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Composite Neutrinos and Double Beta Decay

Neutrinoless double beta decay $(\b\b)_{0ν}$ occurs through the magnetic coupling of dimension five, $λ_W^{(ν*)}/m_{ν*}$, among the excited electron neutrino $ν^*$, electron and $W$ boson if $ν^*$ is a massive Majorana neutrino. If the coupling is not small, i.e., $λ_W^{(ν*)}>1$ the mass of the excited neutrino must not be gless than the $Z$ boson mass, $m_Z$. Since $ν^*$ contributes in the $(\b\b)_{0ν}$ decay as a vertual state, this decay will give an oppotunity to explore the much heavier mass region of $ν^*$. In this paper, we present the decay formula of $(\b\b)_{0ν}$ decay through the $ν^*$ exchange and discuss the constraint on the coupling constant and the mass of the excited neutrino. By comparing the recent data for ${}^{76}$Ge, we find $λ_W^{(ν*)}({1\rm TeV}/m_{ν*})) (m_N/{1\rm TeV})^{\frac 12}< 4.1\cdot 10^{-3}$ where $m_N$ is the Majorana mass of the excited electron neutrino. If $m_N=m_{ν*}$ and $λ_W^{(ν*)}>1$, we find the mass bound for the excited Majorana neutrino as $m_{ν^*} > 5.9\cdot 10^4$TeV. In order to obtain the constraint on the composite scale $Λ$, we have to specify the model. For the mirror type and the homodoublet type models, $λ_W^{(ν*)}/m_{ν*}=f/(\sqrt 2 Λ)$ where $f$ is the relative strength of gauge couplings. Then, we obtain $Λ> 170 f (m_N/{1\rm TeV})^{\frac 12}$TeV. For the sequential type model, $λ/m_{ν*}=fv/(\sqrt 2 Λ^2)$ where $v$ is the vacuum expectation value of the dopublet Higgs boson, i.e., $v=$250GeV. In this model, we find $Λ> 6.6 f^{\frac 12} (m_N/{1\rm TeV})^{\frac 14}$TeV.