Exploring the SMEFT in the top production at the LHC

The Standard Model Effective Field Theory (SMEFT) offers an efficient field theory method for collecting experimental evidence of the New Physics, regardless of the choice of underlying theoretical model. This method treats the Standard Model (SM) as a low energy manifestation of a broader fundamental theory and allows higher energy effects to be encoded by adding higher-dimensional operators to the Lagrangian. Therefore, by fitting the coefficients of these operators by the high-precision data obtained in experiments, it is possible to constrain a set of theoretical models to which a more complete model of reality might belong. The most natural way to look for New Physics effects is certainly to analyse the data obtained from the high energy experiments at the Large Hadron Collider (LHC) and in particular the data of the top quark production. In this thesis, the expressions of key observables, such as the differential and total cross section, are determined analytically at the LO level in the 6-dimensional SMEFT, for the production of top quark-antiquark pairs by proton collisions at the LHC. Expressions are found not only for the linear terms of the Wilson coefficients but also for their quadratic terms. The simulation data obtained with these observables are then compared with simulations retrieved with MadGraph5.