Composite Neutrinos and Double Beta Decay

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