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Leptoquarks have recently received much attention especially because they may provide an explanation to the $R_{D^{(*)}}$ and $R_{K^{(*)}}$ anomalies in rare $B$ meson decays. In a previous paper we proposed a systematic search strategy for all possible leptoquark flavors by focusing on leptoquark pair production. In this paper, we extend this strategy to large (order unity) leptoquark couplings which offer new search opportunities: single leptoquark production and $t$-channel leptoquark exchange with dilepton final states. We discuss the unique features of the different search channels and show that they cover complementary regions of parameter space. We collect and update all currently available bounds for the different flavor final states from LHC searches and from atomic parity violation measurements. As an application of our analysis, we find that current limits do not exclude the leptoquark explanation of the $B$ physics anomalies but that the high luminosity run of the LHC will reach the most interesting parameter space.
Leptoquarks occur in many new physics scenarios and could be the next big discovery at the LHC. The purpose of this paper is to point out that a model-independent search strategy covering all possible leptoquarks is possible and has not yet been full
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