A systematic study of phenomenological implications of dim-6 operators

The Standard Model (SM) of particle physics has been producing reliable estimates to a high precision level in the last few decades. Moreover, the discovery of a scalar particle with properties consistent with the SM Higgs boson, together with the fact that no Beyond Standard Model (BSM) particle has been detected so far, suggests that the New Physics (NP) scale Lambda can be placed above the electro-weak symmetry breaking (EWSB) scale. Therefore, an effective field theory built solely using the SM fields, called Standard Model Effective Field Theory (SMEFT), can be used to describe the low energy limit of BSM physics. This theory should be written adding to the renormalizable SM interactions further terms of higher dimensions, suppressed by suitable powers of the scale Lambda and invariant under the SM gauge group. The schematic Lagrangian is L_SMEFT = LSM + L_5 + L_6 + ... L_5 contains only the Weinberg operator, which can be used to provide masses to neutrinos. Assuming the conservation of baryon number, in L_6 there are 59 operators, many of which have flavour indices (explicitly taking them into account, the number of operators grows up to 2499). The full one-loop anomalous dimension (AD) matrix needed for renormalization group evolution (RGE) of the dimension 6 operators has been recently computed; several entries have been found to be of order 1, therefore suggesting a relevant mixing between some of these operators. The SMEFT approach can be used to interpret several patterns of deviations in SM processes: it allows for model independent analysis, which is a particularly useful feature given our present lack of knowledge regarding the ultraviolet (UV) completion of the SM theory. The BSM fields can in fact be integrated out of the theory at the NP scale, in such a way that there is no evident sign of their presence at the EWSB scale, but their effects can be mimicked by means of the couplings of the higher dimension operators; it will therefore be possible to use experimental informations in order to constrain the bounds of the such couplings, which can be consequently reinterpreted as bounds on the NP scale once the SMEFT is mapped on the desired UV completion of the theory. In my PhD project, I have focused my attention to phenomenological implications due to the effect of dimension 6 operators. As a first step of my project, I have partially recomputing the AD, in order to check the correctness of their results. Subsequently, I have been involved in analyses concerning the status of the anomalies present in B physics, with a particular focus on b to s transitions. My work on the field, aiming at discerning the shape of the potential NP underling such processes and potentially disentangling it from effects stemming from QCD effects, is reported in Refs.~\cite{Ciuchini:2015qxb,Ciuchini:2016weo,Ciuchini:2017gva,Ciuchini:2017mik}. A systematic reinterpretation of such findings in the SMEFT framework is an original contribution to this PhD thesis, and is yet to be published. Moreover, I have spent some time working on the study of the trilinear Higgs self-coupling. Given the large room for NP effects to such coupling, induced by the present status of the experimental constraints, the (SM)EFT approach is not a phenomenologically-meaningful framework to employ in order to study potential BSM effects in this sector. Therefore, I have adopted an alternative method to approach the matter, exploiting the study of electroweak precision observables in order to further constrain the bound that can be put on the Higgs trilinear self-coupling~\cite{Degrassi:2017ucl}.