Measurement of ${\nu }_{\mu }$-induced charged-current neutral pion production cross sections on mineral oil at $E_{\nu }\in 0.5–2.0\mathrm{GeV}$

Using a custom 3-Čerenkov ring fitter, we report cross sections for ${\nu }_{\mu }$-induced charged-current single ${\pi }^0$ production on mineral oil (${\mathrm{CH}}_2$) from a sample of 5810 candidate events with 57% signal purity over an energy range of 0.5–2.0 GeV. This includes measurements of the absolute total cross section as a function of neutrino energy, and flux-averaged differential cross sections measured in terms of $Q^2$, ${\mu }^{-}$ kinematics, and ${\pi }^0$ kinematics. The sample yields a flux-averaged total cross section of $(9.2\pm {0.3}_{\mathrm{stat}}\pm {1.5}_{\mathrm{syst}})\times {10}^{-39}{\mathrm{cm}}^2/{\mathrm{CH}}_2$ at mean neutrino energy of 0.965 GeV.

Figure 1

Top: Fractional Gaussian resolutions as functions of $T_{\mu }$ (solid) and $|{\mathbf{p}}_{{\pi }^0}|c$ (dashed). Bottom: Angular resolutions as functions of $\cos {\theta }_{\mu }$ (solid) and $\cos {\theta }_{{\pi }^0}$ (dashed). The resolutions between each particle type are also correlated.

Figure 2

The one-track fit likelihood ratio vs. vs the one-track muon fit kinetic energy. A separation of CCQE events (red “o”) relative to $\mathrm{CC}{\pi }^0$ events (grey “x”) is performed by selecting events below the black line. For clarity, the events plotted are prescaled by 1000 and 100 for CCQE and $\mathrm{CC}{\pi }^0$, respectively. The cut is optimized on the full non-prescaled MC sample.

Figure 3

The smallest angle between two of the three reconstructed tracks. Displayed are the data (with statistical errors), total MC (solid), identified ${\mu }^{-}$ (dashed), and mis-IDed ${\mu }^{-}$ (dotted). The cut selects events above 0.6 radians.

Figure 4

The logarithm of the ratio of the observable $\mathrm{CC}{\pi }^0$ fit likelihood to a generic three-track fit. Displayed are the data (with statistical errors), total MC (solid), observable $\mathrm{CC}{\pi }^0$ (dashed), backgrounds with a ${\pi }^0$ in the final state or produced after the event (dotted), and backgrounds with no ${\pi }^0$ (dot-dashed). The cut selects events above 0.06.

Figure 5

The reconstructed $\gamma \gamma$ mass. Displayed are the data (with statistical errors), total MC (solid), observable $\mathrm{CC}{\pi }^0$ (dashed), backgrounds with a ${\pi }^0$ in the final state or produced after the event (dotted), and backgrounds with no ${\pi }^0$ (dot-dashed). The vertical dotted line is the known ${\pi }^0$ mass.

Figure 6

The ratio of the measured observable $\mathrm{CC}{\pi }^{+}$ cross section to the Nuance prediction. The ratio is plotted as a function of $T_{{\pi }^{+}}$ and $E_{\nu }$.

Figure 7

The predicted ${\nu }_{\mu }$ flux with systematic uncertainties over the range 0.5–2.0 GeV. A table containing the values of the flux, along with a full-correlation matrix, is provided in Table. 5 of the Appendix.

Figure 8

The total observable $\mathrm{CC}{\pi }^0$ cross section as a function of neutrino energy. The uncertainty is dominated by ${\pi }^{+}$ charge-exchange and absorption in the mineral oil external the target nucleus. The total systematic uncertainty on the cross section is 18.7%. The central-value measurement, uncertainties, and correlation matrix are tabulated in Table 6 of the Appendix.

Figure 9

The flux-averaged ($0.5<E_{\nu }<2.0\mathrm{GeV}$) differential cross section in $Q^2$ with total systematic uncertainty of 16.6%. The central-value measurement, uncertainties, and correlation matrix are tabulated in Table 7 of the Appendix.

Figure 10

The flux-averaged ($0.5<E_{\nu }<2.0\mathrm{GeV}$) differential cross section in $E_{\mu }$ with total systematic uncertainty of 15.8%. The central-value measurement, uncertainties, and correlation matrix are tabulated in Table 8 of the Appendix.

Figure 11

The flux-averaged ($0.5<E_{\nu }<2.0\mathrm{GeV}$) differential cross section in $\cos {\theta }_{\mu }$ with total systematic uncertainty of 17.4%. The central-value measurement, uncertainties, and correlation matrix are tabulated in Table 9 of the Appendix.

Figure 12

The flux-averaged ($0.5<E_{\nu }<2.0\mathrm{GeV}$) differential cross section in $|{\mathbf{p}}_{{\pi }^0}|$ with total systematic uncertainty of 15.9%. The central-value measurement, uncertainties, and correlation matrix are tabulated in Table 10 of the Appendix.

Figure 13

The flux-averaged ($0.5<E_{\nu }<2.0\mathrm{GeV}$) differential cross section in $\cos {\theta }_{{\pi }^0}$ with total systematic uncertainty of 16.3%. The central-value measurement, uncertainties, and correlation matrix are tabulated in Table 11 of the Appendix.

Figure 14

Invariant mass of the hadronic system for both data (points with error bars) and the MC prediction (solid line) for the signal mode. The dotted line indicates the location of the $\Delta (1232)$ resonance.