Bound-state beta decay of tritium: Path to first observation and novel approach to direct neutrino mass measurement

Bound-state $\beta$-decay of tritium, the process, in which the final-state electron is created in a bound atomic state of the produced ${}^3\mathrm{H}\mathrm{e}$ atom instead of freely flying away, is predicted by the standard theory of weak interactions but has not been observed so far. We study the possibility of its experimental observation through the detection of photons from radiative decay of the excited atomic states of neutral ${}^3\mathrm{H}\mathrm{e}$ populated by this process. We also propose a novel approach to direct neutrino mass measurement and sterile neutrino search based on accurate determination of the speed of the produced ${}^3\mathrm{H}\mathrm{e}$ atoms through Doppler broadening of the emitted photon lines.