Recent measurements of b → sµ + µ − processes at LHCb and BELLE have revealed tensions at the 2 − 3 σ level between the Standard Model (SM) prediction and the experimental results in the channels B → K * µ + µ − and B s → φµ + µ − , as well as in the lepton-flavor universality violating observable R K = Br(B → Kµ + µ − )/Br(B → Ke + e − ). Combined global fits to the available b → sµ + µ − data suggest that these tensions might have their common origin in New Physics (NP) beyond the SM because some NP scenarios turn out to be preferred over the SM by 4 − 5 σ. The fact that all these anomalies are related to muons further suggests a connection (and a common NP explanation) with the long-standing anomaly in the anomalous magnetic moment of the muon, a µ . In this article, we study the impact of a generic class of NP models featuring new heavy scalars and fermions that couple to the SM fermions via Yukawa-like interactions. We consider two different scenarios, introducing either one additional fermion and two scalars or two additional fermions and one scalar, and examine all possible representations of the new particles under the SM gauge group with dimension up to the adjoint one. The models induce one-loop contributions to b → sµ + µ − and a µ which are capable of solving the respective anomalies at the 2σ level, albeit a relatively large coupling of the new particles to muons is required. In the case of b → sµ + µ − , stringent constraints from B s − B s mixing arise which can be relaxed if the new fermion is a Majorana particle.

In this article we investigate in detail the possibility of accounting for the b → s + − anomalies via box contributions involving with new scalars and fermions. For this purpose, we first write down the most general Lagrangian which can generate the desired effects and then calculate the generic expressions for all relevant b → s Wilson coefficients. Here we extend previous analysis by allowing that the new particles can also couple to right-handed Standard Model (SM) fermions as preferred by recent b → s + − data and the anomalous magnetic moment of the muon. In the second part of this article we illustrate this generic approach for a UV complete model in which we supplement the Standard Model by a 4 th generation of vector-like fermions and a real scalar field. This model allows one to coherently address the observed anomalies in b → s + − transitions and in a µ without violating the bounds from other observables (in particular B s −B s mixing) or LHC searches. In fact, we find that our global fit to this model, after the recent experimental updates, is very good and prefers couplings to right-handed SM fermions, showing the importance of our generic setup and calculation performed in the first part of the article.

We computed the leading order Wilson coefficients relevant to all the exclusive b → s + − decays in the framework of the two Higgs doublet model (2HDM) with a softly broken Z 2 symmetry by including the O(m b ) corrections. We elucidate the issue of appropriate matching between the full and the effective theory when dealing with the (pseudo-)scalar operators for which keeping the external momenta different from zero is necessary. We then make a phenomenological analysis by using the measured B(B s → μ + μ − ) and B(B → K μ + μ − ) high−q 2 , for which the hadronic uncertainties are well controlled, and we discuss their impact on various types of 2HDM. A brief discussion of the decays with τ -leptons in the final state is provided too.

We compute the generic one-loop contribution involving scalar leptoquarks (LQ) to the W and Z leptonic decay widths. In our computation we include for the first time the finite terms and the corrections due to the external momenta of the electroweak bosons, which is a step beyond the leading-logarithmic approximation considered in the literature so far. We show that the terms we include can be numerically quite significant. They amount to about 20% for scalar LQ masses below 1.5 TeV, as currently allowed by the direct searches at the LHC. To further illustrate the relevance of our results we revisit a model with two light scalar LQs, proposed to accommodate the B-physics anomalies. We show that the finite terms we computed can reduce the tension with the Z-pole data.

We study perturbative unitarity constraints on generic Yukawa interactions where the involved fields have arbitrary quantum numbers under an ∏iSU(Ni) ⊗ U(1) group. We derive compact expressions for the bounds on the Yukawa couplings for the cases where the fields transform under the trivial, fundamental or adjoint representation of the various SU(N) factors. We apply our results to specific models formulated to explain the anomalous measurements of (g − 2)μ and of the charged- and neutral-current decays of the B mesons. We show that, while these models can generally still explain the observed experimental values, the required Yukawa couplings are pushed at the edge of the perturbative regime.