Anatomy of $b \to c \tau \nu$ anomalies

In recent times, one of the strongest hints of Physics Beyond the Standard Model (BSM) has been the anomaly in the ratios RD and $$ {R}_{D^{*}} $$ measured in the charged current decays of B-mesons. In this work, we perform a comprehensive analysis of these decay modes, first in a model independent way and subsequently, in the context of composite Higgs models. We discuss in depth as to how linearly realised SU(2)L × U(1)Y symmetry imposes severe constraint on the various scenarios because of correlations with other ΔF = 1 processes and Z τ τ and Z ν ν couplings. In the composite Higgs paradigm with partial compositeness, we show that, irrespective of the flavour structure of the composite sector, constraints from ΔF = 2 processes bring the compositeness scale down to ∼ 650 GeV which is in tension with electroweak precision observables. In the presence of composite leptoquarks, the situation improves only marginally (a factor of $$ \sqrt{2} $$ in the compositeness scale), thus making the new states soon discoverable by direct searches at the LHC. We also comment on the possible explanation of the $$ {R}_{K,{K}^{*}} $$ anomalies within the composite Higgs framework.