When should rapidity or pseudorapidity be used for particle measurements?

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In summary, rapidity and pseudorapidity are both measures of particle momentum, but they are used in different scenarios. Rapidity is used for massive particles, such as those observed at the LHC, while pseudorapidity is used for all particles regardless of mass. For massless particles, both measures are equivalent, but for massive objects like jets and vector bosons, there is a difference.
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ChrisVer
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I have one question, when should someone use rapidity [itex]y= 0.5 \ln \frac{E + p_z}{E - p_z}[/itex] and when pseudorapidity [itex]\eta = -\frac{1}{2} \ln \tan \theta/2[/itex]?
I've read that rapidity is used for "massive" particles... for experiments like LHC (or more specifically ATLAS), what threshold is considered massive?
I am sure that tau leptons (~1.7GeV) are not considered massive... however I recently read that for particles like J/ψ they use the rapidity... https://arxiv.org/abs/1104.3038
 
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Rapidity is almost Lorentz invariant - it shifts by a constant with a boost. Pseudorapidity is geometric - a detector that covers a particular psedorapidity region does so for all particles.
 
  • #3
For massless particles, both are equivalent. For massive objects there is a difference. At ATLAS and CMS, massive objects are mainly jets and the vector bosons, hadrons only if the measurement happens at very low energy like in your linked example.
 

1. What is the difference between rapidity and pseudorapidity?

Rapidity and pseudorapidity are both measures of the angle of a particle's trajectory in relation to the beam axis in a particle accelerator. However, rapidity takes into account the particle's mass, while pseudorapidity does not. Rapidity is a more precise measure, while pseudorapidity is often used for simpler calculations.

2. How are rapidity and pseudorapidity calculated?

Rapidity is calculated using the formula y = 1/2 ln((E+p)/(E-p)), where E is the energy of the particle and p is its momentum. Pseudorapidity is calculated using the formula η = -ln(tan(θ/2)), where θ is the angle of the particle's trajectory with respect to the beam axis.

3. Which is more commonly used in particle physics experiments, rapidity or pseudorapidity?

Pseudorapidity is more commonly used in particle physics experiments because it is easier to measure and calculate. It also has the advantage of being invariant under boosts along the beam axis, making it useful for comparing particles with different energies.

4. What is the range of values for rapidity and pseudorapidity?

Rapidity can take on any real value, while pseudorapidity is limited to the range -infinity to +infinity. However, in practical applications, pseudorapidity is usually limited to the range -5 to +5.

5. How do rapidity and pseudorapidity affect the behavior of particles in a particle accelerator?

Rapidity and pseudorapidity affect the behavior of particles by determining their angle of trajectory with respect to the beam axis. Particles with higher rapidity or pseudorapidity will have larger angles and thus may interact with different detectors or have different paths through the accelerator. This can also affect the likelihood of particle collisions and production of new particles.

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