Using kinematic boundary lines for particle mass measurements and disambiguation in SUSY-like events with missing energy

TL;DR

This paper analyzes the kinematic endpoint method for SUSY particle mass measurement, revealing ambiguities and proposing a two-variable distribution approach to resolve them, applicable to any SUSY-like cascade decay.

Contribution

It provides analytical formulas for mass inversion, identifies ambiguous regions, and introduces a bivariate distribution method to uniquely determine particle masses.

Findings

Two-fold ambiguity persists even with perfect data.

Boundary shapes of bivariate distributions can resolve ambiguities.

Additional measurements from boundary lines enhance mass determination.

Abstract

We revisit the method of kinematical endpoints for particle mass determination, applied to the popular SUSY decay chain squark -> neutralino -> slepton -> LSP. We analyze the uniqueness of the solutions for the mass spectrum in terms of the measured endpoints in the observable invariant mass distributions. We provide simple analytical inversion formulas for the masses in terms of the measured endpoints. We show that in a sizable portion of the SUSY mass parameter space the solutions always suffer from a two-fold ambiguity, due to the fact that the original relations between the masses and the endpoints are piecewise-defined functions. The ambiguity persists even in the ideal case of a perfect detector and infinite statistics. We delineate the corresponding dangerous regions of parameter space and identify the sets of "twin" mass spectra. In order to resolve the ambiguity, we propose a generalization of the endpoint method, from single-variable distributions to two-variable distributions. In particular, we study analytically the boundaries of the (m_{jl(lo)}, m_{jl(hi)}) and (m_{ll}, m_{jll}) distributions and prove that their shapes are in principle sufficient to resolve the ambiguity in the mass determination. We identify several additional independent measurements which can be obtained from the boundary lines of these bivariate distributions. The purely kinematical nature of our method makes it generally applicable to any model that exhibits a SUSY-like cascade decay.