Pseudorapidity

The pseudorapidity is defined as

For a particle with momentum ( and ) this can be rewritten as:

Wherein

• The Area hyperbolic tangent function, and
• The longitudinal momentum, the pulse component along the beam axis.

In the Hochenergienäherung, ie for particles whose mass is negligible compared to its momentum:

With the energy

Is the pseudorapidity numerically approximately equal to the rapidity:

Which is defined in experimental particle physics

For comparison, the original rapidity according to the special theory of relativity

With

• The particle velocity
• The speed of light

The shape of the differential cross section is invariant under a Lorentz boost. The same applies to a good approximation for the pseudorapidity, only it is easier to measure: It is not the mass of the particle must be determined, but only its direction of flight through the detector.

• Particle Physics
• Dimensionless size