1-loop cancellation in wess zumino model

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In summary, the speaker is struggling to calculate the one loop vacuum energy in the Wess-Zumino model, specifically with the exact cancellation in the symmetry factors for boson diagrams. They mention being familiar with using superfields to solve this problem, but would like to understand the cancellation without relying on this technique. The original lagrangian they are using is in the euclidean, and their question involves figuring out the 1-loop cancellation of divergences for the mass terms and interactions of the scalar and pseudoscalar fields. They admit to possibly making a mistake in their calculations and offer to post them for review if needed. They suspect the issue lies in the diagrams with two vertices for the scalar and pseudoscalar fields, as they
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diegoRED
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Homework Statement


I am calculating the one loop vacuum energy in the Wess-Zumino model, and I don't get the exact cancellation. For sure I've messed up with symmetry factors for boson diagrams, because in the fermion sector i have the cancellation (that is almost trivial). 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 symmetry factors!

The original lagrangian of wess-zumino in component that I'm using is in the euclidean:

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


Homework Equations



the question is how you get the 1-loop cancellation of divergences for the mass terms for the scalar A and the pseudoscalar B and for their interactions.

The Attempt at a Solution



I've tried but I've not written the latex version of something in which there is clearly a stupid mistake, if you need tomorrow I will post my calculations...
 
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  • #2
I think that the problem is in the diagrams with two vertices for A or B, because I get a different sign for the same diagram with different order of A and B
 

FAQ: 1-loop cancellation in wess zumino model

1. What is the Wess-Zumino model?

The Wess-Zumino model is a supersymmetric quantum field theory that describes the interactions between particles with different spin states. It was first proposed by physicists Julius Wess and Bruno Zumino in the 1970s as a way to incorporate supersymmetry into the Standard Model of particle physics.

2. What is 1-loop cancellation in the Wess-Zumino model?

1-loop cancellation refers to a phenomenon in the Wess-Zumino model where certain quantum corrections to the theory cancel each other out at the one-loop level. This cancellation is necessary for the theory to be consistent and free of divergences.

3. How does 1-loop cancellation occur in the Wess-Zumino model?

1-loop cancellation occurs in the Wess-Zumino model due to the specific structure of the theory, which includes a chiral superfield and a vector superfield. These two types of superfields interact in such a way that certain quantum corrections to the theory cancel each other out, leading to a finite and consistent theory.

4. Why is 1-loop cancellation important in the Wess-Zumino model?

1-loop cancellation is important in the Wess-Zumino model because it ensures that the theory is free of divergences and able to make meaningful predictions about physical phenomena. Without 1-loop cancellation, the theory would be inconsistent and could not accurately describe the interactions between particles.

5. Can 1-loop cancellation occur in other supersymmetric models?

Yes, 1-loop cancellation can occur in other supersymmetric models as well. However, the specific conditions and interactions between superfields may be different in each model, so the mechanism of 1-loop cancellation may vary. Nonetheless, it remains an important concept in ensuring the consistency of supersymmetric theories.

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