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

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