# Why prefere pseudorapidity to θ coord

1. Aug 9, 2014

### ChrisVer

The rapidity is defined as:

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

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

$n= -ln (tan(\frac{\theta}{2}))$ or $cos (\theta) = tanh(n)$.

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 $n$ terms...

2. Aug 9, 2014

### Staff: Mentor

The pseudorapidity ($\eta$="eta", not n) scale is more convenient. We had the same question three weeks ago.