Measuring Masses in Semi-Invisible Final States at Electron-Positron Colliders

Mass measurement of a particle whose decay products including invisible particles is a challenging task at colliders. For a new physics model involving a dark matter candidate $N$ and a $Z_2$ symmetry that stabilizes it, a typical new process at $e^+e^-$ colliders is the pair production $e^+e^- \to Y\bar{Y}$ followed by decay processes $Y\to aN$ and $\bar{Y}\to b\bar{N}$, where $a$ and $b$ are visible but $N$ is invisible. In this work, we propose a new method to measure the physical masses in this topology by making use of the kinematic equations given by momentum-energy conservation and on-shell conditions. For each event, the solvability of these equations determines a limited region on the trial $m_Y$-$m_N$ plane. The edge of this region can be used to define two variables, $m_Y^\mathrm{edge}$ and $m_N^\mathrm{edge}$, whose distributions are utilized to derive the measurement values of $m_Y$ and $m_N$. The measurement deviations and uncertainties are also estimated after including detector effects and background contamination.