Advances in High Energy Physics

Advances in High Energy Physics / 2014 / Article
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Neutrino Masses and Oscillations

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Volume 2014 |Article ID 191960 | https://doi.org/10.1155/2014/191960

G. Bellini, L. Ludhova, G. Ranucci, F. L. Villante, "Neutrino Oscillations", Advances in High Energy Physics, vol. 2014, Article ID 191960, 28 pages, 2014. https://doi.org/10.1155/2014/191960

Neutrino Oscillations

Academic Editor: Elisa Bernardini
Received13 Aug 2013
Revised15 Oct 2013
Accepted29 Oct 2013
Published20 Jan 2014

Abstract

In the last decades, a very important breakthrough has been brought about in the elementary particle physics by the discovery of the phenomenon of the neutrino oscillations, which has shown neutrino properties beyond the Standard Model. But a full understanding of the various aspects of the neutrino oscillations is far to be achieved. In this paper the theoretical background of the neutrino oscillation phenomenon is described, referring in particular to the paradigmatic models. Then the various techniques and detectors which studied neutrinos from different sources are discussed, starting from the pioneering ones up to the detectors still in operation and to those in preparation. The physics results are finally presented adopting the same research path which has been crossed by this long saga. The problems not yet fixed in this field are discussed, together with the perspectives of their solutions in the near future.

1. Introduction

Neutrino studies brought us to some of the most relevant breakthroughs in particle physics of last decades. In spite of that, the neutrino properties are still far to be completely understood.

The discovery of the oscillation phenomenon produced quite a revolution in the Standard Model of elementary particles, especially through the direct evidence of a nonzero neutrino mass. The first idea of neutrino oscillations was considered by Pontecorvo in 1957 [13], before any experimental indication of this phenomenon. After several-decades-lasting saga of experimental and theoretical research, many questions are still open around the interpretation of this phenomenon and on the correlated aspects, on the oscillation parameters, on the neutrino masses, on the mass hierarchy, on CP violation in the leptonic sector, and on a possible existence of a fourth, sterile neutrino.

The generally accepted MSW model [46] to interpret solar neutrino oscillations is presently validated for the oscillation in vacuum and in matter, but not yet in the vacuum-matter transition region. The shape of this transition could be influenced in a relevant way, as suggested by various theories going beyond the Standard Model as, for example, the nonstandard neutrino interactions and a possible existence of a very light sterile neutrino. For this reason, the transition region deserves further and refined experimental studies.

Checks on the neutrino oscillations are under way through several experiments in data-taking phase, while few others are in preparation or even construction. These projects exploit various approaches, for example, neutrino-flavor disappearance and appearance, short and long source-to-detector baselines, and measure neutrinos and/or antineutrinos of various origins, as the solar, atmospheric, accelerator, geo-, and reactor (anti)neutrinos.

Neutrinos interact with matter only through weak interactions and, thus, they can bring to the observer almost undistorted information about their source. For example, by studying solar neutrinos and geoneutrinos, we gather information not only about the character of neutrino itself but also about the Sun’s and the Earth’s interior.

This paper consists of five sections. In Section 2, the theoretical aspects of neutrino oscillations are reviewed (for a more detailed discussion, see, e.g., [79]). The principles and the structures of the detectors employed in neutrino-physics experiments are discussed in Section 3. The most important milestones and the results of neutrino-physics experiments are summarized in Section 4. We briefly discuss the opened problems of neutrino physics and what can be expected in the near future of this exciting research field in Section 5.

2. Neutrino Oscillations

In the Standard Model (SM) neutrinos are neutral, massless fermions. They only interact with other particles via weak interactions, which are described by the charged-current (CC) and neutral current (NC) interaction Lagrangians: In the above relation, is the gauge coupling constant, is the weak angle, and the charged and neutral currents and are given by where are the charged lepton fields and we have written only the terms containing the neutrino fields .

If neutrinos have non-zero masses, the left handed components of the neutrino fields with definite flavor (which enter in the CC current definition) can be a superposition of the left handed components of the neutrino fields with definite masses (in this section, we use Greek letters and to refer to neutrino flavors and Latin letters and to refer to neutrino masses). Assuming that neutrinos are ultrarelativistic, we have where is an unitary matrix. By considering that a field operator creates antiparticles, this implies that a flavor eigenstate is a superposition of different mass eigenstates , according to For antineutrinos, we obtain correspondingly In principle, the number of massive neutrinos can be larger than three. In this case, however, we must assume that there are sterile neutrinos, that is, light fermions that do not take part in standard weak interactions (1) and (2) and thus are not excluded by LEP results according to which the number of active neutrinos coupled with the and boson is [10].

In the assumption of 3 massive neutrinos, the neutrino mixing matrix can be expressed in terms of three mixing angles , , and and one Dirac-type CP phase according to where represents an Euler rotation by in the plane and We are considering here the assumption that neutrinos are Dirac particles. In the case of Majorana (or Dirac-Majorana) mass terms, the most general form of the mixing matrix contains two additional phases and it is obtained by , where ; see for example, [7, 8]. The Majorana phases and , however, have no observable effects on neutrino oscillations [11]. In components, the mixing matrix is expressed as

where and . We indicate with . As it is usually done, we order the neutrino masses such that and . With this choice, the ranges of mixing parameters are determined by The sign of determines the neutrino mass hierarchy, being for normal hierarchy (NH) and for inverted hierarchy (IH).

2.1. Neutrino Evolution Equation

The evolution of a generic neutrino state is described by a Schrödinger-like equation: where represents the Hamiltonian operator. The above equation can be expressed in the flavor eigenstate basis . We obtain where is the vector describing the flavor content of the neutrino state given by with , and the matrix is given by:

In vacuum, the neutrino Hamiltonian is determined in terms of neutrino masses and mixing parameters. We have in fact where is the representation of the vacuum Hamiltonian in the mass eigenstate basis, given by In the last equality, we adopted the ultra-relativistic approximation and we implicitly assumed that the neutrino state can be described as a superposition of states with fixed momentum . This corresponds to the so-called plane-wave approximation which is adequate to describe neutrino evolution when coherence of the different components of the neutrino wave packet is not lost in the detection and/or propagation processes (for a wave-packet description of neutrino oscillations see, e.g., [7]).

The presence of a matter can affect neutrino propagation in a nontrivial way. In fact, as it was first realized by [4], when a neutrino propagates through a medium, its dispersion relation (i.e., its energy-momentum relation) is modified by coherent interactions with background particles. This phenomenon, which in optics is accounted for by introducing a refractive index, can be described by adding an effective potential in the evolution equation, so that In the SM, the effective potential is diagonal in the flavor basis. We thus have where we have taken into account that sterile states do not interact with the medium. At low energies, the potentials can be evaluated by taking the average of the effective four-fermion Hamiltonian due to exchange of and bosons over the state describing the background medium. We have with where is the Fermi constant, and are the vector and axial vector coupling constants of the various background particles and we have performed a Fierz reshuffling of the fields; see [7, 12]. In the above equations, it is taken into account that normal matter does not contain muons and taus and, consequently, the CC interactions with the medium only affect electron neutrino propagation. For nonrelativistic unpolarized medium, one obtains where the CC contribution is proportional to difference between the number densities of electrons and positrons. The NC contribution is equal for all active neutrino flavors and it is given by where while and ( and ) are the number densities of protons and neutrons (antiprotons and antineutrons), respectively.

In neutral matter, it necessarily holds that implies that the first term in the r.h.s. of the above equation vanishes. Moreover, in the absence of sterile neutrinos, the neutral current contribution to the total Hamiltonian is proportional to the identity matrix. As a consequence, it only introduces an overall unobservable phase factor in the evolution of and, thus, can be neglected.

Finally, the evolution equation for antineutrinos is obtained by replacing in (16) and in (18). We, thus, understand that CP-violating effects are absent in neutrino oscillations, if the mixing matrix is real (i.e., ) and neutrinos propagate in vacuum or in a CP-symmetric medium (i.e., ).

2.2. Oscillations in Vacuum and in Matter

In formal terms, neutrino oscillations are easily described. Let us assume that a neutrino flavor is created at a time . In the flavor eigenstate basis, this state is represented by a vector with components . After a time interval , the neutrino propagated to a distance and its flavor content has evolved according to where the evolution operator is given by and represents the time ordering of the exponential. In the presence of neutrino mixing and if neutrino masses are not degenerate, the Hamiltonian is not diagonal. Thus, flavor is not conserved and components can appear as a result of the evolution. The probability to detect a neutrino flavor at a distance from the neutrino production point is given by In the following, we discuss the expectations for in few relevant cases.

2.3. Vacuum Neutrino Oscillations

In vacuum, the neutrino Hamiltonian is constant. The evolution operator can be explicitly calculated as where is the evolution operator in the mass eigenstate basis given by with . The probability to observe the oscillation over a distance is thus given by where and we considered that for a relativistic particle .

The above expression can be recast in few alternative forms that are useful to discuss the property of neutrino oscillations. We obtain, for example, which gives the oscillation probability as the sum of a constant and an oscillating term. The oscillating part averages to zero if the phases vary over ranges , as it can be due, for example, to a spread of the neutrino energy and/or the neutrino baseline . The constant part represents the “classical” limit that is obtained by neglecting interference among the different components of the neutrino wave packet and by combining probabilities, rather than amplitudes, to derive .

Alternatively, we can write The first two terms in the r.h.s. of the above equation do not change for and describe the CP-conserving part of the neutrino oscillation probability. The last part, instead, changes sign introducing a difference between neutrino and antineutrino oscillation probabilities that can be quantified as For , this term vanishes showing that CP asymmetry can be measured only in transitions between different neutrino flavors.

If we assume two neutrino mixing, that is, we take only one nonvanishing mixing angle in (8), the oscillation probability reduces to the well known expression where and the involved flavors depend on the mixing angle (an angle induces oscillations; induces oscillations; induces oscillations). The survival probability for the case can be simply deduced by considering that, due to unitarity of the mixing matrix, it always holds that, in this specific case, gives Equation (36) describes an oscillating function of . The amplitude of the oscillation is determined by while the oscillation length is given by The oscillation probabilities are unchanged when or showing that two neutrino oscillations in vacuum do not probe the hierarchy of the masses and (i.e., the states and can be interchanged with no effect on (36) and (37)).

In the three-neutrino case, useful expressions can be derived in the approximation of one-dominant mass scale (i.e., ) which is motivated by the fact that the mass difference required to explain the atmospheric neutrino anomaly is much larger than that required to solve the solar neutrino problem. In this assumption (note that, due to CPT-invariance, it holds ) one obtains where, following [9], we adopted the notation and and we set in the coefficients of the terms. The CP-violating part , which enters with opposite sign in the corresponding expressions for antineutrinos, is given by where showing that CP violation is observed in neutrino oscillations only if all the angles and all the mass differences are nonvanishing. The magnitude of CP violating effects depends on the phase , being maximal for and .

The survival probabilities are given by [9]

We note that, at this level of approximation, there is no sensitivity to neutrino hierarchy since the oscillation probabilities do not depend on the sign of . Moreover, in the limit , the “atmospheric” mass scale does not produce observable effects on electron neutrino oscillations that can be regarded as two neutrino oscillations, driven by the “solar” mass difference , between and the mixed state . This conclusion also holds in presence of matter.

2.4. Neutrino Oscillations in Matter

The evolution of neutrinos in matter is complicated by the fact that the properties of the medium can change along the neutrino trajectory, thus giving a nonconstant Hamiltonian. The evolution equation reads as where, if we neglect sterile neutrinos, the only nonvanishing entry of the matrix is Here, the “+” sign refers to neutrinos while the “−” sign refers to antineutrinos. In the above equations, we omitted the NC contribution to matter potential that is proportional to the identity matrix. We also assumed that the number density of positrons is negligible. See Section 2.1 for details.

It is convenient to diagonalize the Hamiltonian at each point of the space and discuss the evolution in the basis of the local mass eigenstates defined by the following relation: where is the unitary matrix that gives with In this basis, the evolution equation becomes We see that the nondiagonal entries, which may cause the transitions between the local mass eigenstates, are proportional to the derivative of   whose magnitude is essentially determined by the rate of change of the electrons number density in the background medium.

This observation can be used to introduce the so-called adiabatic approximation that applies with good accuracy to the case of solar neutrino oscillations. Let us indicate with the length scale over which the components of the neutrino wave packet with masses and acquire a phase difference . If we assume that the various are much smaller than the distance over which the medium changes its properties , the second term in the r.h.s. of (52) can be neglected. Thus, the components of the vector remain constant (in magnitude) during the evolution, even if the decomposition of in the flavor basis changes along the neutrino trajectory as a result of the variations of . If the length scales are also much smaller than the baseline over which neutrinos propagate, the oscillation probabilities only depends on the properties of at the production point and at the detection point . They can be, in fact, deduced by incoherently combining probabilities of production and detection, obtaining

We now consider the specific case of produced by nuclear reactions occurring at the center of the sun. Let us calculate the electron neutrino survival probability, by first considering a two neutrino scenario in which only . The effective mixing angle in matter can be calculated as while the difference between the effective neutrino masses is given by with Matter effects break the degeneracies and probing the hierarchy in the 1-2 neutrino sector. In particular, when and , the system has a resonance. There exists, in fact, a value of the electron number density, defined by the following condition: for which the local mixing is maximal (i.e., ) while the mass difference reaches the minimal value . As it was discussed by [5, 6], if the resonance region is sufficiently wide, it is possible to achieve a total conversion of into neutrinos of different flavors. This mechanism is called the MSW effect. Considering that the electron density in the Sun is  cm−3 and the typical solar neutrino energies are  MeV, the resonance condition requires  eV2.

The evolution equation in the local mass eigenstate basis becomes and the adiabaticity condition can be explicitly expressed as where the adiabaticity parameter is given by the ratio between the differences of diagonal elements and off-diagonal elements of (58): If condition (59) is fulfilled, the electron neutrino survival probability can be calculated through (53) obtaining where indicates the mixing angle at neutrino production point and we assumed that neutrinos are detected in vacuum.

In order to understand the specific features of , it is useful to define a transition energy , given by: where is the electron number density at the center of the sun. For , matter effects are negligible and (61) reduces to: which, in fact, corresponds to vacuum averaged neutrino oscillations. For , matter potential becomes dominant so that the “heaviest” mass eigenstates in the center of the Sun coincide with . As a consequence, we obtain and For the value of and currently favored by neutrino oscillation analysis (see Section 4), the transition energy is approximately  MeV.

The violations of adiabaticity can be taken into account by introducing the crossing probability that represents the probability of a transition between the local mass eigenstates during the neutrino evolution. If , the electron neutrino survival probability becomes There are different approaches to calculate . For several cases of interest, the following expression holds (see e.g., [9, 13, 14] and references therein): where is the minimal value of along the neutrino trajectory (in the presence of a resonance, one can often approximate where is the value of at the resonance point, see, e.g., [7, 9]) and the parameter depends on the adopted electron density profile. In particular, for an exponential density profile , which is a good approximation for solar neutrinos, one has .

In the case of three mixed neutrinos, the above picture has to be modified to take into account the possibility that and . Since matter potentials are equal for muon and tau neutrinos, the rotation in (8) can be reabsorbed in the “mixed” basis . This shows that, when , electron neutrinos experience two-neutrino oscillations to a mixed state and, thus, the electron neutrino survival probability is unchanged. In the presence of , we have instead non trivial modifications due to the fact that the state mixes with the state being in fact . By repeating the previous calculations, one obtains where it is assumed that matter effects negligibly modify the mixing angle (i.e., ).

We finally remark that the above expression applies to solar neutrinos detected during the day, since these neutrinos do not cross the Earth to reach the detector. Matter effects due to propagation across the Earth can modify (67) by introducing a day-night modulation whose magnitude depends on the specific values of mass and mixing parameters.

3. Neutrino Detectors

The successful series of solar, atmospheric, reactor, and accelerator experiments which led to firmly establish the standard three-flavor neutrino oscillation paradigm involved the realization of sophisticated detectors based on a plurality of techniques. In this paragraph we briefly review their main features, which undoubtedly played a key role in the incredible success of this field.

3.1. Radiochemical Detectors

The emerging hint of the so-called solar neutrino problem at the beginning of the 70s from the first results of the pioneering chlorine experiment (whose final findings are summarized in [24]), carried out by Ray Davies in the Homestake mine, signaled the experimental beginning of the neutrino oscillation saga. The problem, consisting in a sizable discrepancy between the data and the prediction of the Standard Solar Model, persisted for more than 30 years before being explained as a manifestation of the neutrino oscillation phenomenon. A beautiful account of the early stage of this field can be found in the seminal book of Bahcall [25], where all the steps which brought to shape unambiguously the existence of the experimental puzzle are vividly and clearly explained. In the 90s additional evidence of the existence of the solar neutrino problem came from other two radiochemical experiments, GALLEX/GNO [26] at Gran Sasso and SAGE [27, 28] at Baksan. The principle of the radiochemical technique is very simple and elegant: the detection medium is a material which, upon absorption of a neutrino, is converted into a radioactive element whose decay is afterwards revealed and counted. The Homestake experiment used a chlorine solution as a target for inverse -interactions: characterized by a threshold of 0.814 MeV. It is worth reminding that such a technique was proposed independently by two giants of modern physics, Bruno Pontecorvo and Louis Alvarez. The other two experiments, instead, adopted gallium as target, which allows neutrino interaction via The threshold of this reaction is 233 keV, low enough to essentially probe the entire solar neutrino spectrum (see Section 4.1 for details) which on the contrary cannot be revealed with the chlorine reaction due to the higher threshold. Due to the similarity of the methodology in both cases of chlorine and gallium, in the following its description is focused to the specific gallium implementation. In GALLEX/GNO the target consisted of 101 tons of a GaCl3 solution in water and HCl, containing 30.3 tons of natural gallium; this amount corresponds to about nuclei. The solution was contained in a large tank hosted in Hall A of the underground Gran Sasso Laboratory.

produced by neutrinos is radioactive and decays back by electron capture into . The mean life of a nucleus is about 16 days; thus accumulates in the solution, asymptotically reaching equilibrium when the number of atoms produced by neutrino interactions is just the same as the number of the decaying ones. In this equilibrium condition, about a dozen atoms would be present inside the whole gallium chloride solution. Since the exposure time is in practice limited to four weeks, the actual number of atoms is less than the equilibrium value, but still perfectly predictable. Therefore, the solar neutrino flux above threshold is deduced from the number of produced atoms, using the theoretically calculated cross section. The challenging experimental task is thus to identify the feeble amount of atoms. This is accomplished through a complex procedure which contemplates several steps.(1)The solution is exposed to solar neutrinos for about four weeks.(2)The atoms present at the end of the four week period in the solution are in the form of volatile GeCl4, which is extracted into water by pumping about 3000 m3 of nitrogen through the solution.(3)The extracted is converted into gaseous GeH4 and introduced into miniaturized proportional counters mixed with xenon as counting gas. At the end of the process, a quantity variable between 95 and 98% of the present in the solution at the time of extraction is in the counter; extraction and conversion efficiencies are under constant control using nonradioactive germanium isotopes as carriers.(4)Decays and interactions in the counter are observed for a period of 6 months, allowing the complete decay of and a good determination of the counter background. The charge pulses produced in the counters by decays are recorded by means of fast transient digitizers.(5)The data, after application of suitable cuts, are then analyzed with a maximum likelihood algorithm to obtain the most probable number of introduced in the counter, with some final corrections applied to take into account the so-called side reaction, that is interactions in the solution generated by high energy muons from cosmic rays and by natural radioactivity.

The key issue in the overall procedure is the minimization of the possible sources of backgrounds. This is performed through a triple strategy, whose first element is the rigorous application of low-level radioactivity technology in the design and construction of the counters; the second element is the use in the analysis of sophisticated pattern recognition techniques able to perform energy and shape discrimination of the signal and background events; the third and final element is the precise calibration of the counters via an external Gd/Ce X-ray source, to enhance the accuracy of the signal/background discrimination ensured by the pattern recognition method.

Thanks to the effective methodology adopted, the radiochemical experiments were able to provide very important results in the studies of solar neutrinos, demonstrating unambiguously the discrepancy between the measured and predicted solar neutrino fluxes and triggering the subsequent vast theoretical and experimental investigations culminated in the proof of the oscillation effect in the solar neutrino sector.

Such fundamental outputs were achieved despite the incredible challenge of the measurement, which can be well appreciated by considering the smallness of the detected signal. In about two decades of operation, Homestake and SAGE detected 860 and 870 decays, respectively, as reported in [24, 27, 28] (GALLEX/GNO did not publish this number).

In this respect, is worth mentioning another important ingredient of the radiochemical solar neutrino programs, which is the source calibration efforts which were performed to prove unambiguously the validity of the entire neutrino detection concept implied by this technique. In particular, GALLEX and SAGE underwent twice the calibration procedure. GALLEX exploited in both cases a source [34], while SAGE adopted two different isotopes, in the first instance [35] and in the second test [36]. The outcome of the source tests was the definitive validation of the radiochemical approach as an effective method to detect neutrinos. However, the ratio between the detected and predicted neutrino fluxes is significantly less than 1; taking the four tests together, the global result is . This anomaly can be interpreted as a possible indication of disappearance (see, e.g., [37]) within models with additional sterile neutrino states (see Section 4.2.4).

3.2. Čerenkov Detectors

The widespread diffusion of the Čerenkov technique in the field of neutrino physics can be appreciated by considering the many experimental setups based on this method which have been employed to investigate the entire neutrino spectrum, from the lowest to the highest energies.

The Čerenkov radiation is produced in a material with refractive index by a charged particle if its velocity is greater than the local phase velocity of the light. The charged particle polarizes the atoms along its trajectory, generating time dependent dipoles which in turn generate electromagnetic radiation. If , the dipole distribution is symmetric around the particle position, and the sum of all dipoles vanishes. If , the distribution is asymmetric and the total time dependent dipole is different from zero and thus radiates.

The resulting light wavefront is conical, characterized by an opening angle whose cosine is equal to ; the spectrum of the radiation is ultraviolet divergent, being proportional to . The propagation properties of the Čerenkov light are therefore fully equivalent to those of the acoustic Mach cone.

3.2.1. SNO

The SNO experiment [38] is a paradigmatic example of how the Čerenkov light can be used as basis to build a very effective neutrino detector. Since SNO encompasses more experimental features than the other important detector of this kind, the Japanese Super-Kamiokande described in Section 3.2.2, we find convenient, for illustrative purposes, to reverse the historical order (the data taking of Super-Kamiokande actually started before SNO). Located underground, in the Inco mine at Sudbury (Canada), this detector employed heavy water, which acted both as target medium for the neutrinos and as light generating material. The basic idea beyond the choice of heavy water is to perform two independent solar neutrino measurements based on the deuterium target: the first is aimed to detect specifically the electron neutrino component, while the second is sensitive to the all-flavor flux. Thus, the comparison of the two results can permit to unambiguously discern if neutrinos, generated only as electron neutrinos in the core of the Sun, undergo flavor conversion during the path Sun-Earth.

Heavy water makes this possible providing both flavor-specific and flavor-independent neutrino reactions. The first, flavor-specific, reaction is the charged current (CC) reaction sensitive only to electron neutrinos. Due to the large energy of the incident neutrinos, the produced electron will be so energetic that it will be ejected at light speed, which is actually faster than the speed of light in water, therefore creating a burst of Čerenkov photons; after traveling throughout the water volume, they are revealed by the spherical array of photomultipliers instrumenting the detector. The amount of light is proportional to the incident neutrino energy, which can be inferred from the number of hits on the PMTs. From the hit pattern, also the angle of propagation of the light can be determined.

The second flavor-independent reaction is the so-called neutral current (NC) reaction whose net effect is just to break apart the deuterium nucleus; the liberated neutron is then thermalized in the heavy water as it scatters around. The reaction can eventually be observed due to gamma rays which are emitted when the neutron is finally captured by another nucleus. The gamma rays will scatter electrons, which produce detectable light via the Čerenkov process, in the same manner as discussed before.

The neutral current reaction is equally sensitive to all neutrino types; the detection efficiency depends on the neutron capture efficiency and the resulting gamma cascades. Neutrons can be captured directly on deuterium , but this is not very efficient. For this reason SNO has employed two separate systems to enhance the detection of NC interactions. In the so-called second SNO phase, has been added to the heavy water in form of 2 tons of NaCl and neutrons were detected through interaction. In the third SNO phase, the 36 proportional counters have been deployed in the core of the detector which enabled the neutron detection based on interaction.

There is also a third reaction occurring in the detector, flavor independent as well, which is the electron scattering (ES):

This reaction is not unique to heavy water, being instead the primary mechanism in other light water detectors, like Kamiokande/Super-Kamiokande (see Section 3.2.2). Although this reaction is sensitive to all neutrino flavors, due to the different cross sections involved the electron neutrino dominates by a factor of six. The final state energy is shared between the electron and the neutrino, and thus there is very little spectral information from this reaction. On the other hand, good directional information can be obtained.

The general drawback affecting the Čerenkov technique is that, due to the feeble amount of light produced by the Čerenkov mechanism, the effective neutrino threshold is around 4-5 MeV, thus allowing the detection only of the high energy component of the solar flux, essentially the neutrinos.

The SNO experiment is now over; its architectural scheme was very simple (see Figure 1), aimed to get the most from the Čerenkov technique: 1000 tons of heavy water were contained in a thick transparent acrylic vessel, surrounded by an external layer of light water shielding from the gammas from the radioactivity in the rock. A spherical array of 10000 8′′ phototubes detected the light from both volumes of water. A key issue for the success of the experiment was the long standing effort throughout the construction and the operation phases to reduce the natural radioactivity in the target volume, not only in uranium and thorium, but also in the particular ubiquitous radon gas.

As a result of this experimental effort, the multiple, clean, and almost background-free CC, NC, and elastic scattering detection of solar neutrinos provided the unambiguous and model independent proof that neutrinos from the Sun undergo flavor conversion. The specific “smoking gun” indication of the flavor-conversion process was obtained from the comparison of the depleted -only flux of the CC measurement with the all-flavor flux evaluated through the NC reaction. The first publication of this result in 2002 [31] nailed down definitively the explanation of the Solar Neutrino Problem.

3.2.2. Super-Kamiokande

As anticipated before, Super-Kamiokande [39], like its predecessor Kamiokande [40], is conceptually very similar to SNO, the major difference being the use of normal water instead of heavy water. Hence the neutrino detection occurs only via the scattering reaction off the electrons; the afterwards mechanism of Čerenkov light production and detection via an array of PMTs is equal to that already described for SNO.

Another major difference is the quantity of water employed, in total 50 ktons (observed by almost 13000 20′′ PMTs), which makes this detector the most massive among the neutrino oscillation experiments built so far. The sufficiently high statistics implied by this huge volume have made a fairly precise reconstruction of the spectrum of the scattered electrons possible, which plays an important role in the subsequent analysis for the interpretation of the data. With its huge mass Super-Kamiokande clearly outperforms the findings of the old Kamiokande (containing only 3000 tons of water), obtained in the data taking period from 1983 to 1994; however Kamiokande maintains a crucial historical role in the fields of neutrino oscillation and of astrophysical neutrinos, in this case with the detection of the neutrinos from the Supernova SN1987A, as witnessed by the 2002 Nobel Prize. In this context, it is appropriate to mention also another historically important Čerenkov experiment, the IMB (Irvine-Michigan-Brookhaven) detector [41], realized with 10000 tons of water, which shared with Kamiokande the success of detecting the SN1987A neutrinos.

The intrinsic high directionality of the scattering reaction, coupled to the directionality of the Čerenkov light, provides this experiment with a powerful tool to fight the background due to trace impurities of natural radioactivity dissolved in water, by associating the reconstructed direction of the Čerenkov photons with the angular position of the Sun. Clearly, this is done on top of the purification procedure of the light water, which as for SNO was focused generally on the whole natural radioactivity, but with special emphasis on the radon, which is the factor limiting the threshold at low energy.

An additional important analysis tool is the typical feature of the Čerenkov light to generate sharp Čerenkov rings in case of muon particles, while electrons make rings with fuzzy edges. Contrary to SNO, Super-Kamiokande is still currently taking data. The long history of this detector started in 1996 and evolved through four phases: the first phase lasted until a major PMT incident in November 2001 and produced a very accurate measure of the flux via the ES detection reaction. Phase II with reduced number of PMTs, from the end of 2002 to the end of 2005, confirmed with larger error the phase I measurement. After the refurbishment of the detector back to the original number of PMTs, the third phase lasted from the middle of 2006 up to the middle of 2008. Later on, an upgrade of the electronics brought the detector into its fourth, current phase. It is important to highlight the evolution of the energy threshold (total electron energy) in all the phases: 5 MeV in phase I, 7 MeV in phase II, 4.5 MeV in phase III, and 4 MeV for phase IV, thanks to the continuously ongoing effort to reduce the radon content in water.

Undoubtedly Super-Kamiokande played a central role in the long path which led to unveiling of the neutrino oscillation phenomenon, since it has been, and still is, a major player in three of the areas of investigation for neutrino oscillation, that is, those based on solar, atmospheric, and accelerator neutrinos. Actually, it was Super-Kamiokande that in 1998 [16] announced the epochal discovery of neutrino oscillations, which stemmed from the observed anomaly of the number of atmospheric muon neutrino events compared to that of electron neutrino events, and it was Super-Kamiokande that first confirmed the oscillation process with a beam of artificial (accelerator) muon neutrinos in the dedicated K2K experiment [42], which took place from 1999 to 2004. And nowadays this successful story continues with the T2K [43] experiment, another accelerator neutrino experiment which is the successor of K2K.

In the solar neutrino study the results provided by Super-Kamiokande are equally of great importance, as key ingredient of the joint analysis of all the experiments to ascertain the allowed regions of the oscillation parameters [10].

3.3. Scintillation Detectors

Scintillation detectors have a long and established tradition in the area of neutrino physics, starting from the Cowan-Reines Savannah River experiment [44], which performed the first neutrino detection ever. Other pioneer detectors of this kind which deserve to be mentioned for their historical role in the field (but not necessary in the oscillation study) are the Baksan Underground Scintillation Telescope (BUST) [45], which also detected the SN1987A neutrinos, the Liquid Scintillation Detector (LSD) at Mont Blanc [46], the Large Volume Detector (LVD) at Gran Sasso [47] devoted to Supernova search, and the Gosgen [48] and Bugey [49] reactor experiments.

In the following we focus our attention on the more recent implementations of this technique, for the realization of experiments which played a fundamental role in nailing down the neutrino oscillation properties.

3.3.1. Borexino

In the context of the solar neutrino research, the Borexino project was conceived and designed to detect in real time the low energy component of the solar flux, with special emphasis on the neutrinos coming from the electron capture in the core of the Sun, exploiting as simple and effective mean to reveal the incoming particles their scattering reaction off the electrons of the target medium.

Specifically, Borexino is a scintillator detector [50] which employs as active detection medium a mixture of pseudocumene (PC, 1,2,4-trimethylbenzene) and PPO (2,5-diphenyloxazole, a fluorescent dye) at a concentration of 1.5 g/L. Because of its intrinsic high luminosity (50 times more than that in the Čerenkov technique) the liquid scintillation technology is extremely suitable for massive calorimetric low energy spectroscopy. The isotropic nature of the scintillation light does not allow inferring the direction of the incoming particles; it is therefore impossible, contrary to what happens in the Čerenkov experiments, to distinguish neutrino scattered electrons from electrons due to natural radioactivity by the association with the direction from the Sun. Thus the key requirement in the technology of Borexino is an extremely low radioactive contamination.

To reach ultralow operating background conditions in the detector, the design of Borexino, as shown in Figure 2, is based on the principle of graded shielding, with the inner scintillating core at the center of a set of concentric shells of increasing radiopurity. The scintillator mass (278 tons) is contained in a 125 m thick nylon inner vessel (IV) with a radius of 4.25 m. Within the IV a fiducial mass is software-defined through the estimated events position, obtained from the PMTs timing data via a time-of-flight algorithm.

A second nylon outer vessel (OV) with radius 5.50 m surrounds the IV, acting as a barrier against radon and other background contamination originating from outside. The region between the inner and outer vessels contains a passive shield composed of pseudocumene and 5.0 g/L (later reduced to 3.0 g/L) of DMP (dimethyl phthalate), a material that quenches the residual scintillation of PC so that spectroscopic signals arise dominantly from the interior of the IV.

A 6.85 m radius stainless steel sphere (SSS) encloses the central part of the detector and serves also as a support structure for the PMTs. The region between the OV and the SSS is filled with the same inert buffer fluid (PC plus DMP) which is layered between the inner and outer vessels.

Finally, the entire detector is contained in a tank (radius 9 m, height 16.9 m) filled with ultrapure water. The total liquid passive shielding of the central volume from external radiation (such as that originating from the rock) is thus 5.5 m of water equivalent (m.w.e.). The scintillator material in the IV was less dense than the buffer fluid by about 0.1% with the original DMP concentration of 5 g/L; this resulted in a slight upward buoyancy force on the IV, implying the need of thin, low-background ropes made of ultrahigh density polyethylene to hold the nylon vessels in place. This modest buoyancy was further reduced more than a factor 10 by removing via distillation a fraction of the total DMP content in the buffer: the process ended with a final DMP concentration of 3 g/L, still perfectly adequate to suppress the buffer scintillation, while at the same time implying less stress applied to the IV.

The scintillation light is viewed by 2212 8′′ PMTs uniformly distributed on the inner surface of the SSS. All but 371 photomultipliers are equipped with aluminum light concentrators designed to increase the collection efficiency of the light from the scintillator, concurrently minimizing the detection of photons not coming from the active scintillating volume. Residual background scintillation and Čerenkov light that escape quenching in the buffer are thus reduced. The PMTs without concentrators can be used to study this background, and help identify muons that cross the buffer and not the inner vessel.

Besides being a powerful shield against external backgrounds (’s and neutrons from the rock), the water tank (WT) is equipped with 208 PMTs and acts as a Čerenkov muon detector. The muon flux, although reduced by a factor 106 by the 3800 m.w.e. depth of the Gran Sasso Laboratory, is still significant (1.1 muon m-2  h−1) and an additional reduction (by about 104) is necessary. Ultralow radioactive contamination is the distinctive feature of Borexino, achieved through a multiple strategy [51] that implied on one hand the careful selection and screening of all the construction materials and components and on the other the purification of the active scintillator to unprecedented purity levels (see Table 1).


Name Source Typical Required Achieved

C Intrinsic PC ~1  g/g ~1  g/g ~2   g/g
U Dust  g/g <1  g/g  g/g
Th  g/g
Be Cosmogenic ~3   Bq/ton <1  Bq/ton Not observed
K Dust, PPO ~2   g/g (dust) <1  g/g Not observed
Po Surface <7 cpd/ton May 07 : 70 cpd/ton
Contamination May 09 : 5 cpd/ton
Rn Emanation, rock 10 Bq/L (air, water) 10 cpd/100 tons 1 cpd/100 tons
100–1000 Bq/kg (rock)
Ar Air, cosmogenic 17  (air) 1 cpd/100 tons Kr
Kr Air, nuclear weapons ~1  (air) 1 cpd/100 tons  cpd/100 tons

Clearly, in this respect key factors are the many liquid purification and handling systems designed and installed to ensure the proper manipulation of the scintillator at the incredible degree of cleanliness demanded by the experiment. The exceptional low-background environment achieved in the core of the liquid scintillator allowed the unprecedented and precise sub-MeV measure of the component of the solar neutrino flux, which to date is the only direct confirmation of the validity in such a low energy range of the MSW mechanism driving the oscillation of neutrinos produced in the core of the Sun.

Borexino has taken data during the so-called phase 1 (May 2007–July 2010) and started again to collect data (phase 2), after a further campaign of purification of the scintillator, in October 2011. The purification campaign succeeded to further reduce the residual contamination of the scintillator.

3.3.2. Other Scintillation Experiments

Other important scintillator-based experiments which provided milestone results for the understanding of the neutrino oscillation properties are KamLAND [19] and, more recently, Daya Bay [52], RENO [53], and Double Chooz [54]. While in term, of methodology all these experiments are very similar to Borexino, as far as detection criteria, techniques, and architectural scheme are considered, their specific characteristics are the measurement target, constituted by antineutrinos from reactors. KamLAND, in particular, is not close to any specific reactor but rather detects antineutrinos from a number of Japanese power plants located at an average distance of 200 km, thus performing a long-baseline test. Day Bay, RENO, and Double Chooz, instead, are located a 1 km from the reactor, acting thus as medium baseline experiments.

While in general the respective technology resembles closely that of Borexino, there are some variations in the type of liquid scintillator and in the material used for the balloon containing the liquid. The main difference with Borexino stems from the inverse beta reaction which is used to detect antineutrinos (in contrast with the scattering reaction adopted in Borexino to reveal neutrinos): After the occurrence of this interaction, the prompt signal is due to a positron which decelerates and then annihilates producing two 511 keV rays. The neutron thermalizes and is captured by a free proton, generating a typical 2.2 MeV gamma, the so-called delayed signal. The visible energy of the prompt signal is directly correlated with the kinetic energy of the incident antineutrino [MeV]. The mean time between the positron production and the neutron capture is about 200–260 s depending on the scintillator type, and therefore the tight time coincidence between the respective light signals prodices a correlated measurement which ensures a powerful discrimination of a true antineutrino detection with respect to the uncorrelated background events. This kind of signature greatly reduce the requirements for the suppression of the intrinsic radioactivity in the scintillator, marking the major difference between the technology of these reactor experiments and that employed for the solar neutrino detection in Borexino. For example, in KamLAND has been reduced to  g/g, to  g/g, to a limit  g/g, to ~2 mBq/m3, to <1 mBq/m3, and to ~0.1 mBq/m3.

Historically, the measurement of KamLAND, together with that of SNO, closed the solar neutrino problem, showing unambiguously that also reactor antineutrinos undergo the oscillation phenomenon, while concurrently determining rather precisely the associated mass squared difference parameter and, jointly with the outputs of all other solar experiments, the mixing angle .

Daya Bay and RENO (and in future Double Chooz, as well) have the additional characteristics of being equipped with a near detector, so that the far-near arrangement allows determining also the mixing angle.

As additional remark of this section, it has to be emphasized that also some of the experiments whose outputs are used in the analysis concerning the existence of additional sterile state(s) beyond the established three-neutrino oscillation framework (see Section 4.2.4) are liquid scintillator setups. In particular, the LSND [55] and MiniBooNE [23] detectors, at the center of the current hot debate in this area, share essentially all the distinctive features of the other experiments belonging to the same technical “family.” Specifically, LSND was a cylindrical tank containing 167 tons of scintillator viewed by 1220 8 inch PMTs, while MiniBooNE was based on a spherical detector geometry to contain 800 tons of scintillator, though still using a similar number of PMTs, 1280. The peculiarity of both setups was the exploitation of a special scintillator mixture able to produce a comparable amount of Čerenkov and true scintillation light.

The KARMEN experiment [56] was another player in this debate, but on the other side, since it did not detect the same hints of LSND and MiniBooNE. It was a segmented liquid-scintillator detector; the segmentation, technically the more distinctive feature of the set-up, was realized with 1.5 mm thick lucite sheets which ensured the transport of the light to the photomultipliers via total internal reflection. The detector was also instrumented with a veto employing plastic scintillator modules.

Finally, the pioneer MACRO detector [57] at Gran Sasso was, as well, based on segmented liquid-scintillator counters. Actually it comprised three subsystems, being additionally equipped with limited streamer tubes and nuclear track detectors, which altogether provided the experiment with the capability to detect the atmospheric neutrino oscillation phenomenon.

3.4. Further Techniques

To complete the illustration of the techniques adopted for the neutrino oscillation studies, a brief mention is due to other experiments which have shed light on important aspects of the field, while being not ascribable to any of the methodological categories described so far, starting with MINOS [58] and OPERA [59]. We briefly describe also the basic features of the near detectors of the already mentioned T2K experiment [43] (which, we remind, uses Super-Kamiokande as the far detector), as well as of the CHORUS [60], NOMAD [61], and ICARUS [62] experiments.

The MINOS experiment exploits two detectors to register the neutrino interactions: the near detector at Fermilab characterizing the neutrino beam (NuMI, neutrinos at the main injector, beam) is located about 1 km from the primary proton beam target, while the far detector performs similar measurements 735 km downstream. The far detector is located in Soudan, hosted in an inactive iron mine where it is positioned in a cavern excavated on purpose, 705 m underground (2070 meter water equivalent (m.w.e.)), 210 m below sea level.

The rationale of the experiment is to make comparisons between event rates, energies, and topologies at both detectors and to infer from those comparisons the relevant “atmospheric” oscillation parameters. The energy spectra and rates are measured separately for and charged-current (CC) events, as well as for neutral current (NC) events.

Both the near and far MINOS detectors are steel-scintillator sampling calorimeters, equipped with tracking, energy, and topology measurement possibilities. Such a multiple capability is obtained by alternate planes of plastic scintillator strips and 2.54 cm thick magnetized steel plates.

The 1 cm thick by 4.1 cm wide extruded polystyrene scintillator strips are read out using wavelength-shifting fibers coupled to multianode photomultiplier tubes. Both detectors ensure equal transverse and longitudinal sampling for fiducial beam-induced events.

The far detector comprises 486 octagonal steel planes, with edge to edge dimension of 8 m, interleaved with planes of plastic scintillator strips. The total mass is 5400 tons; the set-up is arranged as two “supermodules” separated by a 1.15 m distance, individually equipped with an independently controlled magnet coil.

The near detector, consisting of 282 planes for a total mass of 980 tons, is located at the extreme of the NuMI beam facility at Fermilab, in a 100 m deep underground cavern under a 225 m.w.e. overburden. It exploits the high neutrino flux at this site to identify a relatively small target fiducial volume for selection of events to be employed for the near/far comparison. The upstream part of the detector, that is, the calorimeter portion, contains the target fiducial volume with all the planes instrumented. The downstream part, the spectrometer section dedicated to the measurement of the momenta of energetic muons, has only one plane every five instrumented with scintillator.

The core of the MINOS detector’s active system is thus based on the technique of solid scintillator, whose main features are good energy resolution and hermiticity, excellent transverse segmentation, flexibility in readout, fast timing, simple and robust construction, long-term stability, ease of calibration, reliability, and, last but not least, low maintenance requirements. Furthermore, the whole setup met also safety and practicality of construction requirements.

The performances of both detectors rely on some key parameters which are the steel thickness, the width of scintillator strips, and the degree of readout multiplexing, which were carefully studied and optimized during the design phase.

The MINOS detectors represented a significant increase in size from previous fine grained scintillator sampling calorimeters, and therefore the relevant design and construction efforts ended up with important technical advancements in detector technology of general interest for the field of application of this technique.

This technological effort of the MINOS construction resulted in an impressive scientific success, which brought further evidence to the neutrino oscillation investigation performed by Super-Kamiokande and K2K, sharpening significantly the evaluation of the relevant “atmospheric” oscillation parameters.

The OPERA experiment was designed aiming at the direct observation of appearance stemming from oscillation in a long baseline beam (dubbed CNGS) from CERN to the underground Gran Sasso Laboratory, at a distance of 730 km, where OPERA is located.

The design of OPERA was specifically tailored to identify the via the topological observation of its decay, reinforced by the kinematic analysis of the event. This goal is pursued through a hybrid apparatus based on two “pillars”: real-time detection techniques (“electronic detectors”) and the Emulsion Cloud Chamber (ECC) method. A detector based on the ECC approach is made of passive material plates, used as target, alternated with nuclear emulsion films employed as tracking devices, featuring submicrometric accuracy.

The submicrometric position accuracy, coupled to the adoption of passive material, allows for momentum measurement of charged particles through the detection of multiple Coulomb scattering, as well as for identification and measurement of electromagnetic showers, together with electron/pion separation.

In essence, the main advantage of the ECC technique is the unique property of combining a high accuracy tracker with the capability of performing precise measurements of kinematic variables.

OPERA scaled the ECC technology to an unprecedented size: the basic unit of the experiment is a “brick” realized with 56 plates of lead (1 mm thick) interleaved with nuclear emulsion films, for a total mass of 8.3 kg; 150000 of such target units have been assembled, amounting to an overall mass of 1.25 kton. The bricks are arranged in 62 vertical structures (walls), orthogonal to the beam direction, interleaved with planes of plastic scintillators.

The detector is made of two identical supermodules, each comprising 31 walls and 31 double layers of scintillator planes followed by a magnetic spectrometer.

The electronic detectors accomplish the twofold task to trigger the data acquisition, identify and measure the trajectory of charged particles, and locate the brick where the interaction occurred.

The momentum of muons is measured by the spectrometers, with their trajectories being traced back through the scintillator planes up to the brick where the track originates. In case of no muons observation, the scintillator signals produced by electrons or hadronic showers are used to predict the location of the brick that contains the primary neutrino interaction vertex. The selected brick is then extracted from the target and afterwards the two interface emulsion films attached on the downstream face of the brick are developed. If tracks related to neutrino interaction are observed in these interface films, the films of the brick are developed, too, following the tracks back by fully automated scanning microscopes until the vertex is located.

The analysis of the event topology at the primary vertex leads to the identification of possible candidates. Topologies of special interest might include one track that shows a clear “kink” due to the decay-in-flight of the (long decays) or an anomalous impact parameter with respect to the primary vertex (short decays) compatible with a decay-in-flight in the first lead plate. Once selected, such topologies are double-checked by a kinematic analysis at the primary and decay vertices.

The modular structure of the target ensures to extract only the bricks actually hit by the neutrinos, therefore achieving an efficient analysis strategy of the interaction, while at the same time minimizing the target mass reduction during the run.

In the overall structure of the OPERA detector each brick wall, containing 2912 bricks and supported by a light stainless steel structure, is followed by a double layer of plastic scintillators (Target Trackers, TT) that provide real-time detection of the outgoing charged particles. The instrumented target is further followed by a magnetic spectrometer, consisting of a large iron magnet instrumented with plastic Resistive Plate Chambers (RPC). The bending of charged particles inside the magnetized iron is measured by six stations of drift tubes (Precision Trackers, PT). Left-right ambiguities in the reconstruction of particle trajectories inside the PT are removed by means of additional RPC, with readout strips rotated by ±45° with respect to the horizontal plane and positioned near the first two PT stations.

What was defined before as a supermodule is actually an instrumented target together with its spectrometer.

Finally, two glass RPC planes mounted in front of the first target allow rejecting charged particles originating from outside the target fiducial region, coming from neutrino interactions in the surrounding materials.

As conclusive remark, OPERA is the first very large scale emulsion experiment: the 150000 ECC bricks include about 110000 m2 emulsion films and 105000 m2 lead plates; the scanning of the events is performed with more than 30 fully automated microscopes. The success of this impressive machine is witnessed by the unambiguous detection of 3 events, so far.

In an arrangement similar to MINOS, T2K [43] employs two near detectors located 280 m from the graphite proton target to measure the properties of the unoscillated neutrino beam.

The INGRID near detector comprises 16 modules, 14 of which are positioned in a cross configuration centered on the beam axis. They are made of iron and scintillator layers, allowing the measure of the neutrino rate and profile in the beam axis direction.

The ND280 off-axis near detector is located off the beam axis in the same direction as SK, being exploited to measure the properties of the un-oscillated off-axis beam. It consists of several subdetectors: the so-called Pi-Zero detector () is a plastic scintillator-based detector optimized for detection, followed by a tracking detector made of two fine grained scintillator detector units, in turn sandwiched between three time projection chambers. Both the and tracker are surrounded by electromagnetic calorimeters, including a module located immediately downstream of the tracker itself. The whole detector is located in a magnet with a 0.2 T magnetic field, serving also as mass for a side muon range detector.

Important predecessors of these efforts were two experiments carried out at CERN in the 90s, CHORUS [60] and NOMAD [61].

The active target of CHORUS was realized with nuclear emulsions (total mass of 770 kg). A scintillating fiber tracker was interleaved, both for timing and for extrapolating the tracks back to the emulsions. The set-up comprised also a hexagonal spectrometer magnet for momentum measurement, a high resolution spaghetti calorimeter for measuring hadronic showers, and a muon spectrometer. The scanning of the emulsions was performed with high-speed CCD microscopes.

NOMAD adopted drift chambers as target and tracking medium. The chambers were 44, located in a 0.4 T magnetic field, for a total fiducial mass of 2.7 tons. They were followed by a transition radiation detector (for separation), by additional electron identification devices and by an electromagnetic lead glass calorimeter. The detector comprised also a hadronic calorimeter, 10 drift chambers for muon identification, and an iron-scintillator calorimeter of about 20 tons.

Finally, looking ahead to the future, it must be mentioned that a very promising technique potentially very useful for neutrino oscillation investigation is that based on liquid argon, developed through a very long research and development effort for the ICARUS detector [62]. Such liquid argon time projection chamber allows calorimetric measurement of particle energy together with three-dimensional track reconstruction from the electrons drifting in the electric field applied to a volume of sufficiently pure liquid argon. The technique, thus, successfully reproduces the extraordinary imaging features of a bubble chamber, but with the advantage of being a full electronic detector, potentially scalable to the huge masses required for the next round of experimental neutrino studies.

4. Experimental Results

The experimental results concerning the neutrino oscillations have been obtained studying neutrinos from several sources: solar and atmospheric neutrinos, reactor antineutrinos, and neutrino and antineutrino accelerator beams. The neutrino experiments make use of a variety of techniques: radiochemical methods, water and heavy water Čerenkov detectors, and liquid and plastic scintillators; in some detectors also streamer chambers and time projection chambers are used, in addition to nuclear emulsions.

The experiments can be classified as disappearance and appearance ones: the first are measuring a reduced flux of neutrinos having the same flavor as that at the source, while the second are looking for neutrinos of different flavor with respect to those emitted by the source.

4.1. Neutrino Sources

The Sun is one important source of neutrinos. Energy in the Sun is, in fact, produced by chains of nuclear reactions whose overall result is the conversion of hydrogen into helium Due to lepton number conservation, helium production is accompanied by the production of two-electron neutrinos. The total energy released in reaction (74) is  MeV and only a small part of it (about 0.6 MeV on average) is carried away by the two neutrinos. The total flux of electron neutrinos arriving on Earth (if they do not oscillate) can be then estimated from the radiative flux produced by the Sun on the Earth surface, obtaining Due to the eccentricity of the Earth’s orbit, the solid angle from the Sun to the Earth changes during the year, and thus the solar neutrino flux shows a seasonal variation.

The interpretation of solar neutrino experiments requires a detailed knowledge of the solar neutrino spectrum; see Figure 3. Hydrogen burning in the Sun proceeds through two chains, namely, the chain and the CNO bicycle. At the temperature and density characteristic of the solar interior, hydrogen burns with ~99% probability through the chain that is predominantly initiated by the reaction. This reaction produces the so-called neutrinos which have a continuous spectrum extending up to  MeV and constitutes 90% of the total neutrino flux. Alternatively, the chain can originate with 0.23% probability from the reaction that produces the less abundant monochromatic pep neutrinos with energy  MeV.

The chain has three possible different branches (-I, -II, and -III) whose relative rates depend on the central temperature of the Sun. In the -II termination, the electron capture reaction produces the monochromatic neutrinos with energy  MeV. This value corresponds to transitions to the ground state. With ~10% probability, is produced in the first excited states together with a neutrino with energy  MeV. In the -III branch, the -decay is responsible for the production of the neutrinos. The flux of neutrinos is extremely low, being approximately equal to of the total flux, but the spectrum extends up to a maximal energy  MeV.

In the CNO cycle, the overall conversion of four protons into helium is achieved with the aid of C, N, and O nuclei present in the Sun. The -decays , , and, to a minor extent, produce the so-called , , and neutrinos, respectively, all together referred to as CNO neutrinos. These three components of the solar neutrino flux have continuous spectra extending up to , 1.7, and 1.7 MeV, respectively.

The predictions for each component of the solar neutrino flux are obtained by constructing a Standard Solar Model (SSM) which, according to the definition of [63], is a solution of the stellar structure equations (starting from a chemical homogeneous initial model) that reproduces, within uncertainties, the observed properties of the present Sun, by adopting physical and chemical inputs chosen within their range of uncertainties. In Table 2, we report the neutrino fluxes predicted by two recent SSM calculations that adopt two different assumptions for the admixture of heavy elements in the Sun. Namely, the model labeled GS98 is obtained by using the “old” composition from [29], while the model labeled AGSS09 adopts the “new” admixture of [30]. The reason to consider these two calculations is that, in recent years, a new solar problem, often referred to as solar metallicity puzzle, has emerged. The most recent determinations of the solar photospheric heavy-element abundances (among which [30]) have indicated, in fact, that the solar metallicity is lower by 30 to 40% than previous measurements [29]. However, the internal structure of SSMs calibrated against the newly determined solar surface metallicity does not reproduce the helioseismic constraints; see, for example, [64]. The experimental determination of the solar neutrino fluxes, besides providing crucial information for flavor neutrino oscillations, may help to shed light on the origin of these discrepancies.


AGSS09 GS98

pp ( ) ( )
pep ( ) ( )
hep ( ) ( )
Be ( ) ( )
B ( ) ( )
N ( ) ( )
O ( ) ( )
F ( ) ( )

The neutrino fluxes are given in units of ( ), ( ), ( , , ), ( , ), and ( )   .

The atmospheric neutrinos are produced by cosmic rays, which collide with the atmosphere at its most external regions. In these collisions triggered mostly by the cosmic protons (plus a 5% of He and some minor contributions of heavier nuclei), pions and, at a much smaller rate, kaons are produced [6569].

The main sources of the atmospheric neutrinos are the following reactions: As a consequence, the produced fluxes are approximately Moreover, due to the cosmic ray isotropy and the sphericity of the Earth, the up and down neutrino fluxes (i.e., having the zenith angle corresponding to and , resp.) are expected to have the same magnitude: where is the energy of neutrino with flavor .

The atmospheric neutrino flux can be evaluated with an uncertainty < 10% at  GeV, while at  GeV the error is larger. At  GeV, the relation (78) is valid within 2-3% errors. The accuracy worsens at larger energies due to kaon production. Equation (79) is confirmed at 1% at  GeV and has an uncertainty <1% at 1 GeV.

Nuclear reactors are a source of electron antineutrinos. The energy spectra of antineutrinos released in the fission of the main isotopes used as the fuel in reactor cores (, , , and ) are shown in Figure 4. The reactor antineutrino flux is different from site to site and strongly depends on the presence of reactors in the neighborhoods. Its evaluation [7073] has to take into account different reactor characteristics, some of them time dependent, as their thermal power and the power fractions of fuel isotopes. The reactor-detector distance has a strong influence on the shape of the oscillated, electron antineutrino energy spectrum. The mean energy of reactor antineutrinos which can be detected by the inverse beta-decay reaction given in (73) is about 4 MeV.

Supernova explosions represent another possible source of neutrinos and antineutrinos of all flavors. The observation of neutrinos produced by a galactic Supernova could bring important information to comprehend the explosion mechanism and to study neutrino propagation in the dense Supernova environment. Supernova neutrino oscillations have a complex and interesting phenomenology; their potential in neutrino oscillation studies may be affected by the large uncertainties of the astrophysical Supernova models.

Finally, neutrinos and antineutrinos of various energies can be produced by accelerators. At CERN, FNAL, KEK, and Los Alamos Neutron Science Center, neutrino and antineutrino beams are produced for short and long baseline neutrino experiments.

4.2. The Neutrino Oscillation Study

The experimental study of the neutrino oscillations can be divided into several phases: the solar neutrino problem, the first proof of the oscillation phenomenon from atmospheric and solar neutrino experiments, precise measurements of the oscillation parameters and by studying the nuclear-reactor antineutrinos, extension of the oscillation analysis to the low-energy neutrinos and the vacuum regime, confirmation of the oscillation phenomenon via disappearance and appearance experiments with accelerator beams, measurements of non-zero , and finally indication of a third and therefore of a possible sterile neutrino.

4.2.1. Proof of the Neutrino Oscillation Phenomenon

The road towards the first understanding of the neutrino oscillation phenomenon passed several milestones.

(1) The Solar Neutrino Problem: An Apparent Deficit in the Solar Neutrino Flux. Pioneering experiments used the radiochemical techniques (see Section 3.1) applied to the observation of solar neutrinos; they are Homestake [24], GALLEX [26], and SAGE [27, 28]. These experiments are based upon the charged-current interaction of electron-flavor neutrino on a nucleus. Because the solar ’s oscillate to different flavors, the experiments, which are sensitive only to electron neutrinos, detect a reduced number of events with respect to the expectations based on the Standard Solar Model (SSM). This lack of signal has been called “Solar Neutrino Problem” and the possible explanations were either a wrong description of the Sun by SSMs or the phenomenon of the “Neutrino Oscillations,” a hypothesis introduced by Pontecorvo in 1957 [13].

The radiochemical experiments measure the integrated flux from the detection reaction threshold to the upper limit of the solar neutrino energy spectrum. Homestake measurements start from a threshold of ~0.814 MeV and, thus, do not probe the neutrino component of the solar neutrino flux; it observes  SNU (SNU = solar neutrino unit equals to the neutrino flux producing captures per target atom per second) to be compared with the SSM expectation of  SNU [24]. A deficit of the solar neutrino signal was confirmed later by GALLEX, which, with a threshold at ~0.23 MeV, found SNU to be compared to the expected  SNU [26]. SAGE is still running and its results agree with the GALLEX’s ones. The reduction is higher in the Homestake data (~67%) than in GALLEX (~35%). This difference is partly, but not completely, explained by the dependence of survival probability from the neutrino energy. A recent hypothesis of the existence of a light sterile neutrino [74] could explain the Homestake result.

The solar neutrino problem raised by the radiochemical experiments has been confirmed in 1991 by a real-time experiment based on the water Čerenkov technique, Kamiokande, detecting the elastic scattering [75]. The elastic scattering cross section is lower for flavor neutrino than for the electron-flavor neutrino (for the muon flavor ). Kamiokande finds the solar neutrino flux reduced by 40% with respect to what was expected by the SSM. The measured neutrino energy range includes only the solar neutrinos, because the threshold in Kamiokande is at ~5.0 MeV of the recoil-electron energy (which corresponds to ~5.2 MeV for the neutrino energy).

(2) The First Experimental Proof of Neutrino Oscillations. The experimental evidence for the existence of the neutrino oscillation phenomenon has been provided by three Čerenkov experiments (see Section 3.2), studying the atmospheric neutrinos with water (Kamiokande and Super-Kamiokande) and the solar neutrinos with heavy water (SNO). Here, we demonstrate the atmospheric neutrino measurements on the Super-Kamiokande results, since they are fully compatible with those of Kamiokande but are based on higher statistics.

Super-Kamiokande observed [16] an important discrepancy in the atmospheric up and down fluxes, not observed, on the other hand, in the rates. The measured ratio of up and down fluxes is well different from 1, contrary to what is expected in the absence of neutrino oscillations; see (80).

The results are summarized in Table 3 and in Figure 5. Super-Kamiokande detects the muons produced by and the electrons produced by : muons and electrons are fast enough to produce a Čerenkov-light cone. The sub-GeV events are fully contained in the detector, while this is not the case for the multi-GeV events.


Source “Up/down” asymmetry

Multi-GeV -like
Multi-GeV -like
Sub-GeV -like
Sub-GeV -like

The observed “up/down” asymmetry can be interpreted in terms of oscillations in vacuum. The best fit values of the oscillation parameters obtained from these data are  eV2 and (for Kamiokande data [76], the allowed region is ranging between and  eV2).

This oscillation effect can be understood on the basis of the oscillation length in vacuum, corresponding to a neutrino energy of ~1 GeV and to  eV2 (see Section 2):

The “downgoing” neutrinos are reaching the detector after ~10 km from their production, while the “upgoing” neutrinos travel on average ~6000 km. As a consequence, the distance between production and detection for the downgoing neutrino is too short to observe a relevant flavor change. In Figure 6, the number of events versus ( is the distance between the neutrino production and the detector and is the neutrino energy) is shown.

These Super-Kamiokande results have demonstrated for the first time the existence of an oscillation phenomenon on the atmospheric neutrinos. It is essentially model independent and not influenced by any hypotheses assumed in the cosmic ray simulations. The results obtained by Kamiokande and Super-Kamiokande have been confirmed by MACRO experiment [57] with smaller statistics.

The SNO detector is a heavy water Čerenkov experiment installed in the Sudbury Inco mine (see Section 3.2.1). The use of a deuterium target allowed to study two independent neutrino interactions: charge current (CC, (70)) and neutral current (NC, (71)). In addition, the elastic scattering (72) has been detected. The data have been collected during three phases, characterized by different techniques to capture the neutron emitted in the NC reactions. The 5 MeV SNO threshold limits the detectable neutrinos to the component of the solar neutrino flux. Later SNO has repeated the analysis pushing down the threshold to 3.5 MeV (SNO LETA [77]). The - fluxes measured by SNO are summarized in Table 4.


Data set

Phase 1 (306 live days) [31]
Phase 2 (391 live days) [32]
Phase 3 (385 live days) [32]