Higgs effective potential in the littlest Higgs model at the one-loop level

Abstract

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 $\ensuremath{\Lambda}$ and including all finite parts. We consider both, the $(SU(2)\ifmmode\times\else\texttimes\fi{}U(1){)}_{1}\ifmmode\times\else\texttimes\fi{}(SU(2)\ifmmode\times\else\texttimes\fi{}U(1){)}_{2}$ and the $(SU(2)\ifmmode\times\else\texttimes\fi{}U(1){)}_{1}\ifmmode\times\else\texttimes\fi{}(SU(2)\ifmmode\times\else\texttimes\fi{}U(1))$ 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.