A storm in a “T” cup

Or how (not) to make transverse projections at the LHC

Usual geometry and momentum projection

What to do with time-like component of P when projecting to (1+2)d?

Various options possible & used to construct time-like component: (Here labelled “T”, “V”, “o”)Differences, pros & cons not widely appreciated.

In (1+3)d:

Option 1/3The “T” projectionMass-preserving

Option 2/3The “V” projectionSpeed preserving

After this projection the 1+2-dimensional inner product is no longer M2

However, the 1+2 dimensional speed is preserved:

Option 3/3The “o” projectionAlways massless

A graphical representation

Hierarchy easily proved to be:

Partitioning events

Reconstruct parent masses by summing (1+3) or (1+2) vectors

Operations “add” and “project” do not commute

Example:

Procedures given for constructing variables for given hypothesis

Example of fully leptonictop pair decay

How existing variables fit in ourcategorisation

What common computer libraries

offer