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 $μ^+μ^- \to γγγ$, $γγZ$, $γZZ$, and $ZZZ$. Within the Standard Model Effective Field Theory (SMEFT) framework, we focus on genuine dimension-eight transverse operators ($\mathcal{O}_{T_0}$--$\mathcal{O}_{T_9}$). The analysis is performed at prospective center-of-mass energies of $\sqrt{s} = 3\text{ TeV}$ and $10\text{ TeV}$ with integrated luminosities of $1\text{ ab}^{-1}$ and $10\text{ ab}^{-1}$, respectively. Employing an optimized cut-and-count analysis and a $χ^2$ 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 $f_{T_8}$ and $f_{T_9}$ coefficients, while channels involving $Z$ bosons exhibit reduced sensitivity owing to leptonic branching ratio suppressions. Furthermore, we report constraints on the $f_{T_3}$ and $f_{T_4}$ 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.