By Ben Ayed M., El Mehdi K., Pacella F.

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Thus additional contributions to the fermion mass in the Wess–Zumino model results in a hard breaking of supersymmetry. Similarly, any additional contribution to just the quartic scalar interactions will result in the reappearance of a quadratic divergence in the correction to m 2A since these contributions only affect the last two diagrams in Fig. 2. Are there other soft SUSY breaking terms possible for the WZ model? 47). This tells us that the contribution of the A loop from the trilinear A3 interaction is exactly three times bigger than the contribution from the B loop from the AB 2 interaction (the coupling constants for these interactions are exactly equal).

4 Algebra of the SUSY charges We have already seen in Chapter 1 that a continuous symmetry transformation can be written in terms of the corresponding generator. This is also true of supersymmetry transformations, the difference being that the parameter of the transformation α is a Majorana spinor whose components anticommute with themselves and also with fermionic operators. 4), we may write the change of the field S under an infinitesimal SUSY transformation as, S → S = eiα¯ Q Se−iα¯ Q ≈ S + [iα¯ Q, S] = S + δS ≡ (1 − iα¯ Q)S .

B76, 310 (1974). 1 Lowest order diagrams contributing to quadratic divergences in the one-point function of A. perturbatively to order g gives,5 g −i √ 2 d4 y D FA (x − y) (−1)TrS F (y − y) + m D FB (y − y) + 3m D FA (y − y) , where the factor 3 in the last term arises from three possible contractions involving the A3 interaction term. The factor in the square brackets is proportional to Tr = d4 p −m p/ − m ψ d4 p 4m ψ − m p 2 − m 2ψ d4 p − 3m p 2 − m 2B d4 p − 3m p 2 − m 2B d4 p p 2 − m 2A d4 p .