Why prefere pseudorapidity to θ coord

  1. ChrisVer

    ChrisVer 2,403
    Gold Member

    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...
  2. jcsd
  3. mfb

    Staff: Mentor

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