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Characterizing Invisible Electroweak Particles through Single-Photon Processes at High Energy $e^+e^-$ Colliders

We explore the scenarios where the only accessible new states at the electroweak scale consist of a pair of color-singlet electroweak particles, whose masses are degenerate at the tree level and split only by electroweak symmetry breaking at the loop level. For the sake of illustration, we consider a supersymmetric model and study the following three representative cases with the lower-lying states as (a) two spin-1/2 Higgsino SU(2)$_L$ doublets, (b) a spin-1/2 wino SU(2)$_L$ triplet and (c) a spin-0 left-handed slepton SU(2)$_L$ doublet. Due to the mass-degeneracy, those lower-lying electroweak states are difficult to observe at the LHC and rather challenging to detect at the $e^+ e^-$ collider as well. We exploit the pair production in association with a hard photon radiation in high energy $e^+ e^-$ collisions. If kinematically accessible, such single-photon processes at $e^+e^-$ colliders with polarized beams enable us to characterize each scenario by measuring the energy and scattering angle of the associated hard photon, and to determine the spin of the nearly invisible particles unambiguously through the threshold behavior in the photon energy distribution.