Non-oscillation experiments

Direct kinematic limits on neutrino mass were reviewed by Vissani [46]. At present $m_{\nu_e} < 2.2$ eV from Mainz and Troisk, possibly improvable to around 0.4 eV. There is little room for laboratory improvement on $m_{\nu_\mu}$ or $m_{\nu_\tau}$. We must wait for a supernova.

Klapdor [29] reviewed neutrinoless double beta decay ( $\beta \beta_{0\nu}$), which can be driven by Majorana neutrino masses, as well as by other mechanisms involving supersymmetry with $R$-parity violation, heavy Majorana neutrinos, leptoquarks, extended gauge interactions, compositeness, or the violation of Lorentz invariance or the equivalence principle.

For light Majorana neutrinos, the amplitude is proportional to $\langle m_{\nu_e} \rangle$, defined in (). The current upper limit of 0.35 eV at 90% is from the Heidelberg-Moscow experiment. Some authors would allow larger values because of theoretical uncertainties in the nuclear matrix elements. There can be cancellations between the contributions of the individual terms in (), so that $\langle m_{\nu_e} \rangle$ can be smaller than the mass eigenvalues. In fact, a Dirac neutrino, for which $\langle m_{\nu_e} \rangle = 0$, can be usefully be thought of as two degenerate Majorana neutrinos with equal $U_{ei}$ and opposite CP-parities.

The existing limit eliminates the degenerate 3$\nu$ scenarios motivated by mixed dark matter, unless they are Dirac or there are finely tuned cancellations, and it excludes some of the 4$\nu$ schemes. There are proposals to extend the $\langle m_{\nu_e} \rangle$ sensitivity considerably. These include MOON (0.03 eV), EXO (0.01-0.03 eV) [81], CUORE (0.05 eV), and GENIUS [29]. The latter is a proposed enriched $Ge$ detector shielded by liquid nitrogen. A one ton version could reach 0.02 (0.006) eV in 1 (10) years, with 0.02 a typical expectation for the inverted model. A later 10 ton version could reach $2 \mbox{$\times$}10^{-3}$, slightly above the 0.001 needed to probe the LMA hierarchical solution. GENIUS could also search for WIMPs and could detect solar $pp$ and $^7Be$ $\nu$'s in real time.