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

TL;DR

This paper introduces a method to accurately measure the mass and spin of Dark Matter particles at an $e^+e^-$ collider by analyzing energy spectra of leptons and dijets, using kinematic features and cross section measurements.

Contribution

It proposes a novel approach utilizing lepton and dijet energy spectra to determine Dark Matter particle properties with minimal reliance on complex event reconstruction.

Findings

Singular points in lepton energy distribution enable mass determination.

Measurement of the dijet energy spectrum's upper edge aids in mass estimation.

Cross section measurement helps identify the spin of Dark Matter particles.

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.