Guide to transverse projections and mass-constraining variables

TL;DR

This paper unifies various collider mass-measurement variables under a common framework, clarifies their differences, and discusses their optimal usage, enhancing understanding and application in high-energy physics analyses.

Contribution

It reveals that many existing mass variables are interconnected and can be viewed as specialized mass bounds, providing a comprehensive classification and understanding of their relationships.

Findings

Many mass variables are closely related and can be unified under a common framework.

Clarification of different transversification methods and their implications.

Guidance on choosing appropriate variables for complex collider searches.

Abstract

This paper seeks to demonstrate that many of the existing mass-measurement variables proposed for hadron colliders (mT, mEff, mT2, missing pT, hT, rootsHatMin, etc.) are far more closely related to each other than is widely appreciated, and indeed can all be viewed as a common mass bound specialized for a variety of purposes. A consequence of this is that one may understand better the strengths and weaknesses of each variable, and the circumstances in which each can be used to best effect. In order to achieve this, we find it necessary first to revisit the seemingly empty and infertile wilderness populated by the subscript "T" (as in pT) in order to remind ourselves what this process of transversification actually means. We note that, far from being simple, transversification can mean quite different things to different people. Those readers who manage to battle through the barrage of transverse notation distinguishing mass-preserving projections from velocity preserving projections, and `early projection' from `late projection', will find their efforts rewarded towards the end of the paper with (i) a better understanding of how collider mass variables fit together, (ii) an appreciation of how these variables could be generalized to search for things more complicated than supersymmetry, (iii) will depart with an aversion to thoughtless or naive use of the so-called `transverse' methods of any of the popular computer Lorentz-vector libraries, and (iv) will take care in their subsequent papers to be explicit about which of the 61 identified variants of the `transverse mass' they are employing.