One-loop radiative corrections to theρparameter in the littlest Higgs model

We perform a one-loop analysis of the $\rho$ parameter in the littlest Higgs model, including the logarithmically enhanced contributions from both fermion and scalar loops. We find that the one-loop contributions are comparable to the tree level corrections in some regions of parameter space. The fermion loop contribution dominates in the low cutoff scale f region. On the other hand, the scalar loop contribution dominates in the high cutoff scale f region and it grows with the cutoff scale f. This in turn implies an upper bound on the cutoff scale. A low cutoff scale is allowed for a non-zero triplet vacuum expectation value. Constraints on various other parameters in the model are also discussed. The role of triplet scalars in constructing a consistent renormalization scheme is emphasized.