Why prefere pseudorapidity to θ coord

  • Thread starter ChrisVer
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In summary, rapidity is defined by the equations y = (1/2)ln[(E+p_z)/(E-p_z)] and y' = (1/2)ln[x_A/x_B] for a hard event. When the invariant mass is zero, rapidity is converted to pseudorapidity, represented by n, which is dependent on the polar angle theta. The pseudorapidity scale is preferred over the polar angle because it is a more convenient transformation and allows for better understanding of the process.
  • #1
ChrisVer
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The rapidity is defined as:

[itex]y = \frac{1}{2} ln(\frac{E+p_z}{E-p_z})[/itex]
and for a hard event (hard scattering reaction/two partons reaction) we find that:
[itex]y'= \frac{1}{2} ln(\frac{x_A}{x_B})[/itex]

If the invariant mass is zero the rapidity changes into the pseudorapidity [itex]n[/itex] which depends only on the polar angle [itex]\theta[/itex]:

[itex] n= -ln (tan(\frac{\theta}{2})) [/itex] or [itex]cos (\theta) = tanh(n) [/itex].

Since the pseudorapidity is just a (1-1) transformation of the polar angle theta, why is it prefered? I don't know but I'm losing geometrical intuition of the process when I try to think in [itex]n[/itex] terms...
 
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  • #2
The pseudorapidity (##\eta##="eta", not n) scale is more convenient. We had the same question three weeks ago.
 

1. Why is pseudorapidity preferred over θ coordinate in particle physics?

Pseudorapidity is preferred over θ coordinate in particle physics because it is a more convenient and useful variable for describing the angular distribution of particles in high-energy collisions. Unlike the θ coordinate, which is measured in radians and ranges from 0 to π, pseudorapidity is dimensionless and ranges from -∞ to +∞. This makes it easier to compare the distributions of particles produced at different energies and in different types of collisions.

2. How is pseudorapidity calculated?

Pseudorapidity (η) is calculated using the formula: η = -ln[tan(θ/2)], where θ is the polar angle of the particle with respect to the beam axis. This formula takes into account the fact that particles produced at small angles with respect to the beam axis are more likely to be detected than those produced at large angles, due to the geometry of particle detectors.

3. What are the advantages of using pseudorapidity over θ coordinate?

One advantage of using pseudorapidity over θ coordinate is that it is independent of the particle's energy. This means that the angular distribution of particles will remain the same even if the collision energy changes. Additionally, pseudorapidity is symmetric under charge conjugation, which makes it useful for studying the properties of particles and their anti-particles.

4. How does using pseudorapidity affect the interpretation of experimental data?

Using pseudorapidity instead of θ coordinate can simplify the interpretation of experimental data by reducing the effects of detector limitations. Since particles produced at small angles are more likely to be detected, the pseudorapidity distribution gives a more accurate representation of the actual angular distribution of particles. This allows for more precise measurements and better understanding of the underlying physics processes.

5. Are there any limitations to using pseudorapidity?

While pseudorapidity is a useful variable, it does have some limitations. Since it is based on the polar angle of the particle with respect to the beam axis, it does not take into account the azimuthal angle, which is the angle around the beam axis. This can be important for certain types of collisions and phenomena, and thus other variables, such as rapidity, may be used in conjunction with pseudorapidity to fully describe the distribution of particles.

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