Pseudorapidity
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In experimental particle physics, Pseudorapidity, η, is a commonly used spatial coordinate describing the angle of a particle relative to the beam axis. It is defined as
![\eta = -\ln\left[\tan\left(\frac{\theta}{2}\right)\right],](../../../math/8/6/4/86428c3055cd2b5e2ddab6b849787e98.png)
where 
is the angle relative to the beam axis.
It is numerically close to the rapidity, y, defined in Special Relativity as
when the particle is relativistic. Here, pL is the component of the momentum along the beam direction. However, pseudorapidity depends only on the polar angle of its trajectory, and not on the energy of the particle.
In hadron collider physics, the rapidity (or pseudorapidity) is preferred over the polar angle θ because, loosely speaking, particle production is constant as a function of rapidity. One speaks of the forward direction in a hadron collider experiment, which refers to regions of the detector that are close to the beam axis, at high 
.
The difference in the rapidity of two particles is independent of Lorentz boosts along the beam axis.
Here are some representative values:
-
(degrees)
η 0 infinite 5 3.13 10 2.44 20 1.74 30 1.31 45 0.88 60 0.55 80 0.175 90 0
There is a symmetry about θ = 90 degrees. In other words, η at 180 − θ = − η at θ.
