Lepton flavor violation in hadronic decays of the tau lepton in the simplest little Higgs model

We study lepton flavor violating hadron decays of the tau lepton within the simplest little Higgs model. Namely we consider $\tau \to \mu (P,V,PP)$ where $P$ and $V$ are short for a pseudoscalar and a vector meson. We find that, in the most positive scenarios, branching ratios for these processes are predicted to be, at least, four orders of magnitude smaller than present experimental bounds.

Figure 1

Penguin-like diagrams for $\tau \to \mu {\gamma }^{*}$ in the SLH model.

Figure 2

Penguin-like diagrams for $\tau \to \mu Z$, $Z^{\prime }$ in the SLH model.

Figure 3

Box diagrams for $\tau \to \mu q\overline{q}$ in the SLH model. The internal quark states are $(u,\overline{u})\to \{d,D\}$, $(d,\overline{d})\to \{u\}$, $(s,\overline{s})\to \{c\}$.

Figure 4

Dependence of the scale of compositeness $f$ for the branching ratios of LFV tau decays into hadrons in the SLH model. They are normalized to the present upper bounds in Table 2, i.e. a value of 1 in the y-axis indicates the present upper limit. We use ${\chi }_1=0.25$, ${\chi }_2=10{\chi }_1$, $t_{\beta }=5$ and $\sin 2\theta =0.25$.

Figure 5

Dependence of the LFV branching ratios on $M_{N_1}$. On the left we assume a small splitting of the heavy neutrino spectrum: ${\chi }_2=1.1{\chi }_1$. On the right we assume a large splitting: ${\chi }_1=10{\chi }_2$. We input $t_{\beta }=5$, $\sin 2\theta =0.25$ and $f=6\mathrm{TeV}$. Normalization as in Fig. 4.

Figure 6

Dependence of the LFV branching ratios on $\tan \beta$ (left) and $\sin 2\theta$ (right). We input $(f,\sin 2\theta )=(6\mathrm{TeV},0.25)$ on the left plot and $(f,t_{\beta })=(6\mathrm{TeV},5)$ on the right plot. ${\chi }_1=0.25$, ${\chi }_2=10{\chi }_1$ are used in both panels. Normalization as in Fig. 4.

Figure 7

Scattered plots that show correlations between different branching ratios: $B(\tau \to \mu {\pi }^{+}{\pi }^{-})$ versus $B(\tau \to \mu \gamma )$ (upper plot), $B(\tau \to \mu {\pi }^0)$ versus $B(\tau \to \mu \gamma )$ (middle plot) and $B(\tau \to \mu {\pi }^0)$ versus $B(\tau \to \mu {\pi }^{+}{\pi }^{-})$ (lower plot). We vary $f\in (2\mathrm{TeV},10\mathrm{TeV})$, $\sin 2\theta \in (0,0.25)$, $t_{\beta }\in (1,10)$, ${\chi }_1\in (0,0.25)$ and ${\chi }_2=a{\chi }_1$ for $a\in (1.1,10)$. Red lines indicate the present upper bound for $B(\tau \to \mu \gamma )$ at 90% C.L.

Figure 8

Dependence on the scale of compositeness $f$ for $\tau \to \mu {\pi }^{+}{\pi }^{-}$ showing the relative weights of the different contributions in the unitary gauge. Normalization and input as in Fig. 4.

Figure 9

Dependence on the scale of compositeness $f$ for $\tau \to \mu {\pi }^0$ showing the relative weights of the different contributions in the unitary gauge. Normalization and input as in Fig. 4.