Identifying the production process of new physics at colliders; symmetric or asymmetric?

We propose a class of kinematic variables, which is a smooth generalization of min-max type mass variables such as the cambridge-m t 2 and m 2, for measuring a mass spectrum of intermediate resonances in a semi-invisibly decaying pair production. while kinematic endpoints of min-max type mass variables are only sensitive to a heavier resonance mass, kinematic endpoints of new variables are sensitive to all masses. these new mass variables can be used to resolve a mass spectrum, so that if the true mass spectrum is asymmetric, then the kinematic endpoints are separate while the endpoints are the same for the symmetric true mass spectrum. we demonstrate the behavior of kinematic endpoint of these new variables in pair production of two-body and three-body decays with one invisible particle.