g-2 del muone in SMEFT

We introduce the concept of EFT, and focalise the attention in the SMEFT model in dim=6. We define the Warsaw basis, and the Wilson coefficients. We introduce the tadpoles to treat the spontaneously symmetry breaking and the implications of the added terms in SMEFT. We find the self-energies for the photon, W, Z, leptons and for Z-A transition and fix the counter-terms (parameters and fields) to obtain UV finite quantities. Three points functions are calculated and discuss the necessary of mixing Wilson coefficients to obtain UV finiteness. We introduce the IR divergencies and the dimensional regularisation. We study, briefly, the KLN theorem and what is the correspondence for SMEFT. The g-2 is explicitly calculated and verified the IR finiteness. Finally, we derived, using numerical calculation, a distribution for g-2 observable and estimate the theoretical discrepancy from the SM prediction. In all the thesis, QED is used as a testbed to understand and explain the know-how to make all the precedent steps possible.