Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Scattering Amplitudes BCFW relation (A question)

  1. Jan 1, 2013 #1
    I have a very trivial question to ask and it would be great if someone could
    help me in this.

    The statement that '3-point amplitudes' and the location of poles are sufficient to
    determine any n-point amplitude at tree level is confusing to me. Don't I also need to know
    4-point amlitudes, for example in YM theory ? The reason I say this is
    the 4-point vertex can not be broken down. That is the residues obtained upon putting
    propagators onshell will also contain 4-point functions.

    What am I missing ?

    Thanks for your help in advance.
  2. jcsd
  3. Jan 1, 2013 #2
    In YM, the three point vertex coefficient and the four point coefficient are related to each other; one goes like g p_mu, and the other is g^2. The second is necessary to have a gauge-invariant Lagrangian. What's neat about YM is that given the three-point vertex at tree level, one can use it to build up the n-point function from BCFW, and you get the same answer as if you'd done Feynman rules, without having the miscellaneous gauge degrees of freedom to keep track of.

    In a theory where the three- and four-point vertices were uncorrelated (scalar field theory with V = g phi^3 + lambda phi^4, for example), then you could BCFW up contributions to amplitudes that contained arbitrary powers of g, but no powers of lambda, using just the three-point function, but you wouldn't get the complete answer for the amplitudes. Hope this helps!
  4. Jan 3, 2013 #3
    Thanks a lot Chrispb for a fast reply. It certainly helps.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook