Possibility of measuring Adler angles in charged current single pion neutrino-nucleus interactions

Uncertainties in modeling neutrino-nucleus interactions are a major contribution to systematic errors in long-baseline neutrino oscillation experiments. Accurate modeling of neutrino interactions requires additional experimental observables such as the Adler angles which carry information about the polarization of the $\mathrm{\Delta }$ resonance and the interference with nonresonant single pion production. The Adler angles were measured with limited statistics in bubble chamber neutrino experiments as well as in electron-proton scattering experiments. We discuss the viability of measuring these angles in neutrino interactions with nuclei.

Figure 1

Definition of the Adler Angles at the nucleon (true) level (a) and the nuclear level (b). The momenta of the particles are defined in the $\overrightarrow{q}={\overrightarrow{p}}_{\nu }-{\overrightarrow{p}}_{\mu }$ rest frame.

Figure 2

Angle between the ${\overrightarrow{p}}_p+{\overrightarrow{p}}_{\pi }$ system and the $\overrightarrow{q}$ approximation at the level of the nucleus.

Figure 3

Relative spread of the reconstructed neutrino energy $(E_{\mathrm{reco}}-E_{\nu })/E_{\nu }$ as a function of the true neutrino energy. The black circles (squares) represent the mean value of the relative difference post(pre) FSI. The empty circles (squares) show the RMS of the reconstructed neutrino energy relative error post(pre) FSI.

Figure 4

Reconstructed hadronic invariant mass. The empty histogram shows the CC one-$\pi$ events. The vertical line histogram shows the invariant mass when the pion momentum is modified by the FSI. The horizontal line histogram shows the CC-DIS contribution to the CC one-${\pi }^{+}$ sample and the mesh-filled histogram shows the remaining backgrounds.

Figure 5

Relative $\mathrm{p}\text{−}\pi$ invariant mass reconstruction error [$(W_{\mathrm{reco}}-W)/W$)] as a function of the true $\mathrm{p}\text{−}\pi$ invariant mass. The black circles (squares) represent the mean value of the relative error post(pre) FSI. The empty circles (squares) show the RMS of the reconstructed invariant mass relative error post(pre) FSI.

Figure 6

True (solid line) and reconstructed (dotted line) Adler $\theta$ angle (top panel) and $\varphi$ angle (bottom panel). The true CC $1{\pi }^{+}$ distributions include all interactions with the target nucleon and the reconstructed ones for those events with pions leaving the nucleus. The dashed line histogram shows the result when the Fermi momentum is ignored in the reconstruction of the true CC $1{\pi }^{+}$ result. The histogram filled with vertical lines shows the CC $1{\pi }^{+}$ events in which the pion momentum is modified by the FSI. The histogram filled with horizontal lines is the CC-DIS contribution to the CC $1{\pi }^{+}$ sample and the histogram filled with a mesh contains the rest of the backgrounds. The distributions are normalized to unity.

Figure 7

Reconstructed $\varphi$ angle minus the true $\varphi$ as a function of the $\varphi$ angle. The black circles (squares) show the mean value of the difference post(pre) FSI. The empty circles(squares) points show the RMS of the difference post(pre) FSI.

Figure 8

Reconstructed $\theta$ angle minus the true $\theta$ angle as a function of $\theta$. The black circles (squares) show the mean value of the difference post(pre) FSI. The empty circles(squares) show the RMS of the difference post(pre) FSI.

Figure 9

$\varphi$ distribution at the nucleon (black dots) and nucleus (black triangles) levels weighted by the angular dependence as described in the text. The solid line is the result of the fit to the function $A(1+\alpha \sin \varphi )$.