A Standard Model explanation for the excess of electron-like events in MiniBooNE

We study the dependence of neutral current (NC) neutrino-induced $\pi^0$/photon production ($\nu_\mu + A \to \nu_\mu +1\pi^0 / \gamma + X$) on the atomic number of the target nucleus, A, at 4-momentum transfers relevant to the MiniBooNE experiment: $\Delta$ resonance mass region. Our conclusion is based on experimental data for photon-nucleus interactions from the A2 collaboration at the Mainz MAMI accelerator. We work in the approximation that decays of $\Delta$ resonance unaffected by its production channel, via photon or Z boson. $1\pi^0+X$ production scales as A$^{2/3}$, the surface area of the nucleus. Meanwhile the photons created in $\Delta$ decays will leave the nucleus, and that cross section will be proportional to the atomic number of the nucleus. Thus the ratio of photon production to $\pi^0$ production is proportional to A$^{1/3}$. For carbon $^{12}$C this factor is $\approx$2.3. MiniBooNE normalises the rate of photon production to the measured $\pi^0$ production rate. The reduced neutral pion production rate would yield at least twice as many photons as previously expected, thus significantly lowering the number of unexplained electron-like events.