Detecting non-relativistic cosmic neutrinos by capture on tritium: phenomenology and physics potential

We study the physics potential of the detection of the Cosmic Neutrino Background via neutrino capture on tritium, taking the proposed PTOLEMY experiment as a case study. With the projected energy resolution of $\Delta \sim$ 0.15 eV, the experiment will be sensitive to neutrino masses with degenerate spectrum, $m_1 \simeq m_2 \simeq m_3 = m_\nu \gtrsim 0.1$ eV. These neutrinos are non-relativistic today; detecting them would be a unique opportunity to probe this unexplored kinematical regime. The signature of neutrino capture is a peak in the electron spectrum that is displaced by $2 m_{\nu}$ above the beta decay endpoint. The signal would exceed the background from beta decay if the energy resolution is $\Delta \lesssim 0.7 m_\nu $. Interestingly, the total capture rate depends on the origin of the neutrino mass, being $\Gamma^{\rm D} \simeq 4$ and $\Gamma^{\rm M} \simeq 8$ events per year (for a 100 g tritium target) for unclustered Dirac and Majorana neutrinos, respectively. An enhancement of the rate of up to $\mathcal{O}(1)$ is expected due to gravitational clustering, with the unique potential to probe the local overdensity of neutrinos. Turning to more exotic neutrino physics, PTOLEMY could be sensitive to a lepton asymmetry, and reveal the eV-scale sterile neutrino that is favored by short baseline oscillation searches. The experiment would also be sensitive to a neutrino lifetime on the order of the age of the universe and break the degeneracy between neutrino mass and lifetime which affects existing bounds.