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

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, p_L is the component of the momentum along the beam direction. However, pseudorapidity η does not depend on the energy of the particle, only on the polar angle of its trajectory.

The rapidity (or pseudorapidity) is preferred in hadron colliders over the polar angle θ because, loosely speaking, particle production is constant as a function of rapidity. Furthermore, the difference in the rapidity of two particles is independent of Lorentz boosts along the beam axis.

Here are some representative values:

'' degrees	''
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.