Ebook: Measurements of Neutrino Mass

In the early days, neutrinos were regarded with suspicion. The correspondence of Heisenberg and Pauli recalled in the lecture of F. Gatti, has not been published; the first version of Fermi's theory of weak interactions was rejected by Nature; one year later, a paper of Bethe and Peierls argued that neutrinos were not observable in practice. It took 20 years to change the general pessimistic attitude. This was eventually demonstrated by the Savannah Rivers experiment, recognized by the Nobel prize awarded to Reines. Subsequently, it was realized that it was possible to learn a lot from these particles. We recall three outstanding and relatively recent achievements in neutrino physics. Their neutral current interactions, as seen in Gargamelle, provided the first proof of the correctness of the Standard Model. Neutrino astronomy made its first steps with solar and supernova neutrino observations, as recognized by the Nobel prize awarded to Davis and Koshiba. Finally, and most importantly for us, the fact that neutrino oscillations have been convincingly seen in atmospheric neutrinos closed the discussion on solar neutrino anomaly, present since late sixties in Homestake data. Nowadays, it is a common opinion that there are 3 massive neutrinos with mass difference squared 50 meV² and 9 meV². These lead to oscillations as predicted by Pontecorvo and then, precisely accounted for by Wolfenstein, Mikheyev and Smirnov. The moral is that the study of neutrinos was and remains demanding but also rewarding, as argued by E. Fiorini in this School.

A remarkable review is Pontecorvo's “Pages in the development of neutrino physics”.

The new frontier is the search for other effects of neutrino masses, besides those seen with oscillations; but the search for these effects turned out to be particularly difficult and remains a goal to be achieved. The difficulties were immediately evident to early investigators. It is remarkable that, just after his seminal papers on oscillations (conceived as a quantum phenomenon that provides experimental access to tiny neutrino masses) Pontecorvo wrote the theoretical paper “Superweak interactions and double beta decay”, to remark the possibility that the rate of the neutrinoless double-beta transition is not the small rate controlled by neutrino masses, but much larger and potentially observable. After so many years, we are continuing not only to pursue Majorana's original ideas, but also to elaborate and update the hypothesis that the transition is dominated by other contributions, besides those due to neutrino masses. This was addressed, in particular, in the lectures of P. Vogel.

But neutrinoless double-beta experiments show impressive progresses and we are nearing the mass scales suggested by oscillations. Indeed, we will soon explore the 100 meV region of neutrino masses with a new generation of experiments, including CUORE and GERDA at the Gran Sasso Laboratory, possibly improvable to even smaller values —see the lectures of A. Giuliani. These developments come with many promises, such as clarifying the meaning of the result of Klapdor-Kleingrothaus, probing the Majorana nature of neutrinos, observing for the first time lepton number violating effects, searching for glimpses of new physics, etc. The crucial preliminary need will be to quantify the impact of the nuclear structure on the neutrinoless double-beta transition rate, as stressed by P. Vogel and A. Poves. Signals of improvement with respect to the situation of the recent past, when the uncertainties amounted to a factor of two or larger, are apparently emerging. Certain concrete hopes to solve some aspects of this difficult problem by a campaign of experimental measurements have been discussed by D. Frekers.

A specific remark is in order; the neutrinoless double-beta transition rate varies quadratically with its nuclear matrix element. By increasing the time (or the mass) of measurement we can improve on it but much more slowly, the scaling in the presence of background being with the square root. Thus, a 20% difference in the nuclear matrix element is equivalent to a factor two difference in the time of measurement. In this important case, a theoretical improvement is more urgent than the experimental one to know if we will be able to achieve a measurement.

The oldest method to search for neutrino masses, namely to look for features in beta decay spectra (as already proposed by Fermi) is still very actively pursued and has been widely discussed at the School. C. Weinheimer focused on the study of the end point of the spectrum and explained the impressive effort of KATRIN to cover the region of masses above 200 meV in the next few years. A similar goal in the more distant future is the one of the MARE experiment, based on different experimental principles and covering the whole beta spectrum: this has been discussed in the lecture of F. Gatti. Both lecturers enriched their lecture notes with rich historical overviews and precious introductory material.

The rapid advances of cosmology transformed a field that till recently was dominated by theoretical speculations into a quantitative branch of physics, where the possibility of performing increasingly precise measurements is becoming a reality. This was discussed by P. de Bernardis, whose experiment, BOOMERanG, opened the way to “precision cosmology”. The lectures of S. Pastor provided further introduction to the matter, addressing the question on whether it is possible to measure neutrino masses in cosmology. Despite the observational and theoretical systematics, on which we need to work further, there are ambitious but realistic chances to probe, in the next decade and using different techniques, the minimal neutrino mass of the inverse hierarchy case (i.e., whether the sum of the three neutrino masses exceeds 100 meV). Surely enough, the study of cosmology remains a very exciting field where the numerous links of neutrinos with astroparticle physics get continuously renewed; all this made these two lectures enthusiastically attended.

A large space at the School has been allocated for theoretical topics. A. Bettini gave a learned and stimulating lecture on the evolution of the concept of mass in particle physics. A. Strumia offered a status report of oscillations neutrinos and collected the basic essential material to fully appreciate the other lectures and the current discussion on neutrino masses. A. Yu. Smirnov provided a wide view on the many possible situations that we may be meeting in future years, that now we can only conceive as theoretical possibilities. G. Senjanović lectured on the continuing efforts to understand neutrinos in gauge theories and reminded us of many deep links of the physics of neutrino masses with other lines of research, including the search for new particles in LHC and future accelerators. A. Riotto recalled to us that neutrino masses may also have something to do with the very origin of the matter among us, which is a remarkable fruit of the ideas of Sakharov

Indeed, they are a natural low-energy manifestation of the leptogenesis scenario originally suggested by Fukugita and Yanagida; but, in the absence of further theoretical progresses or experimental inputs, a precise prediction of neutrino masses seems to be very difficult or even impossible at present.

The overall impression is that, although the daily business of theorists (i.e., publishing papers) is comparably easier, the challenges and the difficulties to obtain non-superficial physics results on neutrinos make the best theoretical efforts of similar value as those of their experimental colleagues. Moreover, the time needed to fully develop valid ideas —e.g., neutrino oscillations— often ranges in the ten year scale or longer, that again is comparable with the time of a typical neutrino experimental enterprise. These considerations emphasize the importance that theory and experiment proceed hand in hand toward the understanding of neutrino masses and, finally, toward their measurement.

Various participants in the School enriched the discussion by contributing to the poster session, that permitted to perceive each other's scientific interest immediately. Particularly precious was the time dedicated to discussion and the session when exercises were solved together at the blackboard. In brief, we feel that the main scientific and didactic goals of the School have been reached. As a side remark, we cannot but note that we aimed to perfection also during the moments of free time. This is testified by a number of tough competitions: the prize “B. Slinsega” for the best poster; the “Top Isospin” ping-pong international tournament for physicists; the “Mr. Neutrino” contest (the toughest, arguably), won respectively by E. Ferri, X. F. Navick and G. Senjanovic. We enjoyed the School a lot and the time we spent together.

We would like to conclude by thanking the many people who made this event possible, beginning with the President of SIF, L. Cifarelli for continuous help, encouragement and support. Immediately after, B. Alzani who has been our Guardian Angel, perfectly assisted by R. Brigatti and G. Bianchi Bazzi. A particularly warm “grazie” goes to the Editorial Office of SIF and in primis to A. Oleandri, M. Missiroli and M. Bonetti, for patience and very professional work done with editing. Next, we are glad to thank our sponsors, namely, CAEN of Viareggio, and SIMIC of Camerana, two well-known enterprises with important roles for the success of our experiments. Finally and most importantly, we are most grateful to all our Students, Speakers and Lecturers who worked for the scientific success of the School and apologize to them for any occasional disappointing situations. Now it is time to offer you the efforts of a community, condensed in this Volume, in the hope that it will be a useful guide to progress toward the measurement of neutrino masses. We wish to meet next time to discuss accomplished measurements, perhaps again in the wonderful scenery of Villa Monastero.

C. Brofferio, F. Ferroni and F. Vissani

A few examples will be given of the essential role played by low-energy nuclear physics in the fundaments of elementary particles and in particle astrophysics. The crucial impact in weak-interaction physics by the discovery of parity violation, which is now fifty years old, and the corresponding experiments will be summarized. A brief discussion will be devoted to the recent experiments on neutrino oscillations which prove that the difference between the square masses of two neutrinos of different flavour is different from zero. As a consequence, the mass of at least one neutrino has to be finite, but oscillations cannot provide a direct indication of its value. Stimulated by these exciting results a vast series of experiments aiming to determine directly the neutrino mass has been carried out and is running or planned.

We review experimental and theoretical results related to neutrino physics with emphasis on neutrino masses and mixings, and outline possible lines of development.

Comprehensive description of the phenomenology of the ββ decay is given, with emphasis on the nuclear physics aspects. After a brief review of the neutrino oscillation results and of motivation to test the lepton number conservation, the mechanism of the 0νββ is discussed. Its relation to the lepton flavor violation involving charged leptons and its use as a diagnostic tool of the 0νββ mechanism is described. Next the basic nuclear physics of both ββ decay modes is presented, and the decay rate formulae derived. The nuclear physics methods used, the nuclear shell model and the quasiparticle random phase approximation, are described next, and the choice of input parameters is discussed in the following section. Finally, the numerical values of the nuclear matrix elements, and their uncertainty, are presented. In Appendix A the relation of the search for the neutrino magnetic moment to the Dirac versus Majorana nature of neutrinos is described.

This lecture is meant to be complementary to those dedicated to the main subject of the Course, namely neutrinos, their masses and the corresponding measurements. We shall discuss the concept of mass at an elementary, but not trivial, level. From an operational point of view, mass, as any observable, is defined by the set of operations employed to measure it or, when not observable as in the case of quarks, to calculate it. Consequently, there are several “masses”, which are not necessarily equal. We shall discuss the relationships amongst them. We start by recalling the basic concept of mass and the strictly related ones of energy and momentum. We shall give then a historical perspective and draw the attention on a number of wrong concepts that are still present. Without considering neutrino masses, covered by other lectures, we shall discuss the masses of the neutrally charged flavoured mesons, the masses of the hadrons, the quark masses and their running.

This paper summarizes the relevance of neutrinoless double-beta decay for neutrino physics and the implications of this phenomenon for crucial aspects of particle and astroparticle physics. After discussing general experimental concepts, like the different proposed technological approaches and the sensitivity, the present experimental situation is reviewed. The future searches are then described, providing an organic presentation which picks up similarities and differences. As a conclusion, we try to envisage what we expect round the corner and at a longer time scale.

In this paper we will review the “state of the art” of the calculations of the nuclear matrix element (NME) of the neutrinoless double-beta decays (0νββ) for the nuclei ⁴⁸Ca, ⁷⁶Ge, ⁸²Se, ¹²⁴Sn, ¹²⁸Te, ¹³⁰Te and ¹³⁶Xe in the framework of the Interacting Shell Model (ISM), and compare them with the NME's obtained using the Quasi-particle RPA approach (QRPA). We will also discuss the effect of the competition between the pairing and quadrupole correlations in the value of these NME's. In particular we will show that, as the difference in deformation between parent and grand-daughter grows, the NME's of both the neutrinoless and the two neutrino modes decrease rapidly.

Charge-exchange reactions of (n,p) and (p,n) type at intermediate energies are a powerful tool for the study of nuclear matrix element in ββ decay. The present paper reviews some of the most recent experiments in this context. Here, the (n,p) type reactions are realized through (d,²He), where ²He refers to two protons in a singlet ¹S₀ state and where both of these are momentum analyzed and detected by the same spectrometer and detector. These reactions have been developed and performed exclusively at KVI, Groningen (NL), using an incident deuteron energy of 183 MeV. Final-state resolutions of about 100 keV have routinely been available. On the other hand, the (³He,t) reaction is of (p,n) type and was developed at the RCNP facility in Osaka (JP). Measurements with an unprecedented high resolution of 30 keV at incident energies of 420 MeV are now readily possible. Using both reaction types, one can extract the Gamow-Teller transition strengths B(GT⁺) and B(GT⁻), which define the two “legs” of the ββ decay matrix elements for the 2νββ decay. The high-resolution available in both reactions allows a detailed insight into the excitations of the intermediate odd-odd nuclei and, as will be shown, some unexpected features are being unveiled.

Neutrinos can play an important role in the evolution of the Universe, modifying some of the cosmological observables. In this contribution we summarize the main aspects of cosmological relic neutrinos and we describe how the precision of present cosmological data can be used to learn about neutrino properties, in particular their mass, providing complementary information with respect to beta decay and neutrinoless double-beta decay experiments. We show how the analysis of current cosmological observations, such as the anisotropies of the cosmic microwave background or the distribution of large-scale structure, provides an upper bound on the sum of neutrino masses, with very good perspectives from future cosmological measurements which are expected to be sensitive to neutrino masses well into the sub-eV range.

The investigation of the endpoint region of the tritium β decay spectrum is still the most sensitive direct method to determine the neutrino mass scale. In the nineties and the beginning of this century the tritium β decay experiments at Mainz and Troitsk reached a sensitivity on the neutrino mass of 2 eV/c². They were using a new type of high-resolution spectrometer with large sensitivity, the MAC-E-Filter, and were studying the systematics in detail. Currently, the KATRIN experiment is being set up at Forschungszentrum Karlsruhe, Germany. KATRIN will improve the neutrino mass sensitivity by one order of magnitude down to 0.2 eV/c², sufficient to cover the degenerate neutrino mass scenarios and the cosmologically relevant neutrino mass range.

In this paper we give a tutorial introduction to the Cosmic Microwave Background and its measurements, focusing on the current efforts to obtain the full detailed picture of all its observables: the spectrum, the anisotropy, the polarization.

The tiny neutrino masses and the associated large lepton mixings provide an interesting puzzle and a likely window to the physics beyond the standard model. This is certainly true if neutrinos are Majorana particles, since unlike in the Dirac case, the standard model is not a complete theory. The Majorana case leads to lepton number violation manifested through a neutrinoless double-beta decay and same-sign dileptons possibly produced at colliders such as LHC. I discuss in these lectures possible theories of neutrino mass whose predictions are dictated by their structure only and this points strongly to grand unification. I cover in detail both SU(5) and SO(10) grand unified theories, and study the predictions of their minimal versions. I argue that the theory allows for a (moderate) optimism of probing the origin of neutrino mass in near future.

In the last decade the energy dispersive spectroscopy of nuclear radiation has made impressive progresses by means of small thermal microcalorimeters operating at about 0.1 K. The present status of this technology, which has achieved 2 eV energy resolution, allows to design a true calorimetric experiment for neutrino mass direct determination with sub-eV sensitivity from the β spectrum of ¹⁸⁷Re and the E.C. spectrum of ¹⁶³Ho. The calorimetric method, often indicated as solution for a model-independent measurement, allows to overcome the final states problem of impulse spectroscopy. A further reduction of the systematic uncertatinties might be achived by comparing the finite neutrino mass effect of the two isotopes. Here, the motivations, the principles of operations, the results from the first pilot measurements and the future perspectives are described.

We summarize the state of the art of the theory of thermal leptogenesis according to which the baryon asymmetry in the Universe is produced at very high temperatures from the decay of heavy right-handed neutrinos. The same heavy states might be responsible through the see-saw mechanism of the lightness of the left-handed neutrinos. This opens up the possibility that measuring the low-energy neutrino parameters would lead to know something about the primordial Universe.

Measurements of the neutrino mass are considered in a general context of neutrino studies and searches for new physics beyond the standard model. The topics include: phenomenology of mass, origins and nature of neutrino masses, explanation of their smallness, relation between masses and mixing, implications of mass determination for fundamental theory and a possibility to predict neutrino mass or type of mass spectrum.

The disappearance of electron neutrinos observed in the Gallium radioactive source experiments is analyzed in the effective framework of two-neutrino mixing. We found an indication of neutrino disappearance due to neutrino oscillations with a square-mass difference much larger than those observed in solar and atmospheric neutrino experiments. We studied the compatibility of this result with the data of the Bugey and Chooz reactor short-baseline antineutrino disappearance experiments. We found an indication in favor of neutrino oscillations with 1.8 eV²  eV², from the Bugey data, which is compatible with the Gallium allowed region of the mixing parameters. This indication persists in the combined analyses of Gallium, Bugey, and Chooz data.

The present paper reports a feasibility study for the measurement of the QE CC (Quasi Elastic Charged Current) cross-section for the ν_μ-nucleus interaction in liquid argon in the few GeV region, using the ArgoNeuT detector on the NuMI Beam and the MINOS near detector as muon catcher. The number of QE ν_μ CC events expected in 180 days is about 4700 and the relative statistical error between 1 and 4 GeV is at the level of 4%, below the beam systematics.

In this paper a short summary of results achieved by the DAMA experiment in the investigation of double-beta decay modes in various isotopes is presented.

The ambitious aim of the OPERA experiment is to detect for the first time the appeareance of tauonic neutrinos out of an artificial beam of pure muonic neutrinos. This is achieved with the mature nuclear emulsion technique, greatly improved by the R&D of the OPERA collaboration both in qualityanalisys speed. The huge number of emulsions (over 9 million sheets) of the OPERA experiment requires a completely automated development facility, able to perform photographic development process on up to 3000 emulsion sheets per working day. I will present the project of the development facility and report on the current status.

OPERA is a long-baseline experiment designed to be the conclusive proof of the ν_μ→ν_τ oscillation hypothesis by means of the direct observation of ν_τ in an initially pure ν_μ beam. The detector is located at the underground Gran Sasso laboratory, 730 km from CERN, on the CNGS neutrino beam. It consists of a lead/emulsion film target complemented by magnetic spectrometers and electronic detectors. We give a report on the OPERA detectorwe show the first neutrino events detected in the emulsions.

Large neutrino experiments with an accuracy of better than 1 micron are possible thanks to the recent improvements in the nuclear emulsion detectors. The European Scanning System (ESS) is a fast automatic system developed for the mass scanning of the emulsions of the OPERA experiment. Improvements in the automatic scanning technique and performance of ESS are reported.

GERDA (GERmanium Detector Array) is designed to search for the neutrinoless double-beta (0νββ) decay of ⁷⁶Ge. The experiment is being installed in Hall A of the INFN-Laboratori Nazionali del Gran Sasso. Aiming at a background index of 10⁻³ counts/(kg y keV) at the Q_ββ value of 2039 keVGERDA will operate bare high-purity germanium detectors enriched in ⁷⁶Ge immersed directly in the liquid Argon (LAr). The discovery potential of the GERDA experiment will be presented together with the first results from the operation of natural HPGe detectors directly immersed in LAr.

The only model-independent experiments dedicated to neutrino mass determination are the kinematic ones from single β-decay. In this context an international collaboration is growing around the project of Microcalorimeter Arrays for a Rhenium Experiment (MARE) for a direct calorimetric measurement of the neutrino mass with sub-electronvolt sensitivity. MARE is divided into two phases. The first phase consists of two independent experiments using the presently available detector technology to reach a sensitivity of the order of 1 eV, and to improve the understanding of the systematic uncertainties specific of the microcalorimetric technique. The two experiments are: MARE-1 in Milanin collaboration with NASA/GSFGthe University of Wisconsin at Madison, and MARE-1 in Genoa. The goal of the second phase (MARE-2) is to achieve a sub-electronvolt sensitivity on the neutrino mass. The Milan MARE-1 arrays are based on semiconductor thermistors and dielectric silver perrhenate absorbers, AgReO₄. To optimize the detector performance, crystals of silver perrhenate have been glued to the thermistors with different epoxy resins in order to determine the best thermal coupling. Now a 72 channel measurement is starting. To identify a shielding configuration that minimizes radioactivity background in the energy region of the ¹⁸⁷Re β spectrum, a preliminary study of the cryogenic laboratory environmental background has been performed. Using a planar germanium detector for the energy range below 10keV, different shielding configurations have been realized to find the best thickness and material to shield the microcalorimeter arrays.

Neutrino oscillation experiments have unequivocally demonstrated that neutrinos have mass and that neutrino mass eigenstates mix. One possible way to determine the scale of the neutrino mass and its nature is to investigate the neutrinoless double-beta decay(0νdbd). The CUORE experiment is designed with a sensitivity capable of probing all but a small portion of the Majorana electron neutrino effective mass range. CUORE is an array of 988 TeO₂ bolometers. The signal of neutrinoless double-beta decay for ¹³⁰Te would be a sharp peak at 2530 keV. The rarity of the process under consideration makes its identification very difficult. The main task in 0νdbd searches is to understand and to diminish the background as much as possible. In order to reach this goal, different techniques are employed: Monte Carlo simulations, alpha-spectroscopy and pulse shape discrimination.