Relativistic cyclotron radiation detection of tritium decay electrons as a new technique for measuring the neutrino mass

The shape of the beta-decay energy distribution is sensitive to the mass of the electron neutrino. Attempts to measure the endpoint shape of tritium decay have so far seen no distortion from the zero-mass form, thus placing an upper limit of $m_{\nu \beta }<2.3\mathrm{eV}$. Here, we show that a new type of electron energy spectroscopy could improve future measurements of this spectrum and therefore of the neutrino mass. We propose to detect the coherent cyclotron radiation emitted by an energetic electron in a magnetic field. For mildly relativistic electrons, like those in tritium decay, the relativistic shift of the cyclotron frequency allows us to extract the electron energy from the emitted radiation. We present calculations for the energy resolution, noise limits, high-rate measurement capability, and systematic errors expected in such an experiment.

Figure 1

Schematic of the proposed experiment. A chamber encloses a diffuse gaseous tritium source under a uniform magnetic field. Electrons produced from beta decay undergo cyclotron motion and emit cyclotron radiation, which is detected by an antenna array. See text for more details.

Figure 2

Simulated microwave spectrum, showing the cyclotron emission of ${10}^5$ tritium decays over $30\mu \mathrm{s}$ in a 10 m long uniform magnet (${\omega }_0/2\pi =27\mathrm{GH}z$, $\mathrm{B}\sim 1\mathrm{T}$) with a finely spaced transverse antenna array. ${\mathrm{e}}^{-}\mathrm{\text{−}}{\mathrm{T}}_2$ scattering is neglected. The short arrow points out a triplet of spectral peaks generated by an individual high-energy, high-pitch angle electron; the central peak is the cyclotron frequency and the sidebands are due to AM modulation. The log-scale inset zooms in on this electron and the endpoint region.