Identità di Ward, γ 5 e SMEFT

In this work we have dealt with the problem of γ 5 in dimensional regularization. This an old problem, however it is still actual. The only scheme which allows us to efficiently calculate diagrams contributions is the dimensional regularization (DR), nevertheless this scheme forbids the construction of a proper chiral operator. This fact is due to the impossibility to extend γ 5 to arbitrary dimensions. One possible solution is the t'Hooft-Veltman scheme, in which γ 5 is defined in order to find the correct traces paying the price of a broken gauge symmetry. This break will generate spurious anomalies which spoil Ward identities (WIs), it has been shown how it is possible to fix these anomalies by hand in two-points WIs introducing the proper counterterms in the original Lagrangian. The first two chapters are devoted to a general introduction to effective theories and SMEFT focusing on the technical aspects needed to go through the actual calculations. In the last chapter we have analyzed the presence of anomalies in the three-points Green's functions WI involving Zγγ diagrams. In this case anomalies cancel when the WI is calculated in the SM but they do not if we take into account the SMEFT extension.