Updating $\nu_{3}$ lifetime from solar antineutrino spectra

We study the production of antineutrinos from the solar neutrinos due the Majorana neutrino decays of neutrino to antineutrino. Using the antineutrino spectra from KamLAND and Borexino, we present newest limits on the lifetime of $\nu_{3}$ in this scenario. We consider $\nu_{3} \rightarrow \bar{\nu}_{1} + X$ and $\nu_{3} \rightarrow \bar{\nu}_{2} + X$ channels assuming scalar or pseudo-scalar interactions. For hierarchical mass-splittings, the limits obtained by us are $\tau_{3}/m_{3}~\geq 7\times 10^{-5} s/eV$ and $\tau_{3}/m_{3}~\geq 1\times 10^{-5} s/eV$ for the two channels at $90\%$ C.L. We found that the newest bound is five orders of magnitude better than the atmospheric and long-baseline bounds.