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We present a detailed study concerning a new physics scenario involving fourfermion operators of the Nambu-Jona-Lasinio type characterized by astrong-coupling ultraviolet fixed point where composite particles are formed asbound states of elementary fermions at the scale $\Lambda ={\calO}(\text{TeV})$. After implementing the model in the Universal FeynRules Outputformat, we focus on the phenomenology of the scalar leptoquarks at the LHC andthe High-Luminosity option. Leptoquark particles have undergone extensivescrutiny in the literature and experimental searches, primarily relying on pairproduction and, more recently, incorporating single, t-channel, andlepton-induced processes. This study marks, for the first time, the examinationof these production modes at varying jet multiplicities. Novel mechanismsemerge, enhancing the total production cross-section, especially forleptoquarks couplings to higher fermion generations. A global strategy isdevised to capture all final state particles produced in association withleptoquarks or originating from their decay, which we termed ``exclusive'', inan analogy to the nomenclature used in nuclear reactions. The assessment of thesignificance in current and future LHC runs, focusing on the case of leptoquarkcoupling to a muon - $\textit{c}$ quark pair, reveals superior sensitivitycompared to ongoing searches. Given this heightened discovery potential, weadvocate the incorporation of exclusive leptoquark searches in futureinvestigations at the LHC.

Searching for exclusive leptoquarks with the Nambu-Jona-Lasinio composite model at the LHC and HL-LHC