It would also explain why neutrinos are so light. This hypothetical decay would show that neutrinos are their own antiparticles and that a fundamental law-the conservation of lepton number-is violated in nature. But researchers are also searching for new physics in the “low-energy” environment of the nucleus through a process known as neutrinoless double-beta ( 0 𝜈 𝛽 𝛽) decay. The search for physics beyond the standard model-our current best description of fundamental particles and the interactions between them-is a top priority at high-energy particle accelerators. Different models for the decay describe it in terms of the creation and destruction of a Majorana neutrino (center) or of an unknown heavier particle (right). If neutrinos are Majorana particles then a neutrinoless form of this double-beta decay should be allowed.

Varying the electrostatic retarding potential allows to measure the beta spectrum in an integrating mode.APS/ Alan Stonebraker Figure 1: “Two-neutrino” double-beta decay (left) is allowed in certain isotopes and involves the transformation of two neutrons into two protons, two electrons, and two antineutrinos. The relative sharpness of this filter is given by the ratio of the minimum magnetic field B min in the center plane and the maximum magnetic field B max between beta electron source and spectrometer : Therefore the spectrometer acts as an integrating high-energy pass filter. All electrons with enough energy to pass the electrostatic barrier are reaccelerated and collimated onto a detector, all others are reflected. This parallel beam of electrons is running against an electrostatic potential formed by a system of cylindrical electrodes. This transformation can be summarized as follows: The beta electrons, isotropically emitted at the source, are transformed into a broad beam of electrons flying almost parallel to the magnetic field lines. Due to the slowly varying magnetic field B the momentum transforms adiabatically, therefore the magnetic moment µ keeps constant (equation given in non-relativistic approximation): The animation on the right illustrates this by a momentum vector. Therefore, the magnetic gradient force transforms most of the cyclotron energy into longitudinal motion. On their way into the center of the spectrometer the magnetic field B drops by many orders of magnitude. The beta electrons, which are starting from the tritium source in the left solenoid into the forward hemisphere, are guided magnetically on a cyclotron motion around the magnetic field lines into the spectrometer, thus resulting in an accepted solid angle of up to 2. Two superconducting solenoids are producing a magnetic guiding field B. The main features of the MAC-E-Filter are illustrated here. It combines high luminosity and low background with a high energy resolution, both essential to measure the neutrino mass from the endpoint region of a beta decay spectrum. This type of spectrometer was first proposed in and described in. The high sensitivity of the KATRIN experiments to analyze precisely the electrons kinetic energy will be reached by a special type of spectrometers, so-called MAC-E-Filters ( Magnetic Adiabatic Collimation combined with an Electrostatic Filter). This is the right range with regard to the required amount of Tritum in the range of several gramms and its activity. Finally, Tritium has a suitable lifetime of 12.3 years. This means, no nuclear energy dependant corrections must be applied to the beta spectrum and can be calculated from the first principles of the well proven V-A theory. On top of that, Tritium has a simple nuclear structure with one proton and two neutrons.

Due to the very low endpoint energy of Tritium decay, the effect of a massive neutrinos on the electrons kinetic energy is more significant. However, Tritium is the premium candidate for this experiment. In principle every beta decaying isotope could be used. Therefore, a precision measurement of the electron energy very close to its endpoint gives information on the neutrino mass. at the endpoint of the electron energy spectrum (see second figure on the left side). The subtle effect of the neutrino rest mass to the kinetic energy of the electron is largest, when the neutrino is non-relativistic i.e. They share together the released transition energy, which is distributed to their kinetic energies, the rest mass of the electron and- if the neutrino is massive - also to the rest mass of the neutrino. In the beta decay of Tritium to Helium an electron and anti-neutrino are released.

The measurement principle to derive model independent the neutrino mass is the high precision measurement of the kinetic energy of the beta electron from the Tritium beta decay.

Beta decay neutrino