Probing aQGCs from dimension-eight operators via neutral triboson production at muon colliders

We investigate the sensitivity of a future high-energy muon collider to neutral anomalous quartic gauge couplings (aQGCs) through neutral triboson production processes, specifically μ⁺μ⁻ → γγγ, $γγZ$, $γZZ$, and $ZZZ$. Within the Standard Model Effective Field Theory (SMEFT) framework, we focus on genuine dimension-eight transverse operators (OT₀--OT₉). The analysis is performed at prospective center-of-mass energies of √s = 3 TeV and 10 TeV with integrated luminosities of 1 ab⁻¹ and 10 ab⁻¹, respectively. Employing an optimized cut-and-count analysis and a χ² statistical framework incorporating a $5%$ systematic uncertainty, we derive projected 95% confidence level bounds on the corresponding Wilson coefficients. Our results demonstrate that the triphoton channel yields the most stringent constraints, particularly for the fT₈ and fT₉ coefficients, while channels involving Z bosons exhibit reduced sensitivity owing to leptonic branching ratio suppressions. Furthermore, we report constraints on the fT₃ and fT₄ coefficients, established here for the first time in this neutral triboson context, highlighting the powerful physics reach of multi-TeV muon colliders in probing electroweak gauge sector interactions.