Statistics of neutrinos and the double beta decay

We assume that the Pauli exclusion principle is violated for neutrinos, and thus, neutrinos obey at least partly the Bose-Einstein statistics. The parameter sin2χ is introduced that characterizes the bosonic (symmetric) fraction of the neutrino wave function. Consequences of the violation of the exclusion principle for the two-neutrino double beta decays (2νββ-decays) are considered. This violation strongly changes the rates of the decays and modifies the energy and angular distributions of the emitted electrons. Pure bosonic neutrinos are excluded by the present data. In the case of partly bosonic (or mixed-statistics) neutrinos the analysis of the existing data allows to put the conservative upper bound sin2χ<0.6. The sensitivity of future measurements of the 2νββ-decay to sin2χ is evaluated.