# Kinematic Focus Point Method for Particle Mass Measurements in Missing Energy Events

## TL;DR

This paper introduces a novel kinematic focus point method for particle mass measurements in missing energy events at hadron colliders, leveraging the properties of extreme events and phase space singularities to improve accuracy.

## Contribution

The paper develops a new focus point technique for mass determination that reduces systematic errors and complements existing methods by analyzing the kinematic boundary density.

## Key findings

- Identifies a class of extreme events with true mass points on their kinematic boundary.
- Demonstrates the abundance of extreme events in realistic data samples.
- Shows the focus point method effectively lifts degeneracies in mass space.

## Abstract

We investigate the solvability of the event kinematics in missing energy events at hadron colliders, as a function of the particle mass ansatz. To be specific, we reconstruct the neutrino momenta in dilepton $t\bar{t}$-like events, without assuming any prior knowledge of the mass spectrum. We identify a class of events, which we call extreme events, with the property that the kinematic boundary of their allowed region in mass parameter space passes through the true mass point. We develop techniques for recognizing extreme events in the data and demonstrate that they are abundant in a realistic data sample, due to expected singularities in phase space. We propose a new method for mass measurement whereby we obtain the true values of the mass parameters as the focus point of the kinematic boundaries for all events in the data sample. Since the masses are determined from a relatively sharp peak structure (the density of kinematic boundary curves), the method avoids some of the systematic errors associated with other techniques. We show that this new approach is complementary to previously considered methods in the literature where one studies the solvability of the kinematic constraints throughout the mass parameter space. In particular, we identify a problematic direction in mass space of nearly 100% solvability, and then show that the focus point method is effective in lifting the degeneracy.