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 RK and $$ {R}_{K^{\ast }} $$ R K ∗ to the g − 2 lepton anomalies. The analysis begins with a theoretical, in depth, study of the μ/e ratios RK and $$ {R}_{K^{\ast }} $$ R K ∗ as well as the process Bs→ 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 RK and $$ {R}_K^{\ast } $$ R K ∗ 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.

We analyze the impact of the θ-angle and axion dynamics for two-color (in fact any Sp(2N )) QCD at nonzero baryon charge and as a function of the number of matter fields on the vacuum properties, the pattern of chiral symmetry breaking as well as the spectrum of the theory. We show that the vacuum acquires a rich structure when the underlying CP violating topological operator is added to the theory. We discover novel phases and analyse the order of their transitions characterizing the dynamics of the odd and even number of flavours. We further determine the critical chemical potential as function of the θ angle separating the normal from the superfluid phase of the theory. Our results will guide numerical simulations and novel tests of the model’s dynamics. The results are also expected to better inform phenomenological applications of the model ranging from composite Higgs physics to strongly interacting massive dark matter models featuring number changing interactions. In the companion work [1] we repurpose and upgrade the approach to determine the impact of the θ-angle and axion physics on non-perturbative near conformal dynamics related to the fixed baryon charge sector.

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