCAC based models at multi-GeV $\nu_{\mu}$ energies and at produced $\pi^{+}$ energies and angles, $E_{\pi}>1$ GeV and $\theta_{\pi}<10^{\circ}$. Measurements of the cross-section ratios of Fe and Pb relative to CH reveal the effective $A$-scaling to increase from an approximate $A^{1/3}$ scaling at few GeV to an $A^{2/3}$ scaling for $E_{\nu}>10$ GeV.