Little Higgs theory confronted with the LHC Higgs data

We confront the little Higgs theory with the LHC Higgs search data (up to 17 fb$^{-1}$ of the combined 7 and 8 TeV run). Considering some typical models, namely the littlest Higgs model (LH), the littlest Higgs model with T-parity (LHT-A and LHT-B) and the simplest little Higgs model (SLH), we scan over the parameter space in the region allowed by current experiments. We find that in these models the inclusive and exclusive (via gluon-gluon fusion) diphoton and $ZZ^*$ signal rates of the Higgs boson are always suppressed and approach to the SM predictions for a large scale $f$. Thus, the $ZZ^*$ signal rate is within the $1\sigma$ range of the experimental data while the inclusive diphoton signal rate is always outside the $2\sigma$ range. Especially, in the LHT-A the diphoton signal rate is outside the $3\sigma$ range of the experimental data for $f < 800$ GeV. We also perform a global $\chi^2$ fit to the available LHC and Tevatron Higgs data, and find that these models provide no better global fit to the whole data set (only for some special channels a better fit can be obtained, specially in the LHT-B).