Polarization Correlations in High-Energy Neutrino Reactions

Abstract

We consider the neutrino-induced reaction ${\nu }_{\mu }+N\to B+\mu$ and the two-step reactions of the type ${\nu }_{\mu }+N\to B^{*}+\mu$, $B^{*}\to B+\pi$, where $B^{*}$ is a baryonic resonance of arbitrary half-integer spin $S=\frac{1}{2}, \frac{3}{2}, \cdots$. We calculate the polarizations of the final particles $B$ and $\mu$ and the correlations between these polarizations, the initial nucleon $N$ being arbitrarily polarized. For the two-step process, the calculation is performed in two stages. First, assuming the usual current × current form for the weak interactions, we calculate the spin-density matrix of the $B^{*}$ produced at the first step; then we calculate its strong decay into the baryon $B$ and the pion. It is shown that, using a convenient formalism to describe the baryonic resonance $B^{*}$, this procedure for the calculation allows one to reduce the $\gamma$-matrix calculation in the case of an arbitrary spin $S$ to that of the case $S=\frac{1}{2}$. Some tests of time-reversal invariance are considered for the elastic process.