Improving third-generation leptoquark searches with combined signals and boosted top

Search strategies for the third-generation leptoquarks (LQs) are distinct from other LQ searches, especially when they decay to a top quark and a $\tau$ lepton. We investigate the cases of all TeV-scale scalar and vector LQs that decay to either a top-tau pair (charge-$1/3$ and $5/3$ LQs) or a top-neutrino pair (charge-$2/3$ LQs). One can then use the boosted top (which can be tagged efficiently using jet-substructure techniques) and high-$p_{\rm T}$ $\tau$ leptons to search for these LQs. We consider two search channels with either one or two taus along with at least one hadronically decaying boosted top quark. We estimate the high luminosity LHC (HL-LHC) search prospects of these LQs by considering both symmetric and asymmetric pair and single production processes. Our selection criteria are optimised to retain events from both pair and single production processes. The combined signal has better prospects than the traditional searches. We include new three-body single production processes to enhance the single production contributions to the combined signal. We identify the interference effect that appears in the dominant single production channel of charge-$1/3$ scalar LQ ($S^{1/3}$). This interference is constructive if $S^{1/3}$ is weak-triplet and destructive, for a singlet one. As a result, their LHC prospects differ appreciably.