Direct neutrino-mass measurement with sub-electronvolt sensitivity

Since the discovery of neutrino oscillations, we know that neutrinos have non-zero mass. However, the absolute neutrino-mass scale remains unknown. Here we report the upper limits on effective electron anti-neutrino mass, m ν , from the second physics run of the Karlsruhe Tritium Neutrino experiment. In this experiment, m ν is probed via a high-precision measurement of the tritium β -decay spectrum close to its endpoint. This method is independent of any cosmological model and does not rely on assumptions whether the neutrino is a Dirac or Majorana particle. By increasing the source activity and reducing the background with respect to the first physics campaign, we reached a sensitivity on m ν of 0.7 eV  c –2  at a 90% confidence level (CL). The best fit to the spectral data yields $${{\mbox{}}}{m}_{\nu }^{2}{{\mbox{}}}$$ m ν 2  = (0.26 ± 0.34) eV 2   c –4 , resulting in an upper limit of m ν  < 0.9 eV  c –2  at 90% CL. By combining this result with the first neutrino-mass campaign, we find an upper limit of m ν  < 0.8 eV  c –2 at 90% CL. In its second measurement campaign, the Karlsruhe Tritium Neutrino experiment achieved a sub-electronvolt sensitivity on the effective electron anti-neutrino mass.


How can KATRIN experiment measure m precisely?
through the βdecay, and … we can model the effective decay rate for a given radioactive element: Tritium! Recipe for the most precise ever e mass measurement • A highly stable βradiation source ⟹ Tritium decay!
• A super precise energy filter for the βelectrons • A very tightly controlled environment for the e -, to suppress backgrounds as much as possible

Modelling
The model constructed to fit the data has two major components: 1. The theory 2. The response function

Modelling
The model constructed to fit the data has two major components: 1. The theory (β-decay spectrum given by Fermi's theory) 2. The response function = Experiment (Hardware) ⇒ It makes possible to compare the data and the simulations. • Best fit (MC propagation method) • The independent analyses agree within about 5% of the total uncertainty • Limit setting: 3 methods (2 frequentist, 1 Bayesian) at 90% C.L.

Conclusions and prospects
• Combining this best fit with previous KATRIN results: • First sub-eV measurement!
• The goal: Reduce the upper limit to ~0.2 eV by both taking more data and modelling systematics better. 25 How is Tritium produced • Naturally occurring tritium is extremely rare, and must be synthetically produced • Lithium-6, Lithium-7 and Boron-10 produce tritium via nuclear fission originated by neutron activation • Arising from α-decays of 210Po in the structural material of the spectrometer • The recoiling 206Pb creates highly electronically excited Rydberg states at the inner spectrometer surfaces, which can be ionized during propagation in the inner volume by thermal radiation. • Resulting low-energy electrons are accelerated by retarding energy qUana towards the focal-plane detector, making them indistinguishable from signal electrons using the energy information only. Variations on the potential can lead to spectral distortions. This asymmetry of the potential results in a shift in the energy spectrum associated with the scattered electrons compared with the spectrum of the unscattered 33 Doppler Broadening (backup slide) The Doppler broadening of the spectral energies is an unpleasant circumstance in precision spectroscopy. This is caused by the random motion of the gas molecules.
The source gas is cooled to 30 K to reduce thermal motion of tritium molecules; This also allows a greater density of molecules in the source container.
The differential beta-emission spectrum (R β (E)) includes radiative corrections and the molecular final-state distribution; The final-state distribution uses a gaussian broadening to emulate the doppler broadening (due to the thermal motion of the molecules) as well as energy broadenings due to spatial and temporal variations in the spectrometer and source electric potential.

Feldman-Cousins confidence intervals (frequentist)
• Feldman-Cousins introduces a new ordering principle based on the likelihood ratio: Here x is the measured value, μ is the true value, and is the best fit (maximum likelihood) value of the parameter given the data and the physical allowed region for μ.
• The order procedure for fixed μ is to add values of x to the interval from highest R to lower R until you reach the total probability content you desire. • Taking a ratio "renormalizes" the probability when the measured value is unlikely for any value of μ. The Feldman-Cousins confidence interval is therefore never empty. 37 Lokhov-Tkachov confidence intervals (frequentist) The random variable θ is a function of a set of experimental data X. We define and as: And define the confidence level : Note that the curve cannot exceed Any such a pair of curve forms what will call allowed confidence belt for the confidence level .

Future developments
• KATRIN aims to have sensibility of 0.2 eV at 90% CL • Must have even lower systematics and background rate • Current bkg: 220 mcps (10-3 counts per second) • Need: 10 mcps 39 We can produce e through the βdecay, and … we can model the effective decay rate for a given radioactive element