Hints and Combined Constraints for First Generation Leptoquarks

We present a combined analysis of the existing hints for, and constraints on, the first generation fermion couplings of all ten leptoquark (LQ) representations. At the precision frontier we study the bounds from $K\to\pi \bar{\nu} \nu$, $K\to\pi \ell^+\ell^-$, $K^0-\bar K^0$ mixing, $D^0-\bar D^0$ mixing and parity violation experiments (APV and $Q_{\text{weak}}$), as well as a potential resolution of the Cabibbo Angle Anomaly (CAA) via LQ contributions to the $\beta$-decay. Although the CAA could be explained by the LQ representations $\Phi_3, V_3$, we observe that the necessary parameter space is excluded by other observables barring cancellations between different contributions. On the high-energy side we consider direct searches for single resonant production and pair production of LQs as well as Drell-Yan-like LQ signatures. Particular emphasis is placed on the recent CMS analysis of lepton flavor universality in non-resonant di-lepton pairs. The measured deviations from SM predictions could be a signature of $t$-channel contributions from $\tilde{\Phi}_1, \Phi_2, \Phi_3, \tilde{V}_1, V_2 (\kappa_2^{RL} \neq 0)$ or $V_3$.