Reconstructing masses for semi-invisibly decaying particles pair-produced at lepton colliders

We present a set of Lorentz invariant kinematic variables for reconstructing mass of semi-invisible decaying particles pair-produced at lepton colliders, $m_{\rm RC}^{\rm min}$, $m_{\rm RC}^{\rm max}$ and $m_{\rm LSP}^{\rm max}$, with analytical formulas. They give the minimal and maximum bounds of the decaying particle mass and upper bound of the invisible particle mass. In the search of new physics, these variables can greatly enhance the statistical significance of signal. For the process of smuon pair production at $\sqrt{s}=240~{\rm GeV}$ lepton collider of 5 ab$^{-1}$, the cross section detection limit is pushed by one order, and the expected exclusion and discovery limits are set above $\sqrt{s}\big/2$ and go into the off-shell region. Moreover, these variables can also be used to improve the precision of $W$-boson mass measurement in full leptonic decayed channel. At future lepton collider, the precision can reach to $2\sim 3$ MeV level.