Collinearity angle distribution ine−μevents

Abstract

We present an analytical formula for the collinearity angle distribution of $e$ and $\mu$ in the process $e^{+}{e}^{-}\to L^{+}{L}^{-}$ followed by heavy-lepton decay $L\to {\nu }_L+l+{\overline{\nu }}_l$, $l=e or \mu$. Both $V-A$ and $V+A$ couplings are included, as is a mass for the ${\nu }_L$. At high energies we find that the collinearity angle distribution in $cos\theta$ becomes a function of the single scaling variable $x={\beta }^2{\gamma }^2\frac{(1-cos\theta )}{2}$, where $\beta$ and $\gamma$ are heavy-lepton boost parameters from the rest frame to the $e^{+}{e}^{-}$ laboratory frame. This scaling in $x$ may be compared with the scaling in ${p_T}^2$ in hadron physics, and it holds independently of the detailed coupling scheme. A violation of this scaling is a signal of the appearance of heavier leptons.