The effective neutrino mass of neutrinoless double-beta decays: how possible to fall into a well |
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Authors: | Zhi-zhong Xing Zhen-hua Zhao |
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Institution: | 1.Institute of High Energy Physics and School of Physical Sciences,University of Chinese Academy of Sciences,Beijing,China;2.Department of Physics,Liaoning Normal University,Dalian,China;3.Center for High Energy Physics,Peking University,Beijing,China |
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Abstract: | The neutrinoless double-beta (\(0\nu 2\beta \)) decay is currently the only feasible process in particle and nuclear physics to probe whether massive neutrinos are the Majorana fermions. If they are of a Majorana nature and have a normal mass ordering, the effective neutrino mass term \(\langle m\rangle ^{}_{ee}\) of a \(0\nu 2\beta \) decay may suffer significant cancellations among its three components and thus sink into a decline, resulting in a “well” in the three-dimensional graph of \(|\langle m\rangle ^{}_{ee}|\) against the smallest neutrino mass \(m^{}_1\) and the relevant Majorana phase \(\rho \). We present a new and complete analytical understanding of the fine issues inside such a well, and identify a novel threshold of \(|\langle m\rangle ^{}_{ee}|\) in terms of the neutrino masses and flavor mixing angles: \(|\langle m\rangle ^{}_{ee}|^{}_* = m^{}_3 \sin ^2\theta ^{}_{13}\) in connection with \(\tan \theta ^{}_{12} = \sqrt{m^{}_1/m^{}_2}\) and \(\rho =\pi \). This threshold point, which links the local minimum and maximum of \(|\langle m\rangle ^{}_{ee}|\), can be used to signify observability or sensitivity of the future \(0\nu 2\beta \)-decay experiments. Given current neutrino oscillation data, the possibility of \(|\langle m\rangle ^{}_{ee}| < |\langle m\rangle ^{}_{ee}|^{}_*\) is found to be very small. |
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