The ratio of $γ/ π^0$ production rates in neutrino-nucleus interactions at the $Δ$ resonance mass region
We study the dependence of neutrino-induced $γ/π^0$ production ($\stackrel{ {(-)}}{ν_μ} + A \to \stackrel{ {(-)}}{ν_μ}(μ) +γ/π^0 + X$) on the target nucleus A, at the $Δ$ resonance mass region. Our conclusion is based on experimental data for $π^0$ production rates at photon-nucleus interactions from the A2 collaboration at the Mainz MAMI accelerator. We assume that $Δ$ resonance decays are independent of the production mechanism (via photon, Z, or W boson). In Neutral Current (NC) interactions, the $1π^0 + X$ production scales as A$^{2/3}$. In contrast, photons from $Δ$ decays typically escape the nucleus, resulting in a cross-section proportional to the atomic number A. Thus, in NC interactions, the ratio of $γ$ production to $π^0$ production is proportional to A$^{1/3}$. In Charged Current (CC) $ν_μ$($\bar ν_μ$) -induced production of $Δ^+$ ($Δ^0$) will be proportional to the number of neutrons (protons) in the nucleus. After $Δ$ decay, due to the charge universality in strong interactions, the suppression factor for $π^0$ escaping the nucleus must also follow A$^{-1/3}$, as in NC interactions. We predict the ratio of the $γ/ π^0$ production rates in NC and CC interactions and for $ν_μ$ and $\bar ν_μ$ beams: {Argon target}: $\sim$3.1\% (NC/CC $ν_μ/\bar ν_μ$). {\bf Water target}: $\sim$1.9\% (NC), $\sim$2.3\% (CC $ν_μ$), $\sim$1.7\% (CC $\bar ν_μ$). {Liquid Scintillator target}: $\sim$1.7\% (NC), $\sim$2.1\% (CC $ν_μ$), $\sim$1.6\% (CC $\bar ν_μ$). We also discuss solving the MiniBooNE anomaly by looking at the CC single photon and single neutral pion production rates at the SBN program experiments at Fermilab.