# Jet rapidity vs. Pseudorapidity

Thanks to this post I got a better understanding of what makes (pseudo) rapidity an interesting and often-used concept.

Tangentially working with jet physics (the spray of hadrons kind of jet :), I am wondering why people work with rapidity (no pseudo here) when it comes to jets. What is the reason for this (doesn't pseudo rapidity offer the same convenient properties of Lorentz invariance wrt z boosts)?

More importantly, how does one determine the rapidity (or rapidity difference) in measurement at a hadron collider, where one does not know the full four-vector momentum of any physics object?

I suppose that the above question might be related to the topic of jet mass, which I have read in papers before. Any hints on the definition/usefulness of jet mass would also be appreciated.

Thanks

• Comment to the question (v1): Instead of the pseudorapidity in HEP $\eta:={\rm artanh}\frac{p_L}{|\bf p|}$, it seems OP is asking about the rapidity in HEP $y:={\rm artanh}\frac{p_Lc}{E}$ rather than the rapidity in SR $\varphi:={\rm artanh}\frac{|\bf p|c}{E}$. Here $\tanh y=\tanh\eta~\tanh\varphi$. Ultra-relativistically, $|\bf p|\gg m_0 c ~\Rightarrow~\tanh\varphi\approx 1~\Rightarrow~ y\approx \eta$. Commented May 14, 2015 at 13:04

The pseudorapidity is not Lorentz invariant, while the rapidity is. The pseudorapidity is equal to the rapidity in the limit $m\ll p$ so it is generally used for light particles. For many jets the mass is not expected to be small and therefore the rapidity is a more convenient choice.