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

MINERvA has measured the ${\nu }_{\mu }$-induced coherent ${\pi }^{+}$ cross section simultaneously in hydrocarbon (CH), graphite ©, 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 $A^{1\mathrm{/}3}$ scaling at few GeV to an $A^{2\mathrm{/}3}$ scaling for $E_{\nu }>10$ GeV.