Big corrections from a little Higgs

We calculate the tree-level expressions for the electroweak precision observables in the $\mathrm{SU}\left(5\right)/SO\left(5\right)\mathrm{}$ littlest Higgs model. The source for these corrections are the exchange of heavy gauge bosons and a triplet Higgs vacuum expectation value (VEV). Weak isospin violating contributions are present because there is no custodial $\mathrm{SU}\left(2\right)\mathrm{}$ global symmetry. The bulk of these weak isospin violating corrections arise from heavy gauge boson exchange while a smaller contribution comes from the triplet Higgs VEV. A global fit is performed to the experimental data and we find that throughout the parameter space the symmetry breaking scale is bounded by $f>\mathrm{}4\mathrm{}\mathrm{TeV}$ at 95% C.L. Stronger bounds on f are found for generic choices of the high energy gauge couplings. We find that even in the best case scenario one would need fine-tuning of less than a percent to get a Higgs boson mass as light as 200 GeV.