A composite pNGB leptoquark at the LHC

The measurements of $R_K^{(*)}$ and $R_{D}^{(*)}$ by BaBar, Belle and the LHCb collaborations could be showing a hint of lepton flavor universality violation that can be accommodated by the presence of suitable leptoquarks at the TeV scale. We consider an effective description, with leptoquarks arising as composite pseudo Nambu-Goldstone bosons, as well as anarchic partial compositeness of the SM fermions. Considering the $R_K^{(*)}$ anomaly within this framework, we study pair production of $S_3\sim(\bar 3,3)_{1/3}$ at the LHC. We focus on the component $S_3^{1/3}$ of the triplet, which decays predominantly into $t\tau$ and $b\nu$, and study the bounds from existing searches at $\sqrt{s}=13$ TeV at the LHC. We find that sbottom searches in the $b\bar{b}$+MET final state best explore the region in parameter space preferred by our model and currently exclude $S_3^{1/3}$ masses up to $\sim$1 TeV. Additional searches, considering the $t\tau$ and $t\mu$ decay modes, are required to probe the full physical parameter space. In this paper we also recast existing studies on direct leptoquark searches in the $t\tau t\tau$ channel and SM $t\bar{t}t\bar{t}$ searches, and obtain the regions in parameter space currently excluded. Practically the whole physical parameter space is currently excluded for masses up to $\sim$0.8 TeV, which could be extended up to $\sim$1 TeV with the full Run 3 dataset. We conclude that pair production searches for this leptoquark can benefit from considering the final state $t \tau b$ +MET, where the largest branching ratio is expected. We appraise that future explorations of leptoquarks explaining the B-anomalies with masses beyond the TeV should also consider single and non-resonant production in order to extend the mass reach.