Determination of $sin^{2}\theta_W$ using $\nu(\bar\nu)$-Nucleus scattering

TL;DR

This paper refines the extraction of the weak mixing angle from neutrino-nucleus scattering by accounting for nonisoscalarity and nuclear medium effects, improving the accuracy of measurements in iron nuclei.

Contribution

It introduces a modified Paschos-Wolfenstein relation that includes nuclear medium effects and nonisoscalarity, using a relativistic spectral function approach.

Findings

Dependence of sin^2θ_W on Bjorken variables x and y.

Impact of nuclear medium effects on sin^2θ_W extraction.

Significance of neutron excess in nuclear targets.

Abstract

We have studied nonisoscalarity and medium effects in the extraction of weak mixing angle using Paschos and Wolfenstein relation in the iron nucleus. Paschos and Wolfenstein(PW) relation is valid for an isoscalar target. We have modified the PW relation for nonisoscalar target as well as incorporated the medium effects like Pauli blocking, Fermi motion, nuclear binding energy and pion rho cloud contributions. In our calculations we have used the relativistic nuclear spectral function which includes nucleon correlations. Finally local density approximation is applied to translate the numerical results to the finite nuclei. We have studied the dependence of $sin^{2}\theta_W$ on Bjorken variables $x$ and $y$, four momentum transfer square ($Q^2$), energy of the neutrino and antineutrino, and effect of excess neutrons over protons in the nuclear target.