Status of leptoquark models after LHC Run-2 and discovery prospects at future colliders

We study limits from dilepton searches on leptoquark completions to the Standard Model in the parameter space motivated by anomalies in the $b \rightarrow s$ sector. After a full Run-2 analysis by LHCb, the disparity in lepton flavour violation has disappeared. However, the mismatch in angular distributions as well as in $B_s \rightarrow \mu^+ \mu^-$ partial width is still unresolved and still implies a possible new physics contribution. We probe three models of leptoquarks -- scalar models $S_3$ and $R_2$ as well as vector leptoquark model $U_1$ using non-resonant dilepton searches to place limit on both the mass and couplings to SM fermions. The exclusions of leptoquarks coupling either non-uniformly to different lepton flavours or uniformly is examined. Interestingly, if leptoquark couplings to electrons and muons are indeed universal, then the $U_1$ model parameter space that corresponds to the anomalous contribution should already accessible with Run-2 data in the non-resonant $e\mu$ channel. In the non-universal case, there is a significant exclusion in couplings, but not enough to reach regions that explain observed anomalies. We, therefore, examine the prospective sensitivity at the HL-LHC as well as of a 3 TeV future muon collider. For the vector leptoquark model, we find that a muon collider can probe all of the relevant parameter space at 95% confidence with just 1 fb$^{-1}$ data whereas $R_2$ and $S_3$ models can be excluded at 95% with 5 fb$^{-1}$ and 6.5 fb$^{-1}$ luminosity respectively.