Model for the singlet-triplet leptoquarks

The deviations of $B$-meson decays measured in $R_{D^{(*)}}^{\tau \ell }$ and $R_{K^{(*)}}^{\mu e}$ can be explained by the presence of two scalar leptoquarks, a singlet $S_1$ and a triplet $S_3$, mostly coupled to the third generation. We consider a theory of resonances, as an effective description of a strongly interacting theory, that generates the leptoquarks and the Higgs as Nambu-Goldstone bosons, with the rest of the resonances at a scale of order 10–30 TeV. We assume anarchic partial compositeness for the flavor of the SM fermions. Under this hypothesis, we study whether it is possible to reproduce the deviations in the $B$ decays without being in conflict with flavor and electroweak bounds. We find a tension between $R_{D^{(*)}}^{\tau \ell }$ and some flavor observables, dominated by flavor violating $\tau$ decays and $\mathrm{\Delta }{m}_{B_s}$, that require a tuning of order 10%–25%. We also compute the potential of the scalars showing that leptoquarks with masses $O(2–3)\mathrm{TeV}$ can be naturally expected in the model. We discuss briefly the phenomenology of the other resonances.

Figure 1

Distribution of required values for ${\mathrm{\Delta }}_{R_{D^{(*)}}}$ and ${\mathrm{\Delta }}_{R_{K^{(*)}}}$ for points passing all flavor observables with the other ${\mathrm{\Delta }}_O\simeq 1$. The colored curves show the estimates of the bounds coming from Eq. (85) and below for $M=1.5\mathrm{TeV}$. The regions excluded following those approximations have been shaded.

Figure 2

Scans in each pair of compositeness fraction ${\epsilon }_f$ for fixed $\delta =\mathrm{values}$.

Figure 3

Left panel: current bounds. Right panel: expected increase in sensitivity for LFV in $\tau$ decays.