Effects of the density-dependent weak form factors on the neutrino reaction via neutral current for the nucleon in nuclear medium and $^{12}$C

TL;DR

This study examines how density-dependent modifications of nucleon form factors affect neutrino and antineutrino neutral current reactions in nuclear medium, revealing significant reductions in cross sections especially for antineutrinos due to helicity differences.

Contribution

It introduces the application of the quark-meson-coupling model to evaluate density-dependent form factors and their impact on neutrino reactions in nuclear medium and carbon-12.

Findings

Approximately 12% decrease in neutrino cross section at normal density.

About 18% reduction of neutrino cross section on $^{12}$C.

Antineutrino cross sections decrease by about 30%, showing a large asymmetry.

Abstract

The nucleon form factors in free space are usually thought to be modified when a nucleon is bound in a nucleus or immersed in a nuclear medium. We investigate effects of the density-dependent axial and weak-vector form factors on the electro-neutrino ($\nu_e$) and anti-electro-neutrino $({\bar \nu_e})$ reactions via neutral current (NC) for a nucleon in nuclear medium or $^{12}$C. For the density-dependent form factors, we exploit the quark-meson-coupling (QMC) model, and apply them to the $\nu_e$ and ${\bar \nu_e}$ induced reactions by NC. About 12% decrease of the total cross section by $\nu_e$ reaction on the nucleon is obtained at normal density, $\rho = \rho_0 \sim 0.15 {fm}^{-3} $, as well as about 18% reduction of total ${\nu}_e$ cross section on $^{12}$C, by the modification of the weak form factors of the bound nucleon. However, similarly to the charged current reaction, effects of the nucleon property change in the ${\bar \nu}_e$ reaction reduce significantly the cross sections about 30% for the nucleon in matter and $^{12}$C cases. Such a large asymmetry in the ${\bar \nu}_e$ cross sections is addressed to originate from the different helicities of ${\bar \nu}_e$ and ${\nu}_e$.