Pseudorapidity

In experimental particle physics, pseudorapidity, ${\displaystyle \eta }$, is a commonly used spatial coordinate describing the angle of a particle relative to the beam axis. It is defined as

where ${\displaystyle \theta }$ is the angle between the particle three-momentum ${\displaystyle \mathbf {p} }$ and the positive direction of the beam axis. Inversely,

As a function of three-momentum ${\displaystyle \mathbf {p} }$, pseudorapidity can be written as

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