Mass reconstruction with $M_2$ under constraint in semi-invisible production at a hadron collider

The mass-constraining variable $M_2$, a $(1+3)$-dimensional natural successor of extremely popular $M_{T2}$, possesses an array of rich features having the ability to use on-shell mass constraints in semi-invisible production at a hadron collider. In this work, we investigate the consequence of applying a heavy resonance mass-shell constraint in the context of a semi-invisible antler decay topology produced at the LHC. Our proposed variable, under additional constraint, develops a new kink solution at the true masses. This enables one to determine the invisible particle mass simultaneously with the parent particle mass from these events. We analyze in a way to measure this kink optimally, exploring the origin and the properties of such interesting characteristics. We also study the event reconstruction capability inferred from this new variable and find that the resulting momenta are unique and well correlated with true invisible particle momenta.