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 $R_D$ and $R_{D^{\ast }}$ 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 $\mathrm{S}\mathrm{U}(2{)}_{\mathrm{L}}\times \mathrm{U}(1{)}_{\mathrm{Y}}$ symmetry imposes severe constraint on the various scenarios because of correlations with other $\Delta F =1$processesand$Z,\tau,\tau$and$Z,\nu,\nu$ couplings. In the composite Higgs paradigm with partial compositeness, we show that, irrespective of the flavour structure of the composite sector, constraints from $\Delta F =2$processesbringthecompositenessscaledownto$\sim 650$ 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 $R_{K,K^{\ast }}$ anomalies within the composite Higgs framework.