Direct neutrino mass measurements

The determination of the neutrino rest mass plays an important role at the intersections of cosmology, particle physics and astroparticle physics. This topic is currently being addressed by two complementary approaches in laboratory experiments. Neutrinoless double beta decay experiments probe whether neutrinos are Majorana particles and determine an effective neutrino mass value. Single beta decay experiments such as KATRIN and MARE investigate the spectral shape of β-decay electrons close to their kinematic endpoint in order to determine the neutrino rest mass with a model-independent method. Owing to neutrino flavour mixing, the neutrino mass parameter appears as an average of all neutrino mass eigenstates contributing to the electron neutrino. The KArlsruhe TRItium Neutrino experiment (KATRIN) is currently the experiment in the most advanced status of commissioning. Applying an ultra-luminous molecular windowless gaseous tritium source and an integrating high-resolution spectrometer of MAC-E filter type, it allows β-spectroscopy close to the T ₂ end-point with unprecedented precision and will reach a sensitivity of 200 meV/c ² (90% C.L.) on the neutrino rest mass.     

Review of absolute neutrino mass measurements

The discovery of neutrino flavor oscillations has firmly established that at least two of the three known neutrino mass eigenstates possess a non-vanishing rest mass. Complementary to cosmology and the search for neutrino-less double beta decay laboratory-based measurements of low-energy beta decays provide a direct and model-independent approach to measure the effective electron (anti-)neutrino mass. I have reviewed the recent progress of the field starting from the first molecular tritium spectrum measured with the current state of the art KATRIN experiment before discussing the development of new approaches to achieve the sensitivity required to cover the full neutrino mass parameter range allowed in the inverted mass ordering scheme. The new avenues opened by micro-calorimeteric measurements of the electron capture decay spectrum of ¹⁶³Ho (ECHo, Holmes and Numecs) and by the new technology of cyclotron radiation emission spectroscopy in combination with molecular and atomic tritium sources have been presented.     

Electromagnetic design of the spectrometer section of the KATRIN experiment

The aim of the KATRIN experiment is to determine the neutrino mass directly, with a sensitivity of 0.2 eV (90% CL). KATRIN is located at KIT (Karlsruhe Institute of Technology) and is currently under construction (J. Angrik et al., 2004 [3]).The experiment will analyze the shape of the tritium β-spectrum in the region of the tritium endpoint. A nonzero neutrino mass reduces the maximal energy of the electron and changes the shape of the tritium spectrum, especially close to the endpoint. To reach the sensitivity KATRIN is aiming for, an high energy resolution as well as high statistics and low background are needed. In order to achieve this, KATRIN uses the MAC-E-Filter (Magnetic Adiabatic Collimation followed by Electrostatic Filter) principle, and several background reduction mechanisms. The optimization of both MAC-E-Filter and background reduction is the main challenge of the electromagnetic design. This article describes how these issues are tackled and discusses the actual realization of two major electromagnetic design components.     

Possible new interactions of neutrino and the KATRIN experiment

We analyse the possible role of new interactions of neutrino in the forthcoming tritium beta decay experiment KATRIN aimed at detecting the neutrino mass with the sensitivity of 0.3–0.2 eV. It is shown that under certain circumstances the standard procedure of data analysis would have to be modified by the introduction of an extra parameter describing the strength of the new interactions. Our model simulations show that the modified procedure may improve the quality of the fit compared with the standard case. Ignoring the possibility of new interactions may lead to a systematic error in the neutrino mass determination.     

The status of KATRIN

KATRIN will have the capability to push the limit on the mass of the electron anti-neutrino to 200 meV (90% C.L.) by investigating the kinematics of the electrons from tritium β decay very close to the endpoint of the β spectrum. The importance of this experiment will be discussed in various contributions to this school. KATRIN is currently under construction at KIT (Karlsruhe Institute of Technology). This talk gives an overview over the status of KATRIN with emphasis on the aspects of KATRIN not covered by the talks following this one.     

Precise energy of the 9.4 keV gamma transition observed in the <Superscript>83</Superscript>Rb decay

The energy of the 9.4 keV γ-transition observed in the ⁸³Rb decay was established to be 9405.8(3) eV. This energy value was obtained from photon spectrometry measurements of the differences in the energies of closely spaced lines. The result allows one to determine more precisely the energy of conversion electrons of the 9.4 keV transition, which represent a unique tool for energy calibration of the tritium beta spectrum and systematic measurements in the KATRIN neutrino mass determination experiment.     

The Windowless Gaseous Tritium Source of KATRIN

The objective of KATRIN is the determination of the mass of the electron anti-neutrino with a sensitivity of 200 meV by investigating the kinematics of the electrons from tritium β decay. It is currently under construction at KIT (Karlsruhe Institute of Technology).A key component of the KATRIN experiment is the Windowless Gaseous Tritium Source (WGTS), in which molecular tritium decays with an activity of 10¹¹ Bq. A precise understanding of the properties of the WGTS is mandatory for the neutrino mass determination. In particular the gas dynamics is crucial since the measured energy spectrum is influenced by inelastic scattering of the decay electrons with the tritium molecules as well as Doppler broadening of the electron energy. Therefore parameters of the WGTS such as purity, temperature, density and velocity distributions of the tritium gas and the magnetic field strength inside the WGTS have to be modeled in detail.This talk gives an overview of the simulation and modeling program package currently in development which allows us to study the influence of the WGTS parameters on the measured electron energy spectrum.     

Direct neutrino mass measurements

Direct neutrino mass experiments are complementary to searches for neutrinoless double β-decay and to analyses of cosmological data. The previous tritium beta decay experiments at Mainz and at Troitsk have achieved upper limits on the neutrino mass of about 2 eV/c² . The KATRIN experiment under construction will improve the neutrino mass sensitivity down to 200 meV/c² by increasing strongly the statistics and—at the same time—reducing the systematic uncertainties. Huge improvements have been made to operate the system extremely stably and at very low background rate. The latter comprises new methods to reject secondary electrons from the walls as well as to avoid and to eject electrons stored in traps. As an alternative to tritium β-decay experiments cryo-bolometers investigating the endpoint region of ¹⁸⁷Re β-decay or the electron capture of ¹⁶³Ho are being developed. This article briefly reviews the current status of the direct neutrino mass measurements.     

Kinematical test of large extra dimension in beta decay experiments

The forthcoming experiments on neutrino mass measurement using beta decay, open a new window to explore the large extra dimension model. The Kaluza–Klein tower of neutrinos in large extra dimension contributes to the Kurie function of beta decay that can be tested kinematically. In addition to providing an alternative approach using just the kinematical properties, we show that KATRIN can probe the compactification radius of extra dimensions down to 0.2 μm which is better, at least by a factor of two, than the upper limits from neutrino oscillation experiments.     

Chiral restoration effects on the shear viscosity of a pion gas

In calorimetric neutrino mass experiments, where the shape of a beta decay spectrum has to be precisely measured, the understanding of the detector response function is a fundamental issue. In the MIBETA neutrino mass experiment, the X-ray lines measured with external sources did not have Gaussian shapes, but exhibited a pronounced shoulder towards lower energies. If this shoulder were a general feature of the detector response function, it would distort the beta decay spectrum and thus mimic a non-zero neutrino mass. An investigation was performed to understand the origin of the shoulder and its potential influence on the beta spectrum. First, the peaks were fitted with an analytic function in order to determine quantitatively the amount of events contributing to the shoulder, also depending on the energy of the calibration X-rays. In a second step, Monte Carlo simulations were performed to reproduce the experimental spectrum and to understand the origin of its shape. We conclude that at least part of the observed shoulder can be attributed to a surface effect.     

Measuring neutrino mass with radioactive ions in a storage ring

We propose a method to measure the neutrino mass kinematically using beams of ions which undergo beta decay. The idea is to tune the ion beam momentum so that in most decays, the electron is forward moving with respect to the beam, and only in decays near the endpoint is the electron moving backwards. Then, by counting the backward moving electrons one can observe the effect of neutrino mass on the beta spectrum close to the endpoint. In order to reach sensitivities for m _ν <0.2 eV, it is necessary to control the ion momentum with a precision better than δ p/p<10⁻⁵, identify suitable nuclei with low Q-values (in the few to ten keV range), and one must be able to observe at least O(10¹⁸)\mathcal{O}(10^{18}) decays.     

Internal Ionization of an Atom in the β Decay of Tritium

The problem of internal ionization in the beta decay of tritium due to the scattering of a β electron off a bound electron is discussed. The total probability of the process per a single decay event is calculated. The distributions over the momentum and the kinetic energy of a liberated electron are plotted. A correction to the β spectrum produced by internal ionization is determined. The identity of electrons is taken into account in all calculations. The results of calculations of the modified spectrum are of interest for the KATRIN experiment aimed at measuring the mass of an electron antineutrino. The high-luminosity source also makes it possible to search for keV-scale sterile neutrinos in the middle part of the β spectrum, where the internal ionization effect is significant.     

Neutrino masses from three-particle decays

The purely leptonic decays of the tau and the radiative decay of the pion provide determinations of the tau neutrino and muon neutrino masses, respectively. The shift of the energy at which the tau decay spectrum attains its maximum and the forward-backward ratio are both large enough to determine tau neutrino masses of about 100 MeV. The photon endpoint energy and partially integrated differential decay rate in pion decay are sensitive to a neutrino mass as small as 100 keV. Thus, the present bounds on neutrino masses can be significantly improved.     

Twisted flavors and tribimaximal neutrino mixing

A new framework for handling flavor symmetry breaking in the neutrino sector is discussed where the source of symmetry breaking is traced to the global property of right-handed neutrinos in extra-dimensional space. Light neutrino phenomenology has rich and robust predictions such as the tribimaximal form of generation mixing, controlled mass spectrum, and no need of flavor mixing couplings in the theory.     

Neutrino physics with cryogenic detectors

The recent results on neutrino oscillations and the consequent need to measure the value of the neutrino mass are briefly discussed. The operating principle of cryogenic detectors working at low temperatures, where the small heat capacity allows one to record and measure the temperature increase due to the tiny energy lost by a particle in form of heat is described. An application of these detectors is the measurement, or at least an upper constraint, of the neutrino mass in β decay. This approach is complementary and can, in the future, be competitive with experiments based on the spectrometric measurement of the electron energy. The search for neutrinoless double beta decay could reach a better sensitivity on the mass if a neutrino is a Majorana particle. A large cryogenic detector, named CUORICINO, on neutrinoless double beta decay (DBD) of ¹³⁰Te already yields the best constraint on the absolute value of the Majorana neutrino mass. A much larger detector, named CUORE, for Cryogenic Underground Observatory for Rare Events, is currently under construction. With its active mass of 750 kg of natural TeO₂ it aims to reach the sensitivity in the determination of the Majorana neutrino mass suggested by the results of neutrino oscillation under the inverse hierarchy hypothesis. The problem is closely connected with what I call “the second mystery of Ettore Majorana” who suggested a particle that would violate the lepton number.     

Hiding neutrinoless double beta decay in the minimal seesaw model with the TM1 or μ–τ reflection symmetry

In Asaka et al (2021 Phys. Rev. D 103, 015014), Asaka, Ishida and Tanaka put forward an interesting possibility that the neutrinoless double beta decay can be hidden in the minimal seesaw model with the two right-handed neutrinos having a hierarchical mass structure: the lighter one is lighter enough than the typical Fermi-momentum scale of nuclei while the heavier one is sufficiently heavy to decouple from the neutrinoless double beta decay. Then, in the basis where the mass matrices of the charged leptons and right-handed neutrinos are diagonal, for some particular texture of the Dirac neutrino mass matrix ${M}_{{\rm{D}}}^{}$, the neutrinoless double beta decay can be hidden. In this paper, on top of this specified model, we study the interesting scenario that ${M}_{{\rm{D}}}^{}$ further obeys the TM1 symmetry or μ–τ reflection symmetry which are well motivated by the experimental results for the neutrino mixing parameters.     

Beta decay in the field of an electromagnetic wave and experiments on measuring the neutrino mass

Investigations of the effect of an electromagnetic wave field on the beta-decay process are used to analyze the tritium-decay experimental data on the neutrino mass. It is shown that the electromagnetic wave can distort the beta spectrum, shifting the end point to the higher energy region. This phenomenon is purely classical and it is associated with the electron acceleration in the radiation field. Since strong magnetic fields exist in setups for precise measurement of the neutrino mass, the indicated field can appear owing to the synchrotron radiation mechanism. The phenomenon under consideration can explain the experimentally observed anomalies in the spectrum of the decay electrons; in particular, the effect of the “negative square of the neutrino mass.”     

Direct search for the neutrino mass in the beta decay of tritium: Status of the “Troitsk ν-mass” experiment

The results of the “Troitsk ν-mass” experiment on the search for the neutrino rest mass in tritium beta decay are presented. The investigation of the time dependence of the anomalous, bumplike structure at the end of the beta spectrum, reported earlier, gives an indication of the periodic shift of its position with respect to the endpoint with a period of 0.5 yr. An upper limit on the electron-antineutrino rest mass (m _ν<2.5eV/c ²) is derived after taking the bump into account.