The flavor of a minimal composite $S_1$ leptoquark and the $b\to c\tau \bar{\nu }$ anomaly

Abstract

Several experiments have measured a deviation in $B\to D^{(\ast )}$ semileptonic decays, that point to new physics at the TeV scale violating lepton flavor universality. A scalar leptoquark $S_1$, with a suitable structure of couplings in flavor space, is known to be able to solve this anomaly modifying $b\to c\tau \bar{\nu }$. In the context of composite Higgs models, we consider a theory containing $H$ and $S_1$ as Nambu-Goldstone bosons (NGBs) of a new strongly interacting sector, with ordinary resonances at a scale $\mathcal{O}(10)$ TeV. Assuming anarchic partial compositeness of the Standard Model (SM) fermions we calculate the potential of the NGBs that is dominated by the fermions of the third generation, we compute $R_{D^{(\ast )}}$ and estimate the corrections to flavor observables by the presence of $S_1$. We find that the SM spectrum and $m_{S_1}\sim$ TeV can be obtained with a NGB decay constant of order $\sim 5$ TeV. We obtain a robust correlation between the main corrections to $R_{D^{(\ast )}}$, $B_{K^{(\ast )}\nu \nu }$ and $g_{\tau }/g_{\mu }$, that leads to a sever bound on $R_{D^{(\ast )}}$, roughly $2\sigma$ below the experimental value. Besides the bounds on the flavor observables $g_{\tau }^W$, BR$(\tau \to \mu \gamma )$ and $\Delta m_{B_s}$ are saturated, with the first one requiring a coupling between resonances $g_{\ast }\lesssim 2$, whereas the second one demands $m_{S_1}\gtrsim 1.7$ TeV, up to corrections of $\mathcal{O}(1)$.

Comments: 36 pages, 4 figures, comments welcome, v2: references added, brief mention of recent Belle II measurements added, v3: bound from gtau/gmu added changing the numerical results and conclusions, title and abstract changed accordingly, matches JHEP version