Impact of final state interactions on neutrino-nucleon pion production cross sections extracted from neutrino-deuteron reaction data

The current and near-future neutrino-oscillation experiments require significantly improved neutrino-nucleus reaction models. Neutrino-nucleon pion production data play a crucial role to validate corresponding elementary amplitudes that go into such neutrino-nucleus models. Thus, the currently available data extracted from charged-current neutrino-deuteron reaction data (${\nu }_{\mu }d\to {\mu }^{-}\pi NN$) must be corrected for nuclear effects such as the Fermi motion and final state interactions (FSI). We study ${\nu }_{\mu }d\to {\mu }^{-}\pi NN$ with a theoretical model including the impulse mechanism supplemented by FSI from $NN$ and $\pi N$ rescatterings. An analysis of the spectator momentum distributions reveals that the FSI effects significantly reduce the spectra over the quasifree peak region and leads to a useful recipe to extract information of elementary ${\nu }_{\mu }N\to {\mu }^{-}\pi N$ processes using ${\nu }_{\mu }d\to {\mu }^{-}\pi NN$ data, with the important FSI corrections taken into account. We provide ${\nu }_{\mu }N\to {\mu }^{-}\pi N$ total cross sections by correcting the deuterium bubble chamber data for the FSI and Fermi motion. The results will bring a significant improvement on neutrino-nucleus reaction models for the near-future neutrino-oscillation experiments.

Figure 1

Mechanisms in our ${\nu }_{\mu }d\to {\mu }^{-}\pi NN$ model: (a) impulse; (b) $NN$ rescattering; (c) $\pi N$ rescattering mechanisms. Particle labels and their momenta (in parentheses) are defined.

Figure 2

Neutron (left) and proton (right) momentum distributions in ${\nu }_{\mu }d\to {\mu }^{-}{\pi }^{+}pn$ at $E_{\nu }=0.5\mathrm{GeV}$. The green triangles (blue diamonds) [red crosses] are calculated with the impulse ($\mathrm{impulse}+NN$ rescattering) [$\mathrm{impulse}+NN+\pi N$ rescattering] mechanisms. The errors are only statistical from the Monte Carlo integral and are not shown when smaller than the point size. The black solid curve in the left [right] panel is ${\nu }_{\mu }p\to {\mu }^{-}{\pi }^{+}p$ [${\nu }_{\mu }n\to {\mu }^{-}{\pi }^{+}n$] cross sections convoluted with the deuteron wave function as in Eq. (6).

Figure 3

Coefficients $N_{\alpha }(E_{\nu },p_s)$, defined in Eq. (7), for ${\nu }_{\mu }d\to {\mu }^{-}{\pi }^{+}pn$; $\alpha ={\nu }_{\mu }p\to {\mu }^{-}{\pi }^{+}p$ (${\nu }_{\mu }n\to {\mu }^{-}{\pi }^{+}n$) and $p_s=p_n(p_p)$ for the upper (lower) panels. The neutrino energy is $E_{\nu }=0.5$, 1, and 1.5 GeV for the left, central, and right panels, respectively. The analytic functions $N_{\alpha }^{\mathrm{fit}}(E_{\nu },p_s)$, which are defined in Eqs. (8) and (9) and fitted to the red crosses for $p_s\le 50\mathrm{MeV}$, are also shown by the black solid lines. The other features are the same as those in Fig. 2.

Figure 4

Total cross sections for (a) ${\nu }_{\mu }p\to {\mu }^{-}{\pi }^{+}p$, (b) ${\nu }_{\mu }n\to {\mu }^{-}{\pi }^{+}n$, and (c) ${\nu }_{\mu }n\to {\mu }^{-}{\pi }^{0}p$. The open red circles (open blue squares) are the reanalyzed ANL (BNL) data [20] (no $W$ cut), which are further corrected for the Fermi motion and FSI and shown by the solid red circles (solid blue squares) slightly [0.04 GeV] shifted along the $E_{\nu }$ direction for better visibility. The insert shows an enlargement of the small $E_{\nu }$ region.