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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