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

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 14TeV to 100TeV. 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 500–3000GeV. 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 120fb 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.

💡 Research Summary

The manuscript investigates the prospects of discovering vector leptoquarks (VLQs) at future high‑energy linear electron‑positron colliders, focusing on the impact of longitudinal beam polarization. VLQs are motivated by persistent anomalies in B‑meson decays and the muon anomalous magnetic moment, and the authors consider a concrete extension of the Standard Model that introduces a color‑triplet vector leptoquark U₁, a heavy color‑octet boson G′, and a neutral singlet Z′. The interaction Lagrangian for U₁ includes chiral couplings to left‑handed quark‑lepton doublets (λ⁽ᴸ⁾) and right‑handed down‑type quarks and charged leptons (λ⁽ᴿ⁾), allowing the leptoquark to mediate tree‑level lepton‑quark transitions.

The study implements the model in a FeynRules UFO file and generates events with MadGraph5_aMC@NLO, interfacing to Pythia8 for parton showering. The central process is e⁻e⁺ → VLQ VLQ̄, with subsequent decays VLQ → b τ⁺ and VLQ̄ → b̄ τ⁻. The authors vary the electron (Pₑ⁻) and positron (Pₑ⁺) longitudinal polarizations from –1 to +1 and derive the polarized cross‑section formula (Eq. 6) that decomposes the total rate into helicity‑specific components σ_RR, σ_LL, σ_RL, and σ_LR. Because the s‑channel vector exchange conserves total angular momentum J = 1, only the RL and LR helicity configurations contribute, making the choice of beam polarizations a powerful lever.

A compact expression in terms of an effective polarization P_eff and a left‑right asymmetry A_LR (Eqs. 7–10) shows that the observable cross‑section scales as (1 – Pₑ⁻Pₑ⁺) σ₀