Hadron collider probes of the quartic couplings of gluons to the photon and $Z$ boson

We explore the experimental sensitivities of measuring the gg → Zγ process at the LHC to the dimension-8 quartic couplings of gluon pairs to the Z boson and photon, in addition to comparing them with the analogous sensitivities in the gg → γγ process. These processes can both receive contributions from 4 different CP-conserving dimension-8 operators with distinct Lorentz structures that contain a pair of gluon field strengths, $ {\hat{G}}_{\mu v}^a $, and a pair of electroweak SU(2) gauge field strengths, $ {W}_{\mu v}^i $, as well as 4 similar operators containing a pair of $ {\hat{G}}_{\mu v}^a $ and a pair of U(1) gauge field strengths, B$_{μν}$. We calculate the scattering angular distributions for gg → Zγ and the Z → $ \overline{f}f $ decay angular distributions for these 4 Lorentz structures, as well as the Standard Model background. We analyze the sensitivity of ATLAS measurements of the Z(→ ℓ$^{+}$ℓ$^{−}$,$ \overline{\nu}\nu $,$ \overline{q}q $)γ final states with integrated luminosities up to 139 fb$^{−1}$ at $ \sqrt{s} $ = 13 TeV, showing that they exclude values ≲ 2 TeV for the dimension-8 operator scales, and compare the Zγ sensitivity with that of an ATLAS measurement of the γγ final state. We present combined Zγ and γγ constraints on the scales of dimension-8 SMEFT operators and γγ constraints on the nonlinearity scale of the Born-Infeld extension of the Standard Model. We also estimate the sensitivities to dimension-8 operators of experiments at possible future proton-proton colliders with centre-of-mass energies of 25, 50 and 100 TeV, and discuss possible measurements of the Z spin and angular correlations.