Assessing the theory-data tension in neutrino-induced charged pion production: The effect of final-state nucleon distortion

Abstract

Pion production on nuclei constitutes a significant part of the total cross section in experiments involving few-GeV neutrinos. Combined analyses of data on deuterium and heavier nuclei points to tensions between the bubble-chamber data and the data of the $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$ experiment, which are often ascribed to unspecified nuclear effects. In experimental analysis use is made of approximate treatments of nuclear dynamics, usually in a Fermi gas approach with classical treatments of the reaction mechanism, and fits are often performed by simply rescaling cross sections. To understand the origin of these tensions, check the validity of approximations, and to further advance the description of neutrino pion production on nuclei, a microscopic quantum mechanical framework is needed to compute nuclear matrix elements. We use the local approximation to the relativistic distorted wave impulse approximation to calculate the nuclear matrix elements. We include the distortion of wave functions of the final-state nucleon in a real energy-dependent potential. We compare results with and without distortion. To perform this comparison under conditions relevant to neutrino experiments, we compute cross sections for the $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$ and T2K charged-pion production datasets. The inclusion of nucleon distortion leads to a reduction of the cross section up to 10%, but to no significant change in shape of the flux-averaged cross sections. Results with and without distortion compare favorably to experimental data, with the exception of the low-${Q}^{2}$ $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$ ${\ensuremath{\pi}}^{+}$ data. We point out that hydrogen target data from BEBC is also overpredicted at low ${Q}^{2}$, and the data-model discrepancy is similar in shape and magnitude as what is found in comparison to $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$ data. Including nucleon distortion alone cannot explain the overprediction of low-${Q}^{2}$ cross sections measured by $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$. The similar overprediction of BEBC data on hydrogen means that it is impossible to ascribe this discrepancy solely to a nuclear effect. Axial form factors might not be constrained in a satisfactory way by the Argonne and Brookhaven National Laboratories (ANL/BNL) data alone. Axial couplings and their ${Q}^{2}$ dependence should ideally be derived from more precise data on hydrogen and deuterium. Nuclear matrix elements should be tested with e.g., electron scattering data for which nucleon level physics is better constrained.