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Register a new userEffective neutrino masses in KATRIN and future tritium beta-decay experiments
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Past and current direct neutrino mass experiments set limits on the so-called effective neutrino mass, which is an incoherent sum of neutrino masses and lepton mixing matrix elements. The electron energy spectrum which neglects the relativistic and nuclear recoil effects is often assumed. Alternative definitions of effective masses exist, and an exact relativistic spectrum is calculable. We quantitatively compare the validity of those different approximations as function of energy resolution and exposure in view of tritium beta decays in the KATRIN, Project 8 and PTOLEMY experiments. Furthermore, adopting the Bayesian approach, we present the posterior distributions of the effective neutrino mass by including current experimental information from neutrino oscillations, beta decay, neutrinoless double-beta decay and cosmological observations. Both linear and logarithmic priors for the smallest neutrino mass are assumed.
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The paper reviews recent experiments on tritium beta spectroscopy searching for the absolute value of the electron neutrino mass $m( u_e)$. By use of dedicated electrostatic filters with high acceptance and resolution, the uncertainty on the observable $m^2( u_e)$ has been pushed down to about 3 eV$^2$. The new upper limit of the mass is $m( u_e) < 2$ 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 $m^2( u_e)$-uncertainty by another factor of 100, reaching a sensitivity limit $m( u_e) < 0.2$ eV.
In the near future, the neutrinoless double-beta ($0 ubetabeta$) decay experiments will hopefully reach the sensitivity of a few ${rm meV}$ to the effective neutrino mass $|m^{}_{betabeta}|$. In this paper, we tentatively examine the sensitivity of future $0 ubetabeta$-decay experiments to neutrino masses and Majorana CP phases by following the Bayesian statistical approach. Provided experimental setups corresponding to the sensitivity of $|m^{}_{betabeta}| simeq 1~{rm meV}$, the null observation of $0 ubetabeta$ decays in the case of normal neutrino mass ordering leads to a very competitive bound on the lightest neutrino mass $m^{}_1$. Namely, the $95%$ credible interval turns out to be $1.6~{rm meV} lesssim m^{}_1 lesssim 7.3~{rm meV}$ or $0.3~{rm meV} lesssim m^{}_1 lesssim 5.6~{rm meV}$ when the uniform prior on $m^{}_1/{rm eV}$ or on $log^{}_{10}(m^{}_1/{rm eV})$ is adopted. Moreover, one of two Majorana CP phases is strictly constrained, i.e., $140^circ lesssim rho lesssim 220^circ$ for both priors of $m^{}_1$. In contrast, if a relatively worse sensitivity of $|m^{}_{betabeta}| simeq 10~{rm meV}$ is assumed, the constraint becomes accordingly $0.6~{rm meV} lesssim m^{}_1 lesssim 26~{rm meV}$ or $0 lesssim m^{}_1 lesssim 6.1~{rm meV}$, while two Majorana CP phases will be essentially unconstrained. In the same statistical framework, the prospects for the determination of neutrino mass ordering and the discrimination between Majorana and Dirac nature of massive neutrinos in the $0 ubetabeta$-decay experiments are also discussed. Given the experimental sensitivity of $|m^{}_{betabeta}| simeq 10~{rm meV}$ (or $1~{rm meV}$), the strength of evidence to exclude the Majorana nature under the null observation of $0 ubetabeta$ decays is found to be inconclusive (or strong), no matter which of two priors on $m^{}_1$ is taken.
The interference of charge-changing interactions, weaker than the V-A Standard Model (SM) interaction and having a different Lorentz structure, with that SM interaction, can, in principle, produce effects near the end point of the Tritium beta decay spectrum which are of a different character from those produced by the purely kinematic effect of neutrino mass expected in the simplest extension of the SM. We show that the existence of more than one mass eigenstate can lead to interference effects at the end point that are stronger than those occurring over the entire spectrum. We discuss these effects both for the special case of Dirac neutrinos and the more general case of Majorana neutrinos and show that, for the present precision of the experiments, one formula should suffice to express the interference effects in all cases. Implications for sterile neutrinos are noted.
We perform a statistical analysis with the prospective results of future experiments on neutrino-less double beta decay, direct searches for neutrino mass (KATRIN) and cosmological observations. Realistic errors are used and the nuclear matrix element uncertainty for neutrino-less double beta decay is also taken into account. Three benchmark scenarios are introduced, corresponding to quasi-degenerate, inverse hierarchical neutrinos, and an intermediate case. We investigate to what extend these scenarios can be reconstructed. Furthermore, we check the compatibility of the scenarios with the claimed evidence of neutrino-less double beta decay.
We analyze the impact of a measurement, or of an improved bound, on theta_{13} for the determination of the effective neutrino mass in neutrino-less double beta decay and cosmology. In particular, we discuss how an improved limit on (or a specific value of) theta_{13} can influence the determination of the neutrino mass spectrum via neutrino-less double beta decay. We also discuss the interplay with improved cosmological neutrino mass searches.
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