Using sorted invariant mass variables to evade combinatorial ambiguities in cascade decays

TL;DR

This paper introduces a method using sorted invariant mass variables to determine particle masses in cascade decays, effectively avoiding combinatorial ambiguities common in SUSY-like decay analyses.

Contribution

The authors propose a novel approach that considers all possible invariant mass combinations in a sorted manner, providing analytical formulas for endpoint measurements in SUSY decay chains.

Findings

Analytical formulas for invariant mass endpoints in SUSY decays.

Method effectively resolves combinatorial ambiguities.

Can determine decay topology and resonance structure.

Abstract

The classic method for mass determination in a SUSY-like cascade decay chain relies on measurements of the kinematic endpoints in the invariant mass distributions of suitable collections of visible decay products. However, the procedure is complicated by combinatorial ambiguities: e.g., the visible final state particles may be indistinguishable (as in the case of QCD jets), or one may not know the exact order in which they are emitted along the decay chain. In order to avoid such combinatorial ambiguities, we propose to treat the final state particles fully democratically and consider the sorted set of the invariant masses of all possible partitions of the visible particles in the decay chain. In particular, for a decay to N visible particles, one considers the sorted sets of all possible n-body invariant mass combinations (2 <= n <= N) and determines the kinematic endpoint m_(n,r)^max of the distribution of the r-th largest n-body invariant mass m_(n,r) for each possible value of n and r. For the classic example of a squark decay in supersymmetry, we provide analytical formulas for the interpretation of these endpoints in terms of the underlying physical masses. We point out that these measurements can be used to determine the structure of the decay topology, e.g., the number and position of intermediate on-shell resonances.