### Higgs couplings and Naturalness in the littlest Higgs model with T-parity at the LHC and TLEP

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Motivated by the recent LHC Higgs data and null results in searches for any new physics, we investigate the Higgs couplings and naturalness in the littlest Higgs model with T-parity. By performing the global fit of the latest Higgs data, electroweak precise observables and $R_{b}$ measurements, we find that the scale $f$ can be excluded up to 600 GeV at $2\sigma$ confidence level. The expected Higgs coupling measurements at the future collider TLEP will improve this lower limit to above 3 TeV. Besides, the top parnter mass $m_{T_{+}}$ can be excluded up to 880 GeV at $2\sigma$ confidence level. The future HL-LHC can constrain this mass in the region $m_{T_{+}} < 2.2$ TeV corresponding to the fine-tuning being lager than 1\%.