In-medium effect with muon-neutrino and anti-muon-neutrino quasi-elastic scattering from ¹²C nucleons

We investigated the in-medium effect by density-dependent axial and weakvector form factors on muon-neutrino (V_μ) and anti-muon-neutrino V_μ (V_μ) scattering in the quasi-elastic (QE) region from nucleons (N) bound in a nucleus or immersed in a nuclear medium via neutral current (NC) and charged current (CC). For the density-dependent form factors, we exploited a quarkmesoncoupling (QMC) model. We found that the V_μ V_μ-(V_μ) N scattering cross sections via NC in the QE region usually decrease with an increased medium density, while those using CC were increased. However, their rate of change was sensitive to the four-momentum transfer given to a bound nucleon through scattering. We compared these results obtained by the elementary process corrected by the in-medium effect to the BNL and MiniBooNE data, which measured V_μ scattering cross sections per nucleon through V_μ ¹²C scattering in ¹²C composite targets. The incident energy range was 550 <V< E_V 3000 MeV. We increased the energy up to 100 GeV to compare our results to the NOMAD experimental data. In order to study the density effects on a nucleon embedded in ¹²C, we exploited the QMC form factors evaluated at p = 0.5po, where the normal density po∼0.15 fm^-3. The strangeness contributions in NC scattering are also incorporated into the form factors for comparison with experimental data. Our numerical results show that most of the experimental data can be explained in a satisfactory manner by the densitydependent elementary process, but there are some remaining deviations resulting from the nuclear structure, particularly in the low and high momentum-transfer regions.