Measuring mass and spin of Dark Matter particles with the aid energy spectra of single lepton and dijet at the $e^+e^-$ Linear Collider

Abstract

In many models stability of Dark Matter particles $D$ is ensured by conservation of a new quantum number referred to as $D$-parity. Our models also contain charged $D$-odd particles $D^\pm$ with the same spin as $D$. Here we propose a method to precisely measure the masses and spins of $D$-particles in the process $\epe\to D^+D^-\to DDW^+W^-\to DD (q\bar{q})(\ell\nu)$ with a signature {\it dijet + $\mu$ (or $e$) + nothing}. It is shown that the energy distribution of the lepton has singular points (upper edge and kinks or a peak) whose positions are kinematically determined. For precise determination of $D$ and $D^\pm$ masses, it is sufficient to measure these singular points and upper edge of dijet energy spectrum. After this procedure, even an approximate measurement of the corresponding cross section allows a determination of the spin of $D$ particles to be performed. New points of this work are: 1) We propose to use only the well measurable energy spectra of {\bf individual leptons} and the upper edge of the dijet energy spectrum. 2) We propose to identify the spin of $D$-particles via value of the cross section for the discussed process.