Comparison of the Adler-Nussinov-Paschos model with the data for neutrino induced single pion production from the MiniBooNE and $\mathrm{MINER}\nu \mathrm{A}$ experiments

We present theoretical predictions in the framework of the ANP model for single pion production (${\pi }^{+},{\pi }^0$) in ${\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }$ scattering off mineral oil and plastic. Our results for the integrated cross sections and flux-averaged differential distributions are compared to all available data of the MiniBooNE and $\mathrm{MINER}\nu \mathrm{A}$ experiments. While our predictions slightly undershoot the MiniBooNE data, they reproduce the normalization of the $\mathrm{MINER}\nu \mathrm{A}$ data for the kinetic energy distribution. For the dependence on the polar angle, we reproduce the shape of the arbitrarily normalized data.

Figure 1

Cross section $d^2{V}^{\nu }/d{Q}^{2}dW$ for electroproduction in the $\mathrm{\Delta }$ resonance region in comparison with data from Galster et al. [22]. The solid, dot-dashed and dashed lines have been obtained with a running s-wave width, a running p-wave width, and a constant width, respectively. Also shown is the nonresonant background (dotted line). The resonant curves have been obtained using $C_3^V(0)=2.05$ and ${\mathrm{\Gamma }}_0=0.120\mathrm{GeV}$.

Figure 2

Integrated cross sections for $\mathrm{CC}1{\pi }^{+}$ (left) and $\mathrm{CC}1{\pi }^0$ (right) production in mineral oil (${\mathrm{CH}}_2$) as a function of the neutrino energy $E_{\nu }$. The $\mathrm{CC}1{\pi }^{+}$ data are from Table V (Fig. 20) in [2] and the $\mathrm{CC}1{\pi }^0$ data are from Table VI (Fig. 8) in [3].

Figure 3

Differential cross sections $d\sigma /d{Q}^2$ for $\mathrm{CC}1{\pi }^{+}$ (left) and $\mathrm{CC}1{\pi }^0$ (right) production in mineral oil (${\mathrm{CH}}_2$) versus $Q^2$. The $\mathrm{CC}1{\pi }^{+}$ data are taken from Table VII (Fig. 21) in [2] and the $\mathrm{CC}1{\pi }^0$ data from Table VII (Fig. 9) in [3].

Figure 4

Same as in Fig. 3 for the differential cross sections $d\sigma /d{T}_{\mu }$ as a function of the kinetic energy of the muon $T_{\mu }$. The $\mathrm{CC}1{\pi }^{+}$ data are from Table VIII (Fig. 22) in [2] and the $\mathrm{CC}1{\pi }^0$ data from Table VIII (Fig. 10) in [3].

Figure 5

Differential cross sections for $\mathrm{CC}1{\pi }^{+}$ production in mineral oil as a function of the kinetic energy of the pion $T_{\pi }^{+}$ (cf. Table VI (Fig. 23) in [2]).

Figure 6

Differential cross sections for $\mathrm{CC}1{\pi }^0$ production in mineral oil as a function of the pion momentum $P_{\pi }^0$ [cf. Table X (Fig. 12) in [3]).

Figure 7

Differential cross sections for $\mathrm{CC}1{\pi }^0$ production in mineral oil as a function of the muon polar angle $\cos {\theta }_{\mu }$ (cf. Table IX (Fig. 11) in [3]).

Figure 8

Same as in Fig. 7 for the pion polar angle $\cos {\theta }_{{\pi }^0}$ (cf. Table XI (Fig. 13) in [3]).

Figure 9

Differential cross sections for $\mathrm{NC}1{\pi }^0$ production in ${\nu }_{\mu }$ scattering (left) and ${\overline{\nu }}_{\mu }$ scattering (right) off a mineral oil target as a function of the pion momentum (cf. Table IV (a), (c) and Fig. 7 (a), (c) in [4]).

Figure 10

Same as in Fig. 9 for the distributions in the pion polar angle (cf. Table IV (b), (d) and Fig. 7 (b), (d) in [4]).

Figure 11

Flux-averaged differential cross sections per nucleon for $\mathrm{CC}1{\pi }^{+}$ production in plastic (CH) as a function of the kinetic energy of the pion $T_{\pi }^{+}$ in comparison with $\mathrm{MINER}\nu \mathrm{A}$ data [14].

Figure 12

Flux-averaged $\mathrm{CC}1{\pi }^{+}$ production cross sections per nucleon in plastic (CH) as function of the pion angle in comparison with $\mathrm{MINER}\nu \mathrm{A}$ data [14].

Figure 13

Comparison of theoretical predictions using different values for the axial mass and the mass of the $\mathrm{\Delta }$ resonance with the $\mathrm{MINER}\nu \mathrm{A}$ data for the distribution in the kinetic energy of the pion [14]. The solid line shows the curve with $M_A=1.05$ and $M_{\mathrm{\Delta }}=1.232\mathrm{GeV}$ already presented in Fig. 11. In addition we show results for $M_A=1.05$, $M_{\mathrm{\Delta }}=1.202\mathrm{GeV}$ (dashed line) and $M_A=0.95$, $M_{\mathrm{\Delta }}=1.202\mathrm{GeV}$ (dotted line).