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 ca
n 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.
We present a comment on the kinematic variable $m_{CT2}$ recently proposed in Amplification of endpoint structure for new particle mass measurement at the LHC. The variable is designed to be applied to models such as R-parity conserving Supersymmetry
(SUSY) when there is pair production of new heavy particles each of which decays to a single massless visible and a massive invisible component. It was proposed in Amplification of endpoint structure for new particle mass measurement at the LHC that a measurement of the peak of the $m_{CT2}$ distribution could be used to precisely constrain the masses of the SUSY particles. We show that when Standard Model backgrounds are included in simulations, the sensitivity of the $m_{CT2}$ variable to the SUSY particle masses is more seriously impacted for $m_{CT2}$ than for other previously proposed variables.
