Standard model anomalies: Lepton flavour non-universality and lepton $g-2$

We critically analyze the body of results that hints to the existence of New Physics from possible violations of lepton universality observed by the LHCb experiment in the μ/e ratios R$_{K}$ and $ {R}_{K^{\ast }} $ to the g − 2 lepton anomalies. The analysis begins with a theoretical, in depth, study of the μ/e ratios R$_{K}$ and $ {R}_{K^{\ast }} $ as well as the process B$_{s}$→ μ$^{+}$μ$^{−}$. Here we consider the impact of complex Wilson coefficients and derive constraints on their imaginary and real parts. We then move to a comprehensive comparison with experimental results. We show that, by fitting a single Wilson coefficient, the deviations from the Standard Model are at the 4.7σ level when including only the hadronic insensitive observables while it increases to 6.1σ when including also the hadronic sensitive ones. When switching on all relevant Wilson coefficients and combining both hadronic sensitive and insensitive data into the fit, the deviation from the Standard Model peaks at 7.2σ and decreases at the 4.9σ level if we assume that the central values of R$_{K}$ and $ {R}_K^{\ast } $ are taken to be unity. We further estimate other unaccounted for SM contributions and show that their inclusion still requires New Physics to fit the data. We then introduce the g − 2 lepton anomalies as well as the most recent W-mass results. Different theoretical models are considered that can explain the discrepancies from the Standard Model. In the final part of our work we estimate the impact of the forthcoming data from LHCb (coming from LHC Run3) and Belle II, when it will have accumulated about 5 ab$^{−1}$.