Muon collider probes of the gluonic quartic gauge couplings

We investigate the dimension-8 gluonic quartic gauge couplings (gQGCs) at future high-energy muon colliders through the process $\mu^{+}\mu^{-}\!\to gg\gamma$. Using detailed event simulation and optimized kinematic selections, we derive projected sensitivities to the Wilson coefficients and their associated new-physics scales, showing that muon colliders can probe deep into the multi-TeV regime and significantly surpass current LHC bounds. We further present the positivity bounds on those Wilson coefficients, as theoretical constraints from the fundamental principles of quantum field theory. Our results establish $\mu^{+}\mu^{-}\!\to gg\gamma$ as one of the most sensitive probes of dimension-8 new physics at future muon colliders.