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Double beta decay

The study of nuclear double beta decay sheds light on physics beyond the standard model. First, it provides a unique way to look for neutrino masses of the Majorana type. With such masses neutrinoless double beta decay ( $\beta\beta 0\nu$) $(A,Z)\rightarrow (A,Z+2) +e^- + e^-$ can occur. It violates lepton number conservation by two units. The half life is directly related to the effective neutrino mass: $$\langle m_{\nu} \rangle = \sum _{j=1}^{2N} \epsilon_j m_jU_......[ T_{1/2}^{0\nu}\right] \propto \langle m_{\nu} \rangle^{-2}.$$

Here m_j are the eigenmasses, N the number of flavours, $\epsilon_j$ the corresponding CP eigenvalues ($\pm1$), and U_ej the mixings of the mass eigenstates to the electron neutrino. The two electrons carry away all of the kinetic energy E₀ released in the decay. Second, the study of double beta decay gives insight on the coupling of the neutrino to hypothetical light neutral bosons, generically named Majorons ($\chi^0$). Such Majorons could be emitted in the $(A,Z) \rightarrow (A,Z+2) +e^- + e^- + \chi^0$ double beta decay ( $\beta\beta \chi^0$). The sum energy spectrum of the two electrons extends from 0 to E₀, as the Majoron carries away a fraction of the energy. Many models with Majorons have been built, including some in which two Majorons are emitted. In the oldest scheme the spectral shape is quite hard peaking at 2/3 E₀. The half life depends on $\langle g_{eff}\rangle$, the effective coupling constant of the Majoron to the neutrino:

$$\left[ T_{1/2}^{\chi^0}\right] \propto \langle g_{eff}\rangle ^{-2}.$$

For the sake of comparison, experimentalists usually interpret their results in terms of this model. The study of the allowed double beta decay ( $\beta\beta 2\nu$) $(A,Z) \rightarrow (A,Z+2) +e^- + e^- +\overline{\nu}_e+\overline{\nu}_e$ does not address fundamental questions. It is nevertheless interesting in the sense that it probes the nuclear models with which the nuclear matrix elements for all the decay modes are calculated. The corresponding elements must be known in order to interpret the measured half lives on $\beta\beta 0\nu$ and $\beta\beta \chi^0$ decay in terms of neutrino masses and Majoron coupling. In $\beta\beta 2\nu$ decay the spectrum of the sum energy of the two electrons ranges from 0 to E₀, and peaks at roughly 1/3 E₀.