• anomalos magnetic moment of tau particle

The starting point of the thesis is to understand Beyond the Standard Model (BSM) corrections to $a_{\tau}$ making use of the SM effective field theory (SMEFT). This theory consists in adding to the Standard Model Lagrangian higher dimensional operators with the correct symmetry properties. These terms are suppressed with the correct power of the inverse of an energy scale $\Lambda$ and this scale of new physics is assumed to be much higher than the largest energy scale involved in the process studied.\\
The main contribution to $a_\tau$, according to this formulation, can be included by adding the following operator to the Standard Model Lagrangian:
\begin{equation}
\frac{1}{\Lambda^2} (\bar l_L\sigma_{\mu\nu} \tau_R)HF^{\mu\nu}
\label{eq:operator}
\end{equation}
which describes the interaction between two leptons, (in the case of interest two tau particles), one Higgs boson, and photons.
\\
The study of the effect of the introduction of this operator in high-energy scattering processes can be studied through numerical simulations. \\
Thus, after an introduction to the SM, the historical calculations on $g-2$ and the SMEFT framework we report on the study carried out. We estimate the effects of adding the operator of dimension six [\ref{eq:operator}] to the Lagrangian of the SM by calculating the differential cross sections of the processes $ q \; \bar q \rightarrow \tau^+ \; \tau^-$ and $ q \; \bar q \rightarrow \tau^+ \; \tau^- \; H$ analytically. We optimise the simulation variables by maximising significance. In particular we optimise the choice of simulation parameters such as the minimum momentum (pTmin), the maximum pseudorapidity ($\eta_{max}$) and the invariant mass of the outgoing leptons. Finally we place a bound on the Wilson coefficient of the dimension six operator [\ref{eq:operator}] with a confidence level of 95\%.