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Regge amplitude

  1. Oct 29, 2015 #1
    I am wondering something about the tree amplitude for exchange of a spin J resonance-- the basic calculation that exhibits the famous regge behavior. I see that one way to do the calculation is simply to note that the 4-point function for spin J exchange amongst massless particles arises from an interaction term with J derivatives, and hence J powers of momenta, from which we immediately infer that the t-channel amplitude is of the form
    s^J/(t-M^2) + ... . However another method appears in the literature, which seems to be a partial wave expansion, noting that the spin J term of the expansion for the scattering amplitude is of the form (2J+1) f(t) P_J(cos \theta), where P_J (\cos(\theta) is the Legendre polynomial of spin J and \theta is the angle between the incoming t-channel particles. The asymptotic large s behavior can then be obtained by noting that cos(\theta) --> s/4m^2, and then that P_J (\cos (theta)) --> (cos \theta)^J --> s^J.

    My question is why the two methods? Why does anyone use partial waves if it is so much simpler to get the result from field theory? And this is a very basic question, but what is the validity of a partial wave expansion in a field theory context?
  2. jcsd
  3. Nov 3, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
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