Exploring scalar leptoquarks at muon collider via indirect signatures and right-handed neutrino-assisted decays

Scalar leptoquarks (sLQs) appear in a wide range of ultraviolet-motivated extensions of the Standard Model and provide a natural link between the quark and lepton sectors. In this work, we investigate the discovery potential of an sLQ doublet $\widetilde{R}_2(\mathbf{3},\mathbf{2},1/6)$ that couples to light quarks and right-handed neutrinos (RHNs) at the proposed muon collider. We analyze both indirect probes arising from $t$-channel sLQ exchange that affects the high-$p_T$ behavior of dijet spectra and direct searches exploiting pair and single production of the sLQs, incorporating the full interplay of kinematic thresholds and decay topologies. We find that indirect probes at muon colliders deliver remarkably robust sensitivity to the sLQ-quark-muon coupling over a broad mass range. Assuming a sub-$\mathcal{O}(1)$ Yukawa coupling, we achieve a $5σ$ sensitivity up to sLQ masses $\sim 4.0$ TeV ($7.0$ TeV) at $\sqrt{s}=5$ (10) TeV center-of-mass energy with $\mathcal{L}=3~\mathrm{ab}^{-1}$ ($10~\mathrm{ab}^{-1}$) integrated luminosity. Direct production channels provide complementary reach: pair production dominates below threshold, while single production, driven by the sLQ-quark-muon/RHN interaction, decisively extends the mass reach well into the multi-TeV regime. We demonstrate that with $\mathcal{O}(1)$ Yukawa couplings, the single production channel can probe sLQ masses up to $3.0$ TeV ($6.0$ TeV) for $\sqrt{s}=5$ TeV ($10$ TeV). Together, these channels enable a unified exploration of parameter space far beyond the projected capabilities of the HL-LHC, including regions where conventional charged-lepton signatures are subdominant.