Decay Correlations of Heavy Leptons in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mo>→</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>

Abstract

Assuming that leptons heavier than muons exist in nature, we consider their decay modes and the correlations between the decay products of ${l}^{+}$ and ${l}^{\ensuremath{-}}$ in the colliding-beam experiment: ${e}^{+}+{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{l}^{+}+{l}^{\ensuremath{-}}$. Far above the threshold, the helicities of ${l}^{+}$ and ${l}^{\ensuremath{-}}$ tend to be opposite to each other. Near the threshold the directions of spins of ${l}^{+}$ and ${l}^{\ensuremath{-}}$ prefer to be parallel to each other, and the sum of the two spins prefers to be either parallel or anti-parallel to the direction of the incident electron. Because the parity conservation is violated maximally in the decays of ${l}^{+}$ and ${l}^{\ensuremath{-}}$, the angular distributions of decay products depend strongly on the spin orientation of the heavy leptons. Since the spins of ${l}^{+}$ and ${l}^{\ensuremath{-}}$ are strongly correlated in the production, we found a strong correlation between the energy-angle distributions of the decay products of ${l}^{+}$ and ${l}^{\ensuremath{-}}$. The decay widths of ${l}^{\ensuremath{-}}$ into channels ${\ensuremath{\nu}}_{l}{\overline{\ensuremath{\nu}}}_{e}{e}^{\ensuremath{-}}$, ${\ensuremath{\nu}}_{l}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}{\ensuremath{\mu}}^{\ensuremath{-}}$, ${\ensuremath{\nu}}_{l}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${\ensuremath{\nu}}_{l}{K}^{\ensuremath{-}}$, ${\ensuremath{\nu}}_{l}{\ensuremath{\rho}}^{\ensuremath{-}}$, ${\ensuremath{\nu}}_{l}{K}^{*}$, ${\ensuremath{\nu}}_{l}{A}_{1}$, ${\ensuremath{\nu}}_{l}Q$, and ${\ensuremath{\nu}}_{l}+\mathrm{hadron}$ continuum as functions of the mass of ${l}^{\ensuremath{-}}$ are estimated.