Measurement of ${\overline{\nu }}_{\mu }$ charged-current single ${\pi }^{-}$ production on hydrocarbon in the few-GeV region using MINERvA

The antineutrino scattering channel ${\overline{\nu }}_{\mu }\mathrm{CH}\to {\mu }^{+}{\pi }^{-}X$ (nucleon(s)) is analyzed in the incident energy range 1.5 to 10 GeV using the MINERvA detector at Fermilab. Differential cross sections are reported as functions of ${\mu }^{+}$ momentum and production angle, ${\pi }^{-}$ kinetic energy and production angle, and antineutrino energy and squared four-momentum transfer. Distribution shapes are generally reproduced by simulations based on the GENIE, NuWro, and GiBUU event generators, however GENIE (GiBUU) overestimates (underestimates) the cross section normalizations by 8% (10%). Comparisons of data with the GENIE-based reference simulation probe conventional treatments of cross sections and pion intranuclear rescattering. The distribution of nontrack vertex energy is used to decompose the signal sample into reaction categories, and cross sections are determined for the exclusive reactions ${\mu }^{+}{\pi }^{-}n$ and ${\mu }^{+}{\pi }^{-}p$. A similar treatment applied to the published MINERvA sample ${\overline{\nu }}_{\mu }\mathrm{CH}\to {\mu }^{+}{\pi }^{0}X$[nucleon(s)] has determined the ${\mu }^{+}{\pi }^{0}n$ cross section, and the latter is used with $\sigma ({\pi }^{-}n)$ and $\sigma ({\pi }^{-}p)$ to carry out an isospin decomposition of ${\overline{\nu }}_{\mu }$-induced $\mathrm{CC}(\pi )$. The ratio of magnitudes and relative phase for isospin amplitudes $A_3$ and $A_1$ thereby obtained are: $R^{\overline{\nu }}=0.99\pm 0.19$ and ${\varphi }^{\overline{\nu }}=93°\pm 7°$. Our results are in agreement with bubble chamber measurements made four decades ago.

Figure 1

Data candidates for signal channel (1). For each event, the ${\overline{\nu }}_{\mu }$ entered from the left and interacted within the central scintillator, yielding a ${\mu }^{+}$, a charged pion, originating from a primary vertex that is devoid of (upper panel) or else has (lower panel) additional ionization hits nearby. Horizontal and vertical axes show module and strip numbers, respectively. The right-side linear scale shows energy deposited in the strips.

Figure 2

Initial data distributions of the selected sample for ${\mu }^{+}$ and ${\pi }^{-}$ kinematic variables $p_{\mu }$, ${\theta }_{\mu }$ (upper plots) and $T_{\pi }$, ${\theta }_{\pi }$ (lower plots) compared to the reference MC predictions (histograms with systematics error band). The comparisons here are shown before constraining the background (lowermost gray-shade histogram) via sideband fitting, and prior to correcting the data for detector effects.

Figure 3

Muon and charged pion kinematic distributions for sideband data events (solid points with statistical error bars) compared to the reference simulation (histograms) prior to tuning. The MC describes the shape but slightly overestimates the rate of sideband data. Lower-component histograms (red) show the estimated background content of the sideband. Upper-component histograms (green) depict the signal contamination in the sideband.

Figure 4

Sideband sample distributions, MC vs data, for muon and pion kinematic variables (upper, lower plots respectively) prior to tuning of background and signal-contamination normalizations. The initial MC predictions and total systematic uncertainties are shown by the histograms and shaded error bands.

Figure 5

Sideband distributions, MC vs data, for muon and pion variables as in Fig. 4, plus distributions for $E_{\overline{\nu }}$ and $Q^2$. The MC predictions (histograms with error bands) are shown after the iterative fit of background and signal normalizations to seven kinematic distributions of the sideband and signal samples, and weight-adjusting the MC in 3 bins of $W_{\exp }$. (see main text).

Figure 6

Sideband distributions, MC vs data, for estimated hadronic mass $W_{\exp }$. Left-side plot shows sideband $W_{\exp }$ prior to any adjustment of the MC. Right-side plot the improved agreement of MC (histogram with error bands) with the data after fitting of normalizations and weighting of the MC rate through the peak ($1.2<W_{\exp }<1.5\mathrm{GeV}$).

Figure 7

Composition of fractional uncertainty in terms of systematic error categories plus the statistical uncertainty, for differential cross sections in ${\mu }^{+}$ momentum (upper plot) and ${\pi }^{-}$ kinetic energy (lower plot). The statistical uncertainty (short-dash-line histogram) is the leading error source in all bins, with detector response (fine-dash) and antineutrino flux (dot-dot-dash) uncertainties also contributing significantly.

Figure 8

Bin-by-bin fractional uncertainty in systematic error categories plus statistical uncertainty, for cross section as a function of $E_{\overline{\nu }}$. The flux and detector response uncertainties are comparable to the statistical uncertainty in the 2.0 to 6.0 GeV range of $E_{\overline{\nu }}$.

Figure 9

The flux-integrated muon-momentum differential cross section, $d\sigma /d{p}_{\mu }$ for muons with ${\theta }_{\mu }\le 25°$. Data (solid circles) are shown with inner (outer) error bars that denote the statistical (total) uncertainties. The solid-line (dashed) curves show GENIE predictions with (without) FSI. Short-dash and dot-dash curves show predictions by NuWro and GiBUU-2017. The estimated contribution from CC coherent scattering (4) is given by the shaded region.

Figure 10

Cross section $d\sigma /d{p}_{\mu }$ as in Fig. 9, compared to component reaction processes of the reference simulation. Production of $\mathrm{\Delta }(1232{)}^{-}$ is predicted to dominate the signal channel (gray-shade histogram) in all bins of muon momentum.

Figure 11

Differential cross section for muon production angle, $d\sigma /d{\theta }_{\mu }$. Data (solid circles) is compared to the predictions of GENIE with and without FSI (dashed, solid uppermost curves) and with predictions from NuWro and GiBUU-2017. The distribution shape is reproduced by all generators; NuWro comes closest with predicting the absolute event rate.

Figure 12

Differential cross section $d\sigma /d{T}_{{\pi }^{-}}$ for pion kinetic energy. Upper plot compares the data (solid points) to predictions by the GENIE-based MC, NuWro, and GiBUU-2017. Lower plot shows that GENIE achieves agreement with measured $d\sigma /d{T}_{{\pi }^{-}}$ by combining pion FSI processes that differ in their component shapes.

Figure 13

Differential cross section for pion production angle. Upper plot shows the data with predictions from the GENIE-based MC and from NuWro and GiBUU-2017. The gray-fill distribution depicts CC coherent scattering as measured by MINERvA. Although coherent scattering is included in all the generator predictions, the data rate into forward $<20°$ is underpredicted. Lower plot shows contributions to $d\sigma /d{\theta }_{{\pi }^{-}}$ from component pion FSI processes as estimated by the GENIE MC. Coherent scattering is included in “${\pi }^{-}$ noninteracting.”

Figure 14

Cross section (solid circles) as a function of antineutrino energy for channel (1). Upper plot compares the data to GENIE, NuWro, and GiBUU-2017 expectations. Lower plot shows contributions estimated by GENIE from coherent scattering, ${\mathrm{\Delta }}^{-}$ resonance production, ${\mathrm{N}}^{*}$ states above the $\mathrm{\Delta }$, and pion nonresonance processes.

Figure 15

Differential cross section $d\sigma /d{Q}^2$ for the signal channel. Upper plot: Predictions from the GENIE-based MC, NuWro, and GiBUU-2017 trend above, close to, and below the data respectively. Lower plot: Relative contributions from component processes according to GENIE. Coherent single-pion production is expected to contribute at very low $Q^2$.

Figure 16

Distribution of event vertex energy in the signal sample (solid circles), displayed using linear and log scales (upper, lower plots respectively). Reference MC predictions for contributions by reactions (2) and (3), labeled by their hadronic systems, are shown together with coherent scattering and background contributions. The coherent contribution is calculated from MINERvA measurement [8]; the background rate is constrained by sideband fitting, and the exclusive-reaction rates are tuned to fit the signal sample data.

Figure 17

Plot of the cross section ratios $R_2$ vs $R_1$ for selected ${\overline{\nu }}_{\mu }$ and ${\nu }_{\mu }$ data. Dashed lines denote constant values of $|A_1|/|A_3|$ and solid-line curves denote values of the relative phase. The MINERvA measurements (solid square), as with Gargamelle (not plotted; see Table 1) show that $A_1$ and $A_3$, averaged over a wide-band $\overline{\nu }$ flux, are of similar strength and devoid of interference. Results obtained with ${\nu }_{\mu }\text{−}\mathrm{CC}(\pi )$ reactions (open circles, from overlapping samples) indicate $|A_3|>|A_1|$ in neutrino samples at lower incident energies and lesser reach in $W$ [88].