Neutrino oscillation experiments have provided robust evidence that neutrinos are indeed massive and lepton flavors are significantly mixed. Therefore, both theoretical and experimental investigations of intrinsic properties of massive neutrinos become one of the most important topics at the frontier of particle physics. Currently, it is still unknown whether neutrino mass ordering is normal (i.e., m 1 m 2 m 3) or inverted (i.e., m 3 m 1 m 2), how small the lightest neutrino mass is and if neutrinos are Majorana particles, namely, if they are their own antiparticles. In this article, we mainly concentrate on the last fundamental problem. As neutrinos are electrically neutral, their antiparticles are in principle allowed to be themselves. First of all, we briefly introduce the concepts of antiparticles and Majorana fermions by following their historical development. Then, we explain how to probe the Majorana nature of massive neutrinos. In reality, this can be achieved by observing the neutrinoless double-beta decays of some heavy nuclear isotopes, which consist of even numbers of protons and neutrons and their single beta decays are kinetically forbidden. Although neutrinoless double-beta decays are extremely rare (probably with a half-life longer than 1026 years), a clear experimental signal will unambiguously demonstrate that neutrinos are Majorana particles and there exist lepton-number-violating interactions in nature. In the case of an inverted neutrino mass ordering, a number of next-generation experiments will be able to successfully discover neutrinoless double-beta decays. For instance, the huge liquid-scintillator detector of JUNO experiment in China can be dopped with a few tons of 136Xe and upgraded to measure neutrinoless double-beta decays. Another idea is taken by the PandaX-III collaboration that a ton-scale high-pressure xenon gas time-projection chamber is built to catch the tracks of neutrinoless double-beta decays. The answer to whether neutrinos are their own antiparticles would finally help us explore the origin of neutrino masses, and the new physics beyond the Standard Model of elementary particles.
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