One-loop Radiative Corrections to the rho Parameter in the Littlest Higgs Model

Abstract

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 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 VEV. Constraints on various other parameters in the model are also discussed. The role of triplet scalars in constructing a consistent renormalization scheme is emphasized.

Figures (12)

• Figure 1: Prediction for $M_{W_{L}}$ as a function of the mixing angle $s^\prime$ at the tree level and the one-loop level. Also plotted is the correlation between $M_{Z}$ and $s^\prime$ for fixed $s$, $v^{\prime}$ and $f$. The cutoff scale $f$ in this plot is $2$$TeV$, the $SU(2)$ triplet VEV $v^\prime = 3.4 \; GeV$, the mixing angle $s=0.22$, and $x_{L}=0.4$.
• Figure 2: Prediction for $M_{W_{L}}$ as a function of the mixing angle $s^\prime$ at the tree level and the one-loop level. Also plotted is the correlation between $M_{Z}$ and $s^\prime$ for fixed $s$, $v^{\prime}$ and $f$. The cutoff scale $f$ in this plot is $3$$TeV$, the $SU(2)$ triplet VEV $v^\prime = 1.54 \; GeV$, the mixing angle $s=0.2$, and $x_{L}=0.4$.
• Figure 3: Prediction for $M_{W_{L}}$ as a function of the mixing angle $s^\prime$ at the tree level and the one-loop level. Also plotted is the correlation between $M_{Z}$ and $s^\prime$ for fixed $s$, $v^{\prime}$ and $f$. The cutoff scale $f$ in the plot is $4$$TeV$, the $SU(2)$ triplet VEV $v^\prime = 0.88 \; GeV$, the mixing angle $s=0.2$, and $x_{L}=0.4$.
• Figure 4: Parametric plot of $M_{W_{L}}-M_{Z}$ in terms of $s^\prime$ for different values of the $SU(2)$ triplet VEV, $v^\prime = 0, \, 1.0, \, 1.56, \, 2.0$ and $2.5$. The cutoff scale $f$ is $3$$TeV$, the mixing angle $s=0.2$, and $x_{L}=0.4$. The data point with error bars on $M_{W_{L}}$ and $M_{Z}$ is also shown.
• Figure 5: Allowed parameter space on the $(x_{L},s)$-plane, for $f=2, \; 3, \; 4, \; 5, \; 6$ TeV. The triplet VEV $v^{\prime}$ is allowed to vary between $0$ and the upper bound given by Eq. \ref{['vvprelation']}. For $f=(2,3,4,5,6)$ TeV, this bound is $v^{\prime}_{\hbox{\tiny max}} = (3.78, \, 2.52, \, 1.89, \, 1.51, \, 1.26)$ GeV.