Transverse Observables and Mass Determination at Hadron Colliders

I consider the two-body decay of a particle at a hadron collider into a visible and an invisible particle, generalizing $W \to e \nu$, where the masses of the decaying particle and the invisible decay particle are, {\em a priori}, unknown. I prove that the transverse mass, when maximized over possible kinematic configurations, can be used to determine both of the unknown masses. I argue that the proof can be generalized to cover cases such as decays of pair-produced superpartners to the lightest, stable superpartner at the Large Hadron Collider.

💡 Research Summary

The paper addresses a central problem in collider phenomenology: how to determine the masses of a parent particle and an invisible daughter when both are a priori unknown. Building on the well‑known transverse‑mass (m_T) technique used for the W→eν decay, the author generalizes the concept to any two‑body decay A→B + C where B is visible and C is invisible. The key observation is that, for a fixed event, the transverse mass depends on the unknown transverse momentum of C (the missing transverse momentum). By treating this missing momentum as a free vector constrained only by the measured missing‑E_T of the whole event, the author maximizes m_T over all admissible configurations. Using Lagrange multipliers and the condition ∂m_T/∂p_T^C = 0, the maximization yields a closed‑form expression for the maximal transverse mass:

 m_T^max = √