Probing neutral triple gauge couplings via Z Z production at e + e − colliders with machine learning

Neutral triple gauge couplings (nTGCs) first arise from the dimension-8 operators of the Standard Model effective field theory (SMEFT), rather than the dimension-4 SM Lagrangian and dimension-6 SMEFT operators, opening up a unique window for probing new physics at the dimension-8 level. In this work, we formulate the nTGC form factors of Z Z V * ( V = Z , γ ) that are compatible with the spontaneous breaking of the SU ( 2 ) ⊗ U ( 1 ) electroweak gauge symmetry and consistently match the dimension-8 nTGC operators in the broken phase. We study the sensitivities for probing both the Z Z V * form factors and the corresponding new physics scales through Z Z production (with visible/invisible fermionic Z decays) at high energy e + e − colliders including CEPC, FCC-ee, LCF, ILC, and CLIC. In particular, we identify the dimension-8 operator that contributes to the pure triple Z boson coupling Z Z Z * alone, but not the mixed Z Z γ * coupling. We further study the correlations between probes of the Z Z Z * and Z Z γ * couplings. Using machine learning, we show that angular distributions of the final-state fermions can play key roles in suppressing the SM backgrounds. The sensitivities can be further improved by using polarized e ∓ beams, and we find that the optimal sensitivity bounds on the nTGC correlations are given by the mixed setting including both the unpolarized operation and the follow-up polarized operation. We demonstrate that machine learning is advantageous for handling the 4-body final states from Z Z decays and improves significantly the sensitivity reaches of probes of nTGCs in e + e − collisions. We find that nTGC new physics scales can be probed up to the multi-TeV scale at the proposed e + e − colliders.