The ratio of $\gamma /{\pi }^0$ production rates in neutrino-nucleus interactions at the $\Delta$ resonance mass region

Abstract

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, at the $\Delta$ 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 $\Delta$ 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 $\Delta$ 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) ${\nu }_{\mu }$(${\bar{\nu }}_{\mu }$) -induced production of ${\Delta }^{+}$ (${\Delta }^0$) will be proportional to the number of neutrons (protons) in the nucleus. After $\Delta$ 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 ${\bar{\nu }}_{\mu }$ beams: {Argon target}: $\sim$3.1\% (NC/CC ${\nu }_{\mu }/{\bar{\nu }}_{\mu }$). {\bf Water target}: $\sim$1.9\% (NC), $\sim$2.3\% (CC ${\nu }_{\mu }$), $\sim$1.7\% (CC ${\bar{\nu }}_{\mu }$). {Liquid Scintillator target}: $\sim$1.7\% (NC), $\sim$2.1\% (CC ${\nu }_{\mu }$), $\sim$1.6\% (CC ${\bar{\nu }}_{\mu }$). 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.

Comments: 3 pages, minor changes in the text