The collection of a few anomalies in semileptonic B-decays invites to speculate about the emergence of some strikingly new phenomena. Here we offer a possible interpretation of these anomalies in the context of a weakly broken U (2) 5 flavor symmetry and leptoquark mediators.

The collection of a few anomalies in semileptonic B-decays, especially in b → cτν, invites to speculate about the emergence of some striking new phenomena, perhaps interpretable in terms of a weakly broken U (2) n flavor symmetry and of leptoquark mediators. Here we aim at a partial UV completion of this interpretation by generalizing the minimal composite Higgs model to include a composite vector leptoquark as well.

In this paper we present a detailed analysis of the Electroweak Precision Observables (EWPO) in composite Higgs models based on the coset SO(5)/SO(4). In our study we include both the fermionic top partners and the spin-1 resonances and consider their possible interplay as well. In order to achieve calculability we use the assumptions of i) partial Ultra Violet Completion (PUVC) following [1] and, ii) absence of sizeable effects from physics above the cut-off. Apart from the EWPO, we also take into account the constraints from the top quark, Z and the Higgs boson masses whenever they can be predicted in terms of the model parameters. After presenting our analytic results (often, in certain limits) and discussing their symmetry properties, we also perform detailed fits of the model parameters following the Bayesian approach. We show the posterior probability distributions of the parameters in various scenarios and provide with analytic understanding whenever possible. We find that in certain cases the EWPO allow the compositeness scale to lie well below 1 TeV. Moreover, fermionic top partners of mass around 1 TeV and spin-1 resonances of mass around 2 − 3 TeV are consistent with the precision data. A Mass mixings 42 B Light physics contributions to the parameters 43 4 On the other hand, in order to generate the bottom mass one needs a X = −1/3 representation.

Minimal flavour violation in its strong or weak versions, based on U (3) 3 and U (2) 3 , respectively, allows suitable extensions of the standard model at the TeV scale to comply with current flavour constraints in the quark sector. Here we discuss considerations analogous to minimal flavour violation (MFV) in the context of SU (5)-unification, showing the new effects/constraints that arise both in the quark and in the lepton sector, where quantitative statements can be made controlled by the CKM matrix elements. The case of supersymmetry is examined in detail as a particularly motivated example. Third generation sleptons and neutralinos in the few hundred GeV range are shown to be compatible with current constraints.