Impact of Colliding Beams Helicity on the Production of Leptoquarks and Collider Experimental Parameters

Abstract: Vector Leptoquarks (VLQs) have emerged as primary candidates for resolving discrepancies in the Standard Model, specifically within $B$-meson decay channels and the anomalous magnetic moment of the muon. This work presents a rigorous evaluation of VLQ pair production across $e^{-}e^{+}$ collision modes at future linear colliders with center-of-mass energies ranging from 14~TeV to 100~TeV. Our analysis demonstrates that longitudinal beam polarization is a transformative tool for enhancing signal sensitivity. We find that $e^{-}e^{+}$ annihilation consistently yields superior cross-sections compared to photon fusion processes across a mass range of 500--3000~GeV. By optimizing beam helicity to specific configurations, such as $P_{e^{-}} = -0.8$ and $P_{e^{+}} = +0.6$, the production cross-section can be maximized to 120~fb at $\sqrt{s} = 3$~TeV. We further establish that the Left-Right Asymmetry ($A_{LR}$) serves as a robust discriminator for the chiral structure of new physics, peaking at 0.16 under full polarization. Additionally, we show that effective luminosity can be enhanced to 95\% of the total luminosity, while high polarization degrees significantly suppress relative uncertainties in the effective polarization. These results provide a quantitative roadmap for optimizing discovery potential and minimizing systematic errors in future high-energy physics experiments.