Non-minimal Higgs-gravity coupling and naturalness at the LHC and beyond

The non-minimal Higgs-gravity coupling, $\xi H^{†}HR$, can play an interesting role in particle physics. We utilize the available LHC Run-2 data to obtain the bound on the coupling $\xi$ and discuss the prospects of constraining it at CEPC, FCC-ee and ILC. Also, we investigate its implication on the naturalness.