The Higgs effective potential in the Littlest Higgs model at the one-loop level

In this work we compute the contributions to the Higgs effective potential coming from the fermion and gauge boson sectors at the one-loop level in the context of the SU(5)/SO(5) Littlest Higgs (LH) model using a cutoff Lambda and including all finite parts. We consider both, the (SU(2)xU(1))_{1} x (SU(2)xU(1))_{2} and the (SU(2)xU(1))_{1} x (SU(2)xU(1)) gauge group versions of the LH model. We also show that the Goldstone bosons present in the model do not contribute to the effective potential at the one-loop level. Finally, by neglecting the contribution of higher dimensional operators, we discuss the restrictions that the new one-loop contributions set on the parameter space of the LH model and the need to include higher loop corrections to the Higgs potential.