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Why is pseudorapidity defined as $-\log \tan \theta/2$

I got a better understanding of what makes (pseudo) rapidity an interesting an 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 a measurement at a hadron collider, where one does not know the the full four vector 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/usefullness of jet mass would also be appreciated.


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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, $|\bf p|\gg m_0 c ~\Rightarrow~\tanh\varphi\approx 1~\Rightarrow~ y\approx \eta$. – Qmechanic May 14 at 13:04

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