# A Rapidity vs pseudorapidity

1. Aug 26, 2016

### ChrisVer

I have one question, when should someone use rapidity $y= 0.5 \ln \frac{E + p_z}{E - p_z}$ and when pseudorapidity $\eta = -\frac{1}{2} \ln \tan \theta/2$?
I've read that rapidity is used for "massive" particles.... for experiments like LHC (or more specifically ATLAS), what threshold is considered massive?
I am sure that tau leptons (~1.7GeV) are not considered massive... however I recently read that for particles like J/ψ they use the rapidity... https://arxiv.org/abs/1104.3038

2. Aug 26, 2016

Staff Emeritus
Rapidity is almost Lorentz invariant - it shifts by a constant with a boost. Pseudorapidity is geometric - a detector that covers a particular psedorapidity region does so for all particles.

3. Aug 27, 2016

### Staff: Mentor

For massless particles, both are equivalent. For massive objects there is a difference. At ATLAS and CMS, massive objects are mainly jets and the vector bosons, hadrons only if the measurement happens at very low energy like in your linked example.