Majoron emission in muon and tau decays revisited

In models where the breaking of lepton number is spontaneous a massless Goldstone boson, the Majoron ($J$), appears. We calculate the theoretically allowed range for the branching ratios of Majoron-emitting charged lepton decays, such as $\mathrm{Br}(\mu \to eJ)$ and $\mathrm{Br}(\mu \to eJ\gamma )$, in a supersymmetric model with spontaneous breaking of $R$-parity. $\mathrm{Br}(\mu \to eJ)$ is maximal in the same region of parameter space for which the lightest neutralino decays mainly invisibly. A measurement of $\mathrm{Br}(\mu \to eJ)$ thus potentially provides information on $R$-parity violation complementary to accelerator searches. We also briefly discuss existing bounds and prospects for future improvements on the Majoron coupling to charged leptons.

Figure 1

Feynman diagrams for the decay $\mu \to eJ\gamma$. As in the standard model radiative decay $\mu \to e\overline{\nu }\nu \gamma$ these diagrams contain an infrared divergence for $m_{\gamma }=0$, see text.

Figure 2

Branching ratios for visible lightest neutralino decay (left) and branching ratio $\mathrm{Br}(\mu \to eJ)$ (right) versus $v_R$ in GeV for a number of different choices of $v_{\varphi }$ between $[1,{10}^2]\mathrm{TeV}$ indicated by the different colors. Darker colors indicate larger $v_{\varphi }$ in a logarithmic scale. mSugra parameters are defined in the text. There is very little dependence on the actual mSugra parameters, however; see discussion and Fig. 3.

Figure 3

Branching ratios for visible lightest neutralino decay versus branching ratio $\mathrm{Br}(\mu \to eJ)$ for two mSugra points, for various choices of $v_{\varphi }$, see Fig. 2. To the left, the same mSugra parameters as Fig. 2, to the right SPS1a’.

Figure 4

The phase space integral for the decay $\mu \to eJ\gamma$ as a function of $x_{\min }$ for three different values of $y_{\min }=0.95$, 0.99, 0.995 from top to bottom and for two different values of $\cos {\theta }_{e\gamma }$. To the left $\cos {\theta }_{e\gamma }=-0.99$, to the right $\cos {\theta }_{e\gamma }=-0.99997$.