Can the 125 GeV Higgs be the Little Higgs?

After the discovery of the Higgs-like boson by the LHC 2012 it is the most important task to check whether this new particle is the Standard Model Higgs boson or something else. In this paper, we study whether the 125 GeV boson could be the pseudo-Goldstone boson of Little Higgs models. We derive limits on the parameter space of several Little Higgs models (simple group and product group models, with and without T-parity), both from the experimental data from ATLAS and CMS about the different Higgs discovery channels and the electroweak precision observables. We perform a fit of several Little Higgs models to all electroweak parameters from measurements of SLC, LEP, Tevatron, and LHC. For the Higgs searches, we include all available data from the summer conferences in 2012 as well as the updates from December 2012. We show that there always exists a region in the parameter space of the models under consideration where the measured chi(2) is equal or lower than the SM chi 2: a closer look at the minimum chi 2 will however reveal that the agreement with the collected data is not significantly better as within the SM. While for the models without T-parity the Little Higgs scale f is forced to be of the order 2-4 TeV in order to be compatible with the collected data, in the models with T-parity the scale f is constrained to be only above 0(500) GeV, reducing the amount of fine-tuning. We also show that these results are still driven by the electroweak precision measurements due to the bigger LHC data uncertainties.