Measurement of ${\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }$ induced neutral current single ${\pi }^0$ production cross sections on mineral oil at $E_{\nu }\sim \mathcal{O}$ (1 GeV)

MiniBooNE reports the first absolute cross sections for neutral current single ${\pi }^0$ production on ${\mathrm{CH}}_2$ induced by neutrino and antineutrino interactions measured from the largest sets of NC ${\pi }^0$ events collected to date. The principal result consists of differential cross sections measured as functions of ${\pi }^0$ momentum and ${\pi }^0$ angle averaged over the neutrino flux at MiniBooNE. We find total cross sections of $(4.76\pm {0.05}_{\mathrm{stat}}\pm {0.76}_{\mathrm{sys}})\times {10}^{-40}{\mathrm{cm}}^2/\mathrm{\text{nucleon}}$ at a mean energy of $⟨E_{\nu }⟩=808\mathrm{MeV}$ and $(1.48\pm {0.05}_{\mathrm{stat}}\pm {0.23}_{\mathrm{sys}})\times {10}^{-40}{\mathrm{cm}}^2/\mathrm{\text{nucleon}}$ at a mean energy of $⟨E_{\nu }⟩=664\mathrm{MeV}$ for ${\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }$ induced production, respectively. In addition, we have included measurements of the neutrino and antineutrino total cross sections for incoherent exclusive NC $1{\pi }^0$ production corrected for the effects of final state interactions to compare to prior results.

Figure 1

(a) Distribution of the difference between the $e$ log-likelihood and the $\mu$ log-likelihood for events passing cuts (1)–(4) described in the text for neutrino mode running (top) and antineutrino mode running (bottom). Monte Carlo is depicted by a dark-gray line and data by black dots. Both data and Monte Carlo are absolutely normalized to ${10}^{20}$ POT. Error bars are statistical only. Also shown are the contributions from events containing no ${\pi }^0$ in the detector (translucent light-gray fill), signal NC $1{\pi }^0$ production (dark-gray fill), and incoherent (hatched fill) and coherent (gray fill) exclusive NC $1{\pi }^0$ production according to identification at the neutrino interaction vertex. Candidate NC $1{\pi }^0$ events are selected in the region indicated by the arrows. (b) Distribution of the reconstructed $\gamma \mathrm{\text{−}}\gamma$ invariant mass for events passing cuts (1)–(6) described in the text. The dashed vertical line marks the expected ${\pi }^0$ mass.

Figure 2

(a) The distribution of the reconstructed energy of the more energetic $\gamma$ from the ${\pi }^0$ decay in NC $1{\pi }^0$ candidates from Monte Carlo (dark-gray line) and data (black dots). Results from neutrino mode running appear on the top and antineutrino mode running on the bottom. Error bars are statistical only and distributions are absolutely normalized to ${10}^{20}$ POT. (b) The reconstructed energy of the less energetic $\gamma$. (c) The reconstructed opening angle between the two photons. (d) The reconstructed total momentum in the beam direction.

Figure 3

(a) The reconstructed ${\pi }^0$ momentum distribution for NC $1{\pi }^0$ candidates in neutrino mode running. The Monte Carlo distribution is shown as a dark-gray line and data as black dots. The box histogram is the systematic error on the Monte Carlo distribution; the error bars on the data are statistical only. Distributions are absolutely normalized to ${10}^{20}$ POT. The black filled histogram is the non-NC $1{\pi }^0$ background and the hatched histogram above is the additional contribution from wrong-sign induced NC $1{\pi }^0$ production. (b) The reconstructed ${\pi }^0$ angle distribution in neutrino mode running. (c) The reconstructed ${\pi }^0$ momentum distribution in antineutrino mode running. (d) The reconstructed ${\pi }^0$ angle distribution in antineutrino mode running.

Figure 4

(a) Response matrix for the measurement of ${\pi }^0$ momentum in NC $1{\pi }^0$ events satisfying selection cuts in neutrino mode. (b) The same for ${\pi }^0$ angle in neutrino mode. (c) The same for ${\pi }^0$ momentum in antineutrino mode. (d) The same for ${\pi }^0$ angle in antineutrino mode.

Figure 5

(a) NC $1{\pi }^0$ selection efficiency (solid line) and fractional decrease in the number of events in the fiducial volume when using the true vertex versus the reconstructed vertex (dashed line) as functions of ${\pi }^0$ momentum in neutrino mode. (b) The same for ${\pi }^0$ angle in neutrino mode. (c) The same for ${\pi }^0$ momentum in antineutrino mode. (d) The same for ${\pi }^0$ angle in antineutrino mode.

Figure 6

The predicted flux of ${\nu }_{\mu }$ (solid lines) and ${\overline{\nu }}_{\mu }$ (dotted lines) at the MiniBooNE detector with the horn configured in neutrino mode (black lines) and antineutrino mode (gray lines). The flux prediction is available at the MiniBooNE website [43].

Figure 7

Flux-averaged absolute differential cross sections for NC $1{\pi }^0$ production on ${\mathrm{CH}}_2$ including the effects of FSI. Data are shown as black dots with statistical error bars and systematic error boxes. The dark-gray line is the Monte Carlo prediction [34] using R-S models of single pion production [2, 5] modified as described in the text. (a) $\frac{d\sigma }{d{p}_{{\pi }^0}}$ for ${\nu }_{\mu }$-induced production. (b) $\frac{d\sigma }{d\cos {\theta }_{{\pi }^0}}$ for ${\nu }_{\mu }$-induced production. (c) $\frac{d\sigma }{d{p}_{{\pi }^0}}$ for ${\overline{\nu }}_{\mu }$-induced production. (d) $\frac{d\sigma }{d\cos {\theta }_{{\pi }^0}}$ for ${\overline{\nu }}_{\mu }$-induced production. The numerical values for the cross sections appear in Appendix 3 and are also available at the MiniBooNE website [44].

Figure 8

(a) The differential cross section for inclusive NC $1{\pi }^0$ production as a function of ${\pi }^0$ angle in neutrino mode (above) and antineutrino mode (below). Data is indicated by black dots with statistical error bars and systematic error boxes. The Monte Carlo prediction including the R-S single pion production models [2, 5] as implemented in Nuance adjusted according to [36] is indicated by the thick black line. The prediction omitting the coherent portion of NC ${\pi }^0$ production is indicated by the dashed black line. The arrow indicates the region for which a ${\chi }^2$ is quoted in the text. The horizontal scale is magnified in the forward region.

Figure 9

(a) The flux-averaged total cross sections for ${\nu }_{\mu }$-induced incoherent exclusive NC $1{\pi }^0$ production on ${\mathrm{CH}}_2$ corrected for FSI. Points 1, 2, and 3, are the cross sections extracted using the MiniBooNE implementation of the R-S model for coherent pion production, the model in [4], and the model in [3], respectively. The points are placed at the mean energy of the beam in neutrino mode; the spread is only for clarity. The curve is the Nuance prediction using the R-S model. Also shown for comparison is the measurement made from the Gargamelle data [24]. The Gargamelle experiment used a propane and freon $({\mathrm{C}}_3{\mathrm{H}}_8+\mathrm{C}{\mathrm{F}}_3\mathrm{Br})$ target. (b) The same for ${\overline{\nu }}_{\mu }$-induced incoherent exclusive NC $1{\pi }^0$ production. In this case, there are no external measurements to compare to.

Figure 10

Pion angular distributions in the forward region for NC $1{\pi }^0$ candidates in (a) neutrino and (b) antineutrino mode running. Data is indicated by black dots with statistical error bars. The Monte Carlo prediction using the rescaled [36] R-S model of coherent pion production as implemented in Nuance [2, 34] is indicated by the solid black line with gray systematic error boxes. The predictions using the models of [3, 4] are indicated by the dotted line and the dashed line, respectively. The systematic error in the predictions using the alternative models is of the same relative size as the prediction using R-S; it is omitted for clarity. Distributions are normalized to ${10}^{20}$ POT. (b) The same for antineutrino mode.

Figure 11

(a) The ratio of the ${\nu }_{\mu }$ NC $1{\pi }^0$ angular cross section extracted using the coherent production models in [4] (dotted line) and [3] (dashed line) compared to the principal result extracted using the R-S model. (b) The same for the ${\overline{\nu }}_{\mu }$ NC $1{\pi }^0$ cross section.

Figure 12

Flux-averaged absolute differential cross sections for ${\nu }_{\mu }+{\overline{\nu }}_{\mu }$-induced NC $1{\pi }^0$ production on ${\mathrm{CH}}_2$. Data are shown as black dots with statistical error bars and systematic error boxes. The dark-gray line is the Monte Carlo [34] prediction using R-S models of single pion production [2, 5] modified as described in the text. (a) $\frac{d\sigma }{d{p}_{{\pi }^0}}$ in neutrino mode. (b) $\frac{d\sigma }{d\cos {\theta }_{{\pi }^0}}$ in neutrino mode. (c) $\frac{d\sigma }{d{p}_{{\pi }^0}}$ in antineutrino mode. (d) $\frac{d\sigma }{d\cos {\theta }_{{\pi }^0}}$ in antineutrino mode.