We study the dependence of neutrino-induced $\gamma /{\pi }^0$ production ($\stackrel{(-)}{{\nu }_{\mu }}+A\to \stackrel{(-)}{{\nu }_{\mu }}(\mu )+\gamma /{\pi }^0+X$) on the target nucleus $A$, in the $\mathrm{\Delta }$ resonance mass region. Our conclusion is based on experimental data for ${\pi }^0$ production rates at photon-nucleus interactions from the A2 Collaboration at the Mainz MAMI accelerator. We assume that $\mathrm{\Delta }$ resonance decays are independent of the production mechanism (via photon, Z, or W boson). In neutral current (NC) interactions, the $1{\pi }^0+X$ production scales as $A^{2/3}$. In contrast, photons from $\mathrm{\Delta }$ decays typically escape the nucleus, resulting in a cross-section proportional to the atomic number $A$. Thus, in NC interactions, the ratio of $\gamma$ production to ${\pi }^0$ production is proportional to $A^{1/3}$. In charged current (CC) ${\nu }_{\mu }\text{−}$ (${\overline{\nu }}_{\mu }$)-induced production of ${\mathrm{\Delta }}^{+}$ (${\mathrm{\Delta }}^0$) will be proportional to the number of neutrons (protons) in the nucleus. After $\mathrm{\Delta }$ decay, due to the charge universality in strong interactions, the suppression factor for ${\pi }^0$ escaping the nucleus must also follow $A^{-1/3}$, as in NC interactions. We predict the ratio of the $\gamma /{\pi }^0$ production rates in NC and CC interactions and for ${\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }$ beams: argon target, $\sim 3.1\%$ (NC/CC ${\nu }_{\mu }/{\overline{\nu }}_{\mu }$); water target, $\sim 1.9\%$ (NC), $\sim 2.3\%$ (CC ${\nu }_{\mu }$), and $\sim 1.7\%$ (CC ${\overline{\nu }}_{\mu }$); liquid scintillator target: $\sim 1.7\%$ (NC), $\sim 2.1\%$ (CC ${\nu }_{\mu }$), and $\sim 1.6\%$ (CC ${\overline{\nu }}_{\mu }$). The accuracy of our predictions is limited due to uncertainties in the decay rate ${\mathrm{\Delta }}^{+/0}\to p/n+\gamma$ and the presence of other (minor) channels of neutrino-induced $\gamma /{\pi }^0$ production in the $\mathrm{\Delta }$ mass region. We also discuss solving the MiniBooNE anomaly by looking at the CC single-photon and single-neutral-pion production rates at the short baseline neutrino program experiments at Fermilab.

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• Particle interactions
• Phenomenology
• Hadrons
• Neutrinos
• Neutrino detection