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Mass limits for $\nu_e$

These limits apply to , the dominant mass eigenstate in $\nu_e$. They would also apply to any other which mixes strongly in $\nu_e$ and has sufficiently low mass to appear in the respective decay. The limits are valid for Dirac as well as Majorana mass terms. The most intrusively investigated process, which allows in principle to determine the rest mass of , is the nuclear $\beta$-decay of tritium. Assuming CPT-invariance the results on tritium decays can also be applied on . A non-vanishing neutrino mass would manifestate at the endpoint of the $\beta$-spectrum. The decay rate can be written as , where E is the total electron energy and E0 the total energy released in the nuclear transition. Tritium decay is preferred due to its low endpoint energy of 18.6 keV. The square of the neutrino mass is measured in tritium beta decay by fitting the shape of the beta spectrum near the endpoint. In all of the most sensitive experiments has been found to be significantly negative. Including the endpoint anomaly, Stoeffl et al. find a value of which is more than 5 standard deviations negative, and report a Bayesian limit of 7 eV (95% CL) for $m_\nu$ obtained by setting . The Mainz experiment uses an electrostatic spectrometer with adiabatic magnetic collimation and a molecular tritium source frozen onto an aluminium substrate. At an energy of 137 eV below E0 the value of is found to be compatible with zero within the 1 sigma error bars. An upper limit of 7.2 eV (95% CL) for $m_\nu$ is reported. The Troitsk group is also using an electrostatic spectrometer with adiabatic magnetic collimation. Their source is gaseous tritium. This search for the neutrino rest mass resulted in eV2 [1]. The negative value may be explained by the local enhancement in the region 7-15 eV below the end point with an integral branching ratio of about 10-10. Including this anomaly into a fit procedure shifts the measured value to eV2, finally leading to an upper limit of $m_\nu$ of 4.35 eV (95% CL) [1]. Results from studies of electron capture transitions from 163Ho give limits on the mass of . This value may differ from only in absence of CPT-invariance. The best limit is reported by Springer et al.: eV at 95% CL. 
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