A simple, yet subtle "invariance" of two-body decay kinematics

TL;DR

This paper reveals a simple invariant feature of two-body decay kinematics where the energy distribution peak of a massless decay product in the lab frame equals its rest frame energy, aiding mass measurements without full event reconstruction.

Contribution

The study analytically demonstrates an invariant peak in the energy distribution of decay products, useful for mass determination, tested on top quark data at the LHC.

Findings

Energy distribution peak matches rest frame energy.

The method works with simulated LHC data.

Fitting the distribution accurately estimates the top quark mass.

Abstract

We study the two-body decay of a mother particle into a massless daughter. We further assume that the mother particle is unpolarized and has a generic boost distribution in the laboratory frame. In this case, we show analytically that the laboratory frame energy distribution of the massless decay product has a peak, whose location is identical to the (fixed) energy of that particle in the rest frame of the corresponding mother particle. Given its simplicity and "invariance" under variations of the boost distribution of the mother particle, our finding should be useful for the determination of masses of mother particles. In particular, we anticipate that such a procedure will then not require a full reconstruction of this two-body decay chain (or for that matter, information about the rest of the event). With this eventual goal in mind, we make a proposal for extracting the peak position by fitting the data to a well-motivated analytic function describing the shape of such energy distribution. This fitting function is then tested on the theoretical prediction for top quark pair production and its decay and it is found to be quite successful in this regard. As a proof of principle of the usefulness of our observation, we apply it for measuring the mass of the top quark at the LHC, using simulated data and including experimental effects.