Hadron Collider Probes of the Quartic Couplings of Gluons to the Photon and $Z$ Boson

Abstract

We explore the experimental sensitivities of measuring the $gg\to Z\gamma$ 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 $gg\to \gamma \gamma$ 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, ${\hat{G}}_{\mu \nu }^a$, and a pair of electroweak SU(2) gauge field strengths, $W_{\mu \nu }^i$, as well as 4 similar operators containing a pair of ${\hat{G}}_{\mu \nu }^a$ and a pair of U(1) gauge field strengths, $B_{\mu \nu }$. We calculate the scattering angular distributions for $gg\to Z\gamma$ and the $Z\to \bar{f}f$ decay angular distributions for these 4 Lorentz structures, as well as the Standard Model background. We analyze the sensitivity of ATLAS measurements of the $Z(\to {\ell }^{+}{\ell }^{-},\bar{\nu }\nu ,\bar{q}q)\gamma$ final states with integrated luminosities up to 139 fb${}^{-1}$ at $\sqrt{s}=13$ TeV, showing that they exclude values $\lesssim 2$ TeV for the dimension-8 operator scales, and compare the $Z\gamma$ sensitivity with that of an ATLAS measurement of the $\gamma \gamma$ final state. We present combined $Z\gamma$ and $\gamma \gamma$ constraints on the scales of dimension-8 SMEFT operators and $\gamma \gamma$ 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.

25 pages, 25 figures; part of the results were talked at CLHCP2021: https://indico.ihep.ac.cn/event/14560/session/6/contribution/113; v2, Fig.9 is updated by including combined results. 1 table is added; v3, several typos are corrected; v4, match to published version

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