Sharpening m_T2 cusps: The mass determination of semi-invisibly decaying particles from a resonance

We revisit mass determination techniques for the minimum symmetric event topology, namely X pair production followed by X → ℓN, where X and N are unknown particles with the masses to be measured, and N is an invisible particle, concentrating on the case where X is pair produced from a resonance. We consider separate scenarios, with different initial constraints on the invisible particle momenta, and present a systematic method to identify the kinematically allowed mass regions in the (m_N, m_X ) plane. These allowed regions exhibit a cusp structure at the true mass point, which is equivalent to the one observed in the m_T2 endpoints in certain cases. By considering the boundary of the allowed mass region we systematically define kinematical variables which can be used in measuring the unknown masses, and find a new expression for the m_T2 variable as well as its inverse. We explicitly apply our method to the case that X is pair produced from a resonance, and as a case study, we consider the process pp → A → χ̃⁺₁ χ̃₁^-, followed by χ̃₁^±→ℓ ^± ν̃_ℓ, in the Minimal Supersymmetric Standard Model and show that our method provides a precise measurement of the chargino and sneutrino masses, m_X and m_N, at 14 TeV LHC with 300 fb^-1 luminosity.