Neutrino mass limit from tritium beta decay

Abstract

The paper reviews recent experiments on tritium beta spectroscopy searching for the absolute value of the electron neutrino mass $m(ν_e)$. By use of dedicated electrostatic filters with high acceptance and resolution, the uncertainty on the observable $m^2(ν_e)$ has been pushed down to about 3 eV$^2$. The new upper limit of the mass is $m(ν_e) < 2$ eV at 95% C.L. In view of erroneous and unphysical mass results obtained by some earlier experiments in beta decay, particular attention is paid to systematic effects. The mass limit is discussed in the context of current neutrino research in particle- and astrophysics. A preview is given of the next generation of beta spectroscopy experiments currently under development and construction; they aim at lowering the $m^2(ν_e)$-uncertainty by another factor of 100, reaching a sensitivity limit $m(ν_e) < 0.2$ eV.

Figures (34)

• Figure 1: Squared neutrino mass values obtained from tritium$\beta$-decay in the decisive period 1990-2005 plotted against the year of publication (see text for the references). The results from the more recent experiments in Mainz and Troitzk, presented in section 4, are already included.
• Figure 2: Neutrino mass eigenvalues$m\left(v_{\mathrm{i}}\right)$ (solid lines) and one third of the cosmological relevant sum of the three neutrino mass eigenvalues $\Sigma m\left(v_{\mathrm{i}}\right) / 3$ (dashed line) as a function of the smallest neutrino mass eigenvalue $m_{\text{min }}$ for normal hierarchy $m\left(v_{3}\right)>m\left(v_{2}\right)>m\left(v_{1}\right)$ (left) and inverted hierarchy $m\left(v_{2}\right)>m\left(v_{1}\right)>m\left(v_{3}\right)$ (right). The upper limit from tritium $\beta$-decay on $m\left(v_{e}\right)$ (solid line), which holds in the degenerate neutrino mass region for each $m\left(v_{\mathrm{i}}\right)$, and for $\Sigma m\left(v_{\mathrm{i}}\right) / 3$ (dashed line) is also marked. The hot dark matter contribution $\Omega_{\mathrm{v}}$ to the universe relating to the average neutrino mass $\Sigma m\left(v_{\mathrm{i}}\right) / 3$ is indicated by the right scale in the normal hierarchy plot and compared to all other known matter/energy contributions in the universe (middle). With the relic neutrino density of $336 / \mathrm{cm}^{3}$ the laboratory neutrino mass limit from tritium $\beta$-decay $m\left(v_{\mathrm{e}}\right)<2 \mathrm{eV}$ corresponds to a maximum allowed neutrino matter contribution in the universe of $\Omega_{v}<0.12$.
• Figure 3: Schematic view on different ways to generate light neutrino masses (charge conjugate neutrino states$v^{c}$ are plotted moving backward in time): a) Coupling a left-handed neutrino $v_{\mathrm{L}}$ to a right-handed light neutrino $\nu_{R}$ via the Higgs $\Phi$ (Dirac mass term). b) Coupling a left-handed neutrino $\nu_{L}$ to a right-handed heavy neutrino $\nu_{R}$ (via Higgs), transforming to its charge and parity conjugated mass state and back to the conjugate of the lefthanded neutrino (via Higgs) within the time allowed by the uncertainty principle (the heavy neutrino is integrated out and gives rise to the suppression of the light neutrino mass $\mathrm{m}_{\mathrm{v} 1}$ ). This mechanism is termed the Type 1 Seesaw-mechanism. c) Neutrino mass term by coupling of a left-handed neutrino to its charge and parity conjugated state via a Higgs-triplet $\Delta$, which couples twice to the Standard Model Higgs. This mechanism is called Type 2 Seesaw-mechanism.
• Figure 4: Observables of neutrinoless double$\beta$-decay $m_{\mathrm{ee}}$ (open band) and of direct neutrino mass determination by single $\beta$-decay $m\left(v_{\mathrm{e}}\right)$ (thin gray area sitting at the upper end of the $m_{\mathrm{ee}}$ band) versus the cosmological relevant sum of neutrino mass eigenvalues $\Sigma m\left(v_{\mathrm{i}}\right)$ for the case of normal hierarchy (left) and of inverted hierarchy (right). The width of the bands/areas is caused by the experimental uncertainties of the neutrino mixing angles (6) and in the case of $m_{\mathrm{ee}}$ also by the completely unknown Majorana- and CP-phases $\alpha_{2},\left(\alpha_{3}+2 \varphi\right)(13)$. Uncertainties of the nuclear matrix elements, which enter $m_{\mathrm{ee}}$, are not considered.
• Figure 5: Level diagram illustrating the relation between mass difference$\Delta M\left({ }^{3} \mathrm{He}, \mathrm{T}\right)$ measured by cyclotron resonance in a Penning trap [30] and the Q-values of molecular and atomic tritium decay.