Lepton number violation in a little Higgs model

In this note we examine the constraints imposed by muon anomalous magnetic moment ($(g-2{)}_{\mu }$) and ${\mu }^{-}\to e^{+}{e}^{-}{e}^{-}$ on lepton number violating (LNV) couplings of the triplet Higgs in Little Higgs (LH) model.

Figure 1

Feynman diagrams contributing to $(g-2{)}_{\mu }$. The photon is to be hooked to all possible internal charged lines.

Figure 2

Feynman diagrams contributing to ${\mu }^{-}\to e^{+}{e}^{-}{e}^{-}$.

Figure 3

Contour plots in $m_{\varphi }$ and $Y$ plane. In the left panel we have assumed $Y_{\mu i}=0$ with $i=e,\mu ,\tau$ and $i\ne \mu$ and in the right panel we have assumed $Y_{\mu i}=Y_{\mu \mu }$. The shaded area indicates the region of $1\sigma$ and $2\sigma$ deviations.

Figure 4

Plot of $△a_{\mu }$ as a function of Higgs mass for various values of $Y$. In the left panel we have assumed $Y_{\mu i}=0$ with $i=e,\mu ,\tau$ and $i\ne \mu$ and in the right panel we have assumed $Y_{\mu i}=Y_{\mu \mu }$. The shaded area indicates $1\sigma$ and $2\sigma$ deviations.

Figure 5

Contour plot of branching ratio of ${\mu }^{-}\to e^{+}{e}^{-}{e}^{-}$ in $m_{\Phi }$- $Y_{ee}^{*}{Y}_{\mu e}$ plane (left). Plot of branching ratio of ${\mu }^{-}\to e^{+}{e}^{-}{e}^{-}$ as a function of Higgs mass for various Yukawa couplings (right). In the right panel the legends $a$, $b$, $c$, $d$ correspond to $Y_{ee}^{*}{Y}_{\mu e}$ values of $(1.5,1,0.5,0.2)\times {10}^{-5}$, respectively. The shaded area indicates the region ruled out by experimental data.