Muonium-antimuonium oscillations in an extended minimal supersymmetric standard model with right-handed neutrinos

The electron and muon number violating muonium-antimuonium oscillation process in an extended minimal supersymmetric standard model is investigated. The minimal supersymmetric standard model is modified by the inclusion of three right-handed neutrino superfields. While the model allows the neutrino mass terms to mix among the different generations, the sneutrino and slepton mass terms have only intragenerational lepton number violation and not intergenerational lepton number mixing. Thus, the muonium-antimuonium conversion can then be used to constrain those model parameters, which avoid further constraints from the $\mu \to e\gamma$ decay bounds. For a wide range of parameter values, the contributions to the muonium-antimuonium oscillation time scale are at least 2 orders of magnitude below the sensitivity of current experiments. However, if the ratio of the two Higgs field vacuum expectation values, $\tan \beta$, is very small, there is a limited possibility that the contributions are large enough for the present experimental limit to provide an inequality relating $\tan \beta$ to the light neutrino mass scale $m_{\nu }$, which is generated by the seesaw mechanism. The resultant lower bound on $\tan \beta$ as a function of $m_{\nu }$ is more stringent than the analogous bounds arising from the muon and electron anomalous magnetic moments as computed using this model.

Figure 1

Feynman graphs contributing to the muonium-antimuonium mixing.

Figure 2

The contribution of graphs (e) and (f) as a function of $m_{\tilde{\nu }}$ when fixing the $W$-ino mass to its lower limit $M_{{\tilde{W}}^{-}}$.

Figure 3

The lower limit on $\tan \beta$ as a function of the light neutrino mass scale $m_{\nu }$ provided by the muonium-antimuonium oscillation experiment. The area above the curve is allowed by the experiment results.

Figure 4

The Feynman graphs contributing to the muon anomalous magnetic moment beyond the standard model.

Figure 5

The lower limit on $\tan \beta$ as a function of the light neutrino mass scale $m_{\nu }$ provided by the muon anomalous magnetic moment experiment. The area above the curve is allowed by the experiment results.

Figure 6

The Feynman graphs contributing to the electron anomalous magnetic moment beyond the standard model.

Figure 7

The lower limit on $\tan \beta$ as a function of the light neutrino mass scale $m_{\nu }$ provided by the electron anomalous magnetic moment experiment. The area above the curve is allowed by the experiment results.