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.


  • $\begingroup$ 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, $|\bf p|\gg m_0 c ~\Rightarrow~\tanh\varphi\approx 1~\Rightarrow~ y\approx \eta$. $\endgroup$
    – Qmechanic
    May 14, 2015 at 13:04

1 Answer 1


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.

At hadron colliders jets are defined starting from the energy deposit of the particles in the calorimeter. Jets are groups of topologically related energy deposits in the calorimeters. Incoming particles usually deposit their energy in many calorimeter cells. Cluster algorithms are designed to group cells deposits belonging to the same particle forming three-dimensional clusters. The cluster energy is calculated as the sum of the cell energies and calibrated to account for the energy deposited outside the cluster and in dead material. The choice of the cluster algorithm to be used depends on the details of the calorimeter.

Jets are then reconstructed by applying a "jet algorithm" to the ensemble of reconstructed clusters. The cluster associated to the jet are selected by the jet algorithm. The cluster variables which are relevant for the jet definition are the direction with respect to the interaction point and the sum of the energy in its cells. From these variables, a 0 mass four-vector is associated to each single cluster. The four-vector associated to the jet, and therefore its mass, is given by the sum of the four-vectors of the jet clusters.


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