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

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 $2σ$ 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 $2σ$ 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%.