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Anyone has done the 1-loop cancellation for the Wess-Zumino model?

  1. Jan 31, 2011 #1
    I am calculating the one loop vacuum energy in the Wess-Zumino model, and I don't get a cancellation. For sure I've messed up with the symmetry factor for the boson diagram, because in the fermion sector i have the cancellation (that is almost trivial). I an old post 2 guys were discussing of the 2-loop check, but would be nice for me to see the explicit cancellation for the original lagrangian of wess-zumino at 1-loop.
    I say in advance that I know that in superfields formalism the problem of susy UV cancellations is almost straightforward and that it's possible to go easily to higher loop calculations for simple models like the Wess-Zumino, but I would like to get rid of this problem, because it makes me think that I can not calculate the symmetry factor!

    The original lagrangian of wess-zumino in component is in the euclidean:

    L= 1/2g^2(A^2+B^2)^2+Mg(A^3+AB^2)+A\bar{\psi}\psi+igB\bar{psi}\gamma_{5}\psi

    thanks for your attention
  2. jcsd
  3. Feb 1, 2011 #2


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    I saw your earlier post in a thread between nrqed and me years ago. I didn't reply b/c I don't have my notes handy. But this is done in several major textbooks. For example, check out "Supersymmetric gauge field theory and string theory," by David Bailin, Alexander Love.
  4. Feb 20, 2011 #3
    thank you very much.
    However I want to stress that in the book that you have cited, the authors carefully avoid to use the standard lagrangian for the wess-zumino model. They introduce 3 different chiral superfiled and this trick eliminates the problem of the combinatorial factors (that was clearly my problem)... If you have done the computation in detail for wess-zumino with the right combinatorial factors I would really like to see were I get wrong my calculations.
  5. May 15, 2011 #4
    I,m not sure to understand your problem. But probably the calculation of cancellation of contributions to Higgs mass helps you to check the symmetry factors. This calculation is done precisely for the Wess-Zumino model in :

    "Cambridge Lectures on Supersymmetry and Extra Dimensions"
    Lectures by: Fernando Quevedo pages 48 , 49

    Now I have checked it in the homepage of Dr.Quevedo and seen that in that version this calculation is not present. So if you think it might be useful to look at it
    I can send it to your mail.( I could not copy from pdf to paste on this page )
    Last edited: May 15, 2011
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