Pseudorapidity

Article summary

, an angle of zero is usually along the beam axis, and thus particles with high pseudorapidity values are generally lost, escaping through the space in the detector along with the beam. In experimental particle physics, pseudorapidity, \eta , is a commonly used spatial coordinate representing the angle of a particle relative to the beam axis. It is defined as : \eta \equiv -\ln\left[\tan\left(\frac{\theta}{2}\right)\right], where \theta is the angle between the particle three-momentum \mathbf{p} and the positive direction of the beam axis. Inversely, : \theta = 2\arctan\left(e^{-\eta}\right). As a function of three-momentum \mathbf{p} , pseudorapidity can be written as : \eta = \frac{1}{2} \ln \left(\frac{\left|\mathbf{p}\right|+p_\text{L}}{\left|\mathbf{p}\right|-p_\text{L}}\right) = \operatorname{arctanh}\left(\frac{p_\text{L}} {\left|\mathbf{p}\right|}\right), where p_\text{L} is the component of the momentum along the beam axis (i.e. the longitudinal momentum – using the conventional system of coordinates for hadron collider physics, this is also commonly denoted p_z ).…

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