Improved Statistical Determination of Absolute Neutrino Masses via Radiative Emission of Neutrino Pairs from Atoms

The atomic transition from an excited state $|{\rm e}\rangle$ to the ground state $|{\rm g}\rangle$ by emitting a neutrino pair and a photon, i.e., $|{\rm e}\rangle \to |{\rm g}\rangle + |\gamma\rangle + |\nu^{}_i\rangle + |\bar{\nu}^{}_j\rangle$ with $i, j = 1, 2, 3$, has been proposed by Yoshimura and his collaborators as an alternative way to determine the absolute scale $m^{}_0$ of neutrino masses. More recently, a statistical analysis of the fine structure of the photon spectrum from this atomic process has been performed [N. Song {\it et al.}, Phys.\ Rev.\ D {\bf 93}, 013020 (2016)] to quantitatively examine the experimental requirements for a realistic determination of absolute neutrino masses. In this paper, we show how to improve the statistical analysis and demonstrate that the previously required detection time can be reduced by one order of magnitude for the case of a $3\sigma$ determination of $m_0^{} \sim 0.01~\text{eV}$ with an accuracy better than $10\%$. Such an improvement is very encouraging for further investigations on measuring absolute neutrino masses through atomic processes.