Neutrino Oscillations in the Atmospheric Parameter Region: From the Early Experiments to the Present

The aim of this paper is to provide a historical perspective on the main experimental steps which led to the current picture of neutrino oscillations in the “atmospheric parameter region.” In the 1980s a deficit of atmospheric muon neutrinos was observed with the first generation of underground experiments. In the following decade new experiments provided fundamental results which led to the discovery claims in 1998. At the beginning of the new century neutrino beams of medium and high energy became available and several long baseline experiments were performed and added new information to the atmospheric neutrino puzzle. The interpretation of the results of atmospheric and long baseline neutrino experiments was in terms of dominant ] μ → ] τ oscillations. Short recollections are made of the SNO solar neutrino measurements, of the results with neutrino telescopes, and of reactor neutrinos to measure sinθ 13 . Over the years the phenomenological picture improved in completeness and increased in complexity. A short perspective concludes the paper.


Introduction
A first hypothesis on neutrino oscillations of the type ] ↔ ] was introduced in the 50s by Pontecorvo in analogy with strangeness oscillations in the quark sector [1,2].Later the idea was extended to include mixing between mass and flavor eigenstates and transitions between different neutrino flavors [3,4].Pontecorvo predicted possible variations of the solar ] flux on Earth due to neutrino oscillations [4].
Experimentally the first indication of a neutrino flux deficit with respect to expectations came from solar neutrinos.Since the late 1960s it was observed that the neutrino flux from the sun measured with a chlorine target experiment [5][6][7][8] was significantly smaller than that computed with theoretical predictions based on the solar standard model (SSM) [9,10].The anomaly was confirmed in the 80s by experiments using gallium (GALLEX [11], SAGE [12,13], and GNO [14]) and water targets (Kamiokande [15,16]).The deficit-referred to as the "solar neutrino problem"-was interpreted in different ways, in particular, invoking neutrino oscillations, namely, the conversion in flight of solar ]  in other neutrino flavors.The final proof of the solar neutrino problem came in 2001 and 2002 with the results of the SNO heavy-water experiment [17,18].Measuring the rates of charged current (CC) interactions (sensitive only to ]  ) and of neutral current (NC) interactions (sensitive to all neutrino flavors) it was proved that the deficit existed only for ]  while the total neutrino flux rate was consistent with the SSM predictions.These results lead to the following conclusions: (i) neutrinos oscillate during their travel toward the Earth, (ii) solar neutrino fluxes are in agreement with the SSM predictions if neutrino oscillations are taken into account, and (iii) it was indirectly proved that neutrino flavors at the detection level are different from those produced at the source.In 2002 the KamLAND experiment [19]-free from the systematics related to solar models-provided a positive indication/evidence for neutrino oscillations in the solar energy sector using artificial ]  beams from a large number of nuclear reactors.More recently, the Borexino experiment at the Gran Sasso Laboratory confirmed the solar oscillation scenario measuring the flux of the low energy 7 Be neutrinos [20,21].
At another energy scale and much shorter distances, a flux reduction with respect to expectations was observed in The atmospheric neutrino flux was computed in the early 1990s [39,40] and 2000s [41][42][43].At low energies,  ] ≃ 1 GeV, the predicted number of neutrinos differed by ∼20-30%.At higher energies,  ] ≥ 10 GeV, the computations were more reliable and had an estimated systematic uncertainty of about 15%.The predicted relative rates of ]  and ]  and the shapes of the zenith distributions were affected by lower systematic errors.
Atmospheric neutrino experiments were mainly disappearance experiments, that is, experiments which measured a reduction of the ]  flux compared with the ]  flux or a depletion in the number of ]  with the distance from production to detection.The observation of the appearance of some ]  's in a ]  beam would prove the present paradigm of neutrino oscillations.
This paper is organized as follows.In Section 2 the formalism underlying the phenomenon of neutrino oscillations is recalled.Section 3 is devoted to the atmospheric neutrino experiments, separated on a historical basis into "early" experiments, experiments in the "discovery" phase, and precise confirmation accelerator experiments.In Section 4 are discussed the measurements with reactor antineutrinos of the  13 mixing angle and in Section 5 are described the results from the long baseline neutrino oscillation experiments operating in the "atmospheric parameter region" (K2K, NuMi, and CNGS).Section 5.1 is dedicated to the LSND Δ 2 scale and to a discussion of new proposals on the subject of sterile neutrinos.In Section 6 we review existing experimental results which cannot be accommodated in the standard neutrino oscillation framework.In Section 7 are briefly summarized the present experimental efforts to measure neutrino cross sections and kinematical quantities useful for a correct interpretation of the neutrino data.In Section 8 are examined the roles that large neutrino telescopes could have in the framework of neutrino oscillations.We conclude in Section 9 with comments on some important open issues in neutrino physics.

Neutrino Oscillations and Masses
The standard model (SM) of particle physics has been experimentally verified to a high degree of accuracy over a broad range of energies and processes [44][45][46][47][48][49].The SM cosmology has received confirmations from the Planck experiment [50].The Higgs particle  0 was recently discovered at the CERN LHC by the ATLAS and CMS experiments, using mainly the cleanest decays  0 →  and  0 →  0  0 → 4 charged leptons [51,52].The two experiments are now making precise measurements of all the  0 properties to check if the discovered particle is really the Higgs boson of the SM.In the SM, neutrinos are described as massless left-handed (LH) fields (the opposite for antineutrinos which are right-handed, RH).Each LH neutrino is a component of an SU (2) doublet together with the corresponding charged lepton fields.In case of neutrino mixing and nonzero neutrino masses RH neutrinos (and correspondingly LH antineutrinos) form an SU (2) electroweak singlet with no coupling to SM vector bosons (sterile neutrinos).
The existence of neutrino oscillations-and therefore of massive neutrinos-is the first direct and unambiguous evidence for physics beyond the SM.Moreover any theory able to accommodate neutrino masses should provide an explanation for the fermion mass pattern as presently known in the SM, where neutrinos masses are orders of magnitudes smaller than other massive particles (Figure 1).We recall that all particle masses arise from the interactions with the Higgs field.The SM in its present form is not able to predict the mass spectrum illustrated in Figure 1.
The Grand Unified Theory, GUT, is usually obtained assuming the absence of new physics between the electroweak scale and the GUT scale (10 16 eV).The GUT scale cannot be reached with present or future accelerators.Several theorists consider intermediate energy scales and discuss possible new phenomenological effects [53].
If neutrinos have nonzero masses, the V - ]  ( = , , ) are linear combinations of the  - ]  ( = 1, 2, 3) via the elements of the unitary mixing matrix   , usually called the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix: where the  index in the summation is extended to the number of mass eigenstates.Neutrino oscillation experiments measure the probability of a ]  flavor to convert into a ]   after a time  from production at some distance  =  from the source.The corresponding probability can be expressed as  where   is the energy of the mass eigenstate ]  .In vacuum, if CPT holds, (] For the neutrinos the mixing matrix   is specified by three rotation angles,  23 ,  13 , and  12 (0 ≤   ≤ ), and three phases ,  1 , and  2 ( ≥ 0,   ≤ 2).In the conventional parameterization the matrix   reads as follows: with  12 ≡ sin  12 ,  12 ≡ cos  12 and similarly for the other sines ( 13 ) and cosines ( 13 ,  23 ,  12 ).The action of the three rotation matrices is illustrated in Figure 2 with approximate values of the three mixing angles  12 ,  13 , and  23 , as presently known [49].Neutrino oscillations depend on six independent parameters: two mass squared differences,  and the (1-2) sector with oscillations at the solar scale; the (1-3) sector concerns ]  → ]  and, for nuclear reactors, ]  disappearance.The two phases,  1 and  2 , do not affect neutrino oscillations but may have physical consequences (e.g., in neutrino-less double beta decay) if neutrinos turn out to be Majorana particles.

Advances in High Energy Physics
In the approximation of two flavors (]  , ]  ) and two mass eigenstates (] 2 , ] 3 ) one can write In this case the oscillation probability (2) of a ]  beam becomes where  is the distance traveled by the neutrino from production to interaction in a detector and  ] is the neutrino energy.The survival probability for the initial In several cases one needs oscillations including three flavors [54].
Since neutrino oscillations are sensitive to (unsigned) neutrino mass differences (5) the present experimental data leave open two possibilities for mass ordering.Since Δ 2  21 > 0 (from solar matter effects measurements), there are two In matter (e.g., inside the sun) CC coherent scattering of ]  with atomic electrons changes the weak potential, a phenomenon known as the Wolfenstein-Mikheyev-Smirnov (MSW) effect [55,56].
The oscillation parameters are modified according to where  = 2 √ 2     ] /Δ 2 , with   the electron density in matter and   the Fermi constant.We now recall the existing limits on neutrino masses, on the number of light neutrinos, and on neutrino lifetime obtained from searches at accelerators and from observational cosmology [41-43, 57, 58].
Direct Measurements of Neutrino Masses.Many direct measurements were and are being performed using mainly tritium decay, 3  → 3  + +  − + ]  , measuring, with magnetic spectrometers of ever increasing precision, the electron spectrum near its kinematical limit where the number of events is small, ∼10 −3 times of the whole sample.The present best limit is (]  ) < 2 eV (95% CL) [49].Notice that in direct searches the upper limits correspond to a weighted average of the neutrino mass contributing to a given flavor since the measured quantity is Limits on ]  and ]  masses were obtained at accelerators using muon and tau decays which yielded (]  ) < 0.19 MeV, (]  ) < 18 MeV [49].The last limit comes from the combination of results from different experiments, mainly at LEP.In these experiments the most sensitive conditions are when the  decays into many charged pions [59].
Neutrino-less double- decay searches provide limits on the effective Majorana mass ⟨  ⟩ = | ∑ 3 =1  2 1  ]  |.The present best upper limit ranges from 0.19 eV to 0.68 eV depending on the nuclear matrix calculation used [60].It is worth noting that the discovery of the Majorana nature of neutrinos would have a deep impact on the general framework of the SM in which all fermions obey the Dirac equation: neutrinos would be the only exceptions.Massive ]'s and Cosmology.Massive stable neutrinos contribute to the overall energy density of the universe.In particular if ∑  ] < 1 eV the neutrinos would affect the clustering of galaxies at relatively large cosmological scales.A limit on ∑  ] < 0.3 eV was obtained by the Planck satellite collaboration [50].
Number  ] of Light Neutrino Types.The most precise measurements of the number of light "active" neutrinos (i.e., neutrinos with electroweak couplings) come from the four LEP experiments.The combined result is  ] = 2.984 ± 0.008 [49].
The density of radiation in the universe, besides photons, is usually parametrized by the effective neutrino number  eff .In the standard model of cosmology,  eff = 3.046.
Neutrino Lifetime.The indications from experiments and from cosmology are that neutrinos are either stable or long lived [62].Specific experiments which searched for radiative solar neutrino decays during total solar eclipses yielded  ] > 10 − 10 9 s depending on the ] 1 mass [63].

Atmospheric Neutrino Experiments
The main sources of atmospheric neutrinos are the decays of charged mesons ( and ) produced in the primary cosmic ray interactions with atmospheric atomic nuclei.Mesons in turn decay into  and ]  .At low energies muon decay gives rise to electron, electron neutrinos, and muon neutrinos: with fluxes Φ(]  ) ∼ Φ(]  ) ∼ 2Φ(]  ) and flux ratios Φ(]  )/Φ(]  ) ∼ Φ( + )/Φ( − ).In this energy region the total atmospheric neutrino flux is of the order of 0.1 cm −2 s −1 and the energy spectrum can be approximated with a power law Φ ] ∼  −2  ] .The zenith angle distribution is asymmetric since at low energy the primary CR flux depends on the geomagnetic location and so does the neutrino flux.
At high energy muon decay can be neglected and meson decay remains the dominant atmospheric neutrino source.The neutrino flux steepens and it becomes asymptotically steeper than the primary flux (∼  −3.7  ] ).In this case the zenith angle distribution is symmetric around the horizontal direction where the neutrino flux is maximum since the path length in atmosphere is maximum and hence the probability of mesons to decay into neutrinos is symmetric.
Atmospheric neutrinos are well suited to study neutrino oscillations, since they have energies from a fraction of a GeV up to more than 100 GeV and they may travel distances  from few tens of km up to 13000 km; thus the ratio / ] in (5) ranges from ∼1 km/GeV to ∼10 5 km/GeV.In particular they cover regions for Δ 2  23 of the order of 10 −3 ÷ 10 −2 eV 2 .Atmospheric neutrino oscillations can be studied by means of three observables.
(i) First, one can measure the ratio of the measured number of ]  events over the predicted one.In order to reduce the systematic error related to the limited knowledge of the absolute flux normalization, one can use the double ratio in which the ]  flux is referred to the ]  flux.
(ii) One may consider that there are two identical sources for a single detector: a near one (downgoing neutrinos) and a far one (upgoing neutrinos) which correspond, respectively, to a short and to a large baseline .For relatively high energy neutrinos ( ] > 10 GeV) the outgoing muon preserves with good accuracy the original neutrino direction ⟨ scattering ⟩ ≃ 10 ∘ and the path length can be measured.Assuming Δ 2 ∼ 10 −3 eV 2 , from (5), (]  → ]  ) ≃ 0 for downgoing neutrinos and (]  → ]  ) ≃ 1 − sin 2 2 23 /2 for upgoing neutrinos.Therefore the measurement of the flux ratio can directly provide information of the mixing angle  23 .
(iii) A third approach is to measure the ]  flux reduction as a function of the baseline  (and therefore of the zenith angle).In this case one may explore the argument of the second sinusoidal term in (5) (which was averaged to ∼1/2 in the previous case).

Early
Experiments.The first experimental information on atmospheric neutrinos came in the 1960s and 1970s from two small detectors located at great depths in South Africa (KGF) [64] and in India (CWI) [65], then followed the experiments Baksan, IMB, Kamiokande, NUSEX, and Fréjus.
For all these studies the main motivation was the search for proton decay and atmospheric neutrinos were a background; only later the search for neutrino oscillations became an interesting possibility.
The Baksan Underground Scintillation Telescope is located at a depth of 850 m.w.e. in the Caucasus region.It is made of liquid scintillation counters placed to form a parallelepiped of 17 m × 17 m × 11 m.The selection of muon events produced by up-through-going neutrinos is made with time of flight methods.In the early data the zenith angle distribution deviated from expectations and seemed to agree with oscillations [30].Later they considered also the absolute number of events and there is an agreement with Monte Carlo predictions; the ratio data/MC is 1.00 ± 0.04 (stat.)± 0.08 (syst.)[31].
The IMB detector was an 8000 t cylindrical water box placed in the Morton salt mine in Ohio, 1750 m.w.e.deep underground [22,23].The Cherenkov light produced by relativistic charged particles passing in the water was detected by photomultipliers installed in the tank walls.The detector started operation in 1982 and was upgraded by increasing the size of the photomultipliers.
The Kamiokande cylindrical detector had a water mass of 3000 t seen by 1000 large PMTs of 50 cm diameter [24][25][26]49].It was installed in the Kamioka mine in Japan at a depth of 2700 m.w.e.It started operations in 1983 and had several upgrades, known as Kamiokande I, II, and III.
The NUSEX detector was a fine granularity detector with a total mass of 150 t, placed in the Mont Blanc tunnel between Italy and France at a depth of 4800 m.w.e.The detector was made of horizontal 3 mm iron plates interleaved with layers of limited streamer tubes [27].
At the same depth was located the 912 t Fréjus detector.It was made of pairs of vertical iron slabs each 1.5 mm thick interleaved with pairs of planes of flash tubes; their trigger was made with Geiger tube layers inserted every 8 layers of flash tubes [28,29].
The early water Cherenkov detectors and the tracking calorimeters detected ]  and ]  charged current interactions.The results were expressed in terms of the double ratio   =  obs / MC , where  obs =( ]  / ]  ) obs is the ratio of observed muon and electron events and  MC is the same ratio for Monte Carlo (MC) events.In   many systematic uncertainties cancel.The double ratios from IMB and Kamiokande were smaller than expectations, while for NUSEX and Fréjus they were in agreement with expectations without oscillations.The IMB collaboration concluded that "however the magnitude of the deviation is not sufficient to require neutrino oscillations to explain our data." The overall spectra and total number of interactions were in agreement with predictions.Furthermore there was no correlation of deficit with energy or angle [22,23]  Super-Kamiokande (SK) presented strong indications in favor of atmospheric neutrino oscillations [33][34][35][36][37][38].After 1998 several additional results were presented [66][67][68][69][70].
The Soudan-2 experiment [69,70] used a modular fine grained tracking and showering calorimeter of 963 t, located at a depth of 2100 m.w.e. in the Soudan Gold mine in Minnesota.The bulk of the target was 1.6 mm thick corrugated steel sheets interleaved with drift tubes.In the final analysis fully contained high resolution events, consisting mostly of quasi-elastic neutrino interactions were used.The data were compared with the Bartol Monte Carlo neutrino flux [39].The double ratio   = (  /  ) DATA /(  /  ) MC integrated over the zenith angle was (0.68 ± 0.11), consistent with ]  → ]  oscillations with maximal mixing and Δ The MACRO experiment operated at the Gran Sasso underground Lab (3800 m.w.e.) from 1989 to 2000. Figure 3 shows a global view and a cross section of the detector.It used 3 different subdetectors: scintillation counters, limited streamer tubes, and nuclear track detectors [71].Up-throughgoing muons with   > 1 GeV came from CC interactions in the rock below the detector and had ⟨ ] ⟩ ∼ 50 GeV.The angular distribution of these muons is highly sensitive to neutrino oscillations as can be seen in Figure 4.
The MC scale uncertainties on the expected muon flux arising from the neutrino flux, cross section, and muon propagation were estimated at ∼17%.In Figure 5  the zenith angle distribution is compared with MC predictions.A measurement of the up-through-going muon energies was made via multiple Coulomb scattering in the dense structure of the apparatus using the streamer tubes in "drift mode" [72,73].The ratios Data/MC no-osc as a function of log 10 (/ ] ) give additional information on neutrino oscillations.Low energy neutrino events ⟨ ] ⟩ ≃ 2-3 GeV (Figure 5(b)) included (i) semicontained upgoing muons (IU) from ]  interactions inside the lower part of the apparatus, (ii) upgoing muons stopping in the detector (UGS) due to external ]  interactions, and (iii) semicontained downgoing muons (ID) originating from ]  interactions in the lower detector.The lack of time information prevented distinguishing between ID and UGS samples.In Figure 5(b) the number of IU events and the angular distributions are compared with MC predictions.The data show a uniform deficit over the whole angular distribution with respect to MC.
In 1998 MACRO results were consistent with neutrino oscillations, with Δ 2 23 = 2.5 × 10 −3 eV 2 and maximal mixing [34][35][36][37].In the final analysis [68] three different ratios were considered in order to reduce systematic uncertainties and MC prediction effects: (1) the ratio  1 =  vert / hor of vertical over horizontal neutrino events in the up-throughgoing data sample; (2) the ratio  2 =  low / high of low energy over high energy neutrino events; (3) the double ratio  3 = (Data/MC) IU /(Data/MC) ID+UGS for the semicontained data sample.Fitting the three ratios to the ]  ↔ ]  oscillation hypothesis MACRO obtained sin 2 2 = 1 and |Δ 2  23 | = 2.3 × 10 −3 eV 2 .In Figure 6(b) the 90% CL allowed parameter region is shown.The addition of the absolute flux information in the global fit increased the statistical significance of the result to the 6 level.Since ]  and ]  interactions with matter share the same weak potential whereas sterile neutrinos do not experience weak interactions, a possibility to discriminate between ]  ↔ ]  and ]  ↔ ] sterile oscillations is to study the neutrino flux emerging from different matter amounts.That was realized by comparing events near the vertical direction with the event number near the horizontal direction [74,75].The angular regions were chosen by MC methods to obtain the best discrimination (Figure 6(a)).In the ratio most of the uncertainties cancel.MACRO excluded at the 99.8% CL the ]  ↔ ] sterile oscillations compared to the ]  ↔ ]  channel [76].
The Super-Kamiokande (SK) detector is a large cylindrical water Cherenkov detector containing 50 kt of water, with a fiducial mass of 22.5 kt.The experiment is still taking data.The Cherenkov light is seen by 50 cm diameter inner-facing phototubes (PMTs) (Figure 7).The 2 m thick outer layer of water acts as an anticoincidence using smaller outward facing PMTs.The detector is located in the Kamioka mine, Japan.The experiment was originally planned mainly to search for proton decay.Atmospheric neutrinos are detected through the Cherenkov light generated by the charged particles produced in neutrino CC interactions in the water.The large detector mass allows defining a fiducial volume large enough to collect good samples of fully contained events (FC) up to ∼5 GeV.The events are further subdivided into sub-GeV and multi-GeV events, with energies below and above 1.particle, a muon, exits the detector without releasing all of its energy (Figure 8).In this case the light pattern is a filled circle.For these events the energy resolution is worse than that for FC interactions.Upward-going muons (UPMU), produced by upgoing neutrinos coming from interactions in the rock, are subdivided into stopping muons (⟨ ] ⟩ ∼ 7 GeV) and upthrough-going muons (with ⟨ ] ⟩ ∼ 70 ÷ 80 GeV) if they stop or not in the detector.Particle identification in SK is performed using likelihood functions to parameterize the sharpness of the Cherenkov rings, which are more diffuse for electrons than for muons.The algorithms discriminate the two flavors with high purity.The zenith angle distributions for -like and -like sub-GeV and multi-GeV events, for PC events and upward-going or stopping muons, are shown in Figure 8.
At the time of Neutrino '98 Conference the values for the double ratio   previously defined were 0.658 ± 0.016 stat ± 0.035 sys for the sub-GeV sample and 0.702 ± 0.031 stat ± 0.101 sys for multi-GeV [66,67].
SK uses a selected sample of events with good resolution in / ] to search for the dip in the oscillation pattern expected when the argument of the second sine-squared term in ( 5) is /2.The dip is observed at / ] ≃ 500 km/GeV (Figure 9).These results favor ]  → ]  oscillations and provide a further constraint on |Δ 2  23 |.Other models that could explain the zenith angle and energy dependent deficit of the atmospheric muon neutrinos are disfavored since they do not predict any dip in the / ] distribution.For ]  ↔ ]  oscillations the best fit yields maximal mixing and |Δ 2  23 | = 2.3 × 10 −3 eV 2 [66,67].
Several tests were performed by the SK experimenters and by several groups of phenomenologists on the ]  ↔ ] sterile possibility [78], on the possible LVI [79,80], and so forth.SK made also a variety of fits of the SK I, II III, and IV data sets in the 3-flavor oscillation scenario obtained at 90% CL: 1.7 < Δ 2  23 < 2.7 ⋅ 10 −3 eV 2 and 0.41 < sin 2  23 < 0.58.In the 3flavor analysis there is no preference for normal or inverted neutrino mass hierarchy [78,81].
SK also searches for ]  → ]  appearance studying several event-related variables with a neural network.Despite the complicated ]  event topology and the high background they claimed a 2.4  significance [82], recently updated with SK I + II + III data to 3.8.
Super-Kamiokande has the largest statistics in different energy regions, all in agreement with atmospheric ]  oscillations.The SK main results are summarized in Table 2 and Figures 8, 9, 10, and 11(b).With more data and a 3-flavor analysis SK may be able to find if  23 is smaller than its maximum and to determine in which octant it lies [83,84].
Several proposals were made for the Gran Sasso Lab, for example, the MONOLITH proposal for a massive magnetized iron detector for atmospheric neutrinos [85].For the future there should be the INO proposal for an India-based Neutrino Observatory [86].

The Mixing Angle 𝜃 13
In the limit  13 → 0, atmospheric and solar neutrino oscillations decouple and can be analyzed separately in the 2-neutrino-flavor approximation.The knowledge of  13 is very important since it is strictly connected with the CP-violating  phase in the matrix element,  3 = sin  13   .Its precise knowledge is decisive for further experiments.
The first two ]  experiments at nuclear reactors, which attempted to measure  13 in disappearance mode, were CHOOZ and Palo Verde [87,88].No evidence for ]  disappearance was found.They obtained limits for ]  → ]  at the level of Δ 2 > 10 −3 eV 2 for sin 2 2 13 > 0.1.
Recently 3 experiments, Daya Bay, Double Chooz, and RENO, each using several nuclear reactors, measured the neutrino oscillation angle  13 , the last parameter needed to really understand the phenomenon of neutrino oscillations.The nuclear reactors are of the latest French-German design (EPR of generation 3 or 3 + ) [89][90][91][92][93][94][95] These experiments used refined detectors.They obtained important results taking advantage of the very large fluxes of low energy ]  from the power reactors. 13 was found to be small but not zero: the average value is sin 2  13 = 0.098 ± 0.013 [49].T2K confirmed the measurement [96].The measured value of  13 opens the possibility of performing many types of precision measurements in the leptonic sector [97][98][99][100][101].

Long Baseline High Energy ] Oscillation Experiments
Long baseline accelerator experiments provide independent measurements of oscillation parameters.Some of these experiments may be complementary to reactor experiments.By combining the results of two such experiments at different baselines, the sign of Δ 2 23 could be determined.High energy neutrino beams are produced accelerating protons up to tens of GeV and impinging them on a target.The produced secondaries are momentum-selected by a series of lensing devices ("horns") which focus them into a parallel beam in an evacuated decay tunnel of ∼1 km length.Table 2 summarizes the main parameters of atmospheric ] experiments.In Table 3 the main parameters of past, present, and possible future long-baseline neutrino oscillation experiments are listed.
The K2K experiment confirmed the atmospheric muon neutrino oscillation picture [102,103].Near detectors located at ∼300 m from the target measured the energy spectrum and the flux normalization.In total 112 beam-originated neutrino events were observed in the SK fiducial volume with an expectation of 158.1 +9.2 −8.6 events for no oscillations, providing a statistical significance against no oscillations of ∼4.3.A subsample of 58 one-ring events was assumed to be quasi-elastic interactions and energy reconstructed using the known beam direction.The energy spectrum in Figure 10(a) shows the energy-dependent distortion expected from oscillations.In a 2-flavor oscillation scenario, the best-fit value yielded |Δ 2  23 | = 2.8 × 10 −3 eV 2 and maximal mixing.The K2K allowed region for the oscillation parameters is consistent with that from atmospheric neutrino data (Figure 10(b)).
The NuMi 3.7 GeV energy neutrino beam uses neutrinos produced by the Fermilab Main Injector, a 120 GeV proton synchrotron capable of accelerating 5 × 10 13 protons with a cycle time of 1.9 s.The flavor composition of the beam is 98.7% (]  + ]  ), with a relatively large fraction of ]  .
MINOS on the NuMi beam uses a near detector at Fermilab and a far detector at the Soudan mine site, 735 km away, at a depth of 2090 m.w.e.Both are iron-scintillator sandwich calorimeters with a toroidal magnetic field in the octogonal iron plates, interleaved with active planes of long scintillator strips providing both calorimetric and tracking information.The far detector (Figure 11(b)) has a total mass of 5400 t.The magnetic field is 1.3 T. The near detector, with a total mass of 920 tons, is installed 250 m downstream from the end of the decay pipe.
The CERN to Gran Sasso Neutrino Beam (CNGS).The 400 GeV proton beam from the CERN-SPS is transported to an underground target.Secondary pions and kaons are focused into a parallel beam and decay into  and ]  .The remaining hadrons are absorbed in the hadron stopper.12 Advances in High Energy Physics  The muons are monitored by two silicon detectors.The mean ]  energy is 17 GeV.The muon beam size at the second muon detector at CERN is ∼1 m; the ]  beam size at Gran Sasso is ∼1 km. Figure 12 shows the 730 km path of the ]  beam from CERN to the Gran Sasso Lab (LNGS).It also indicates the synchronization via GPS of the atomic clocks at CERN and at LNGS.The CNGS beam was conceived to study the oscillation phenomenon in appearance mode; the  ] spectrum was tuned to maximize the  lepton production above its 3.5 GeV kinematic threshold.
During the 90s the ]  appearance was searched for in the "cosmologically relevant region" Δ 2 > 1 eV 2 by two short-baseline experiments, CHORUS [110] and NOMAD [111], which relied on different techniques to search for  appearance.Both experiments excluded ]  → ]  oscillations for Δ 2 ≳ 1 eV 2 .
OPERA at LNGS is a hybrid emulsion-electronic detector (Figure 13), designed to search the ]  appearance in the CNGS ]  beam [112][113][114][115], in the parameter region indicated by the atmospheric neutrino experiments.The ]  appearance search is based on the detection of the  lepton in nuclear emulsions.The 1.25 kt target is segmented in units (bricks) consisting of 56 lead plates (1 mm thick) and 57 emulsion layers; each brick weighs 8.3 kg.Events may be analyzed in the electronic detector and/or in the emulsions.Fast automated scanning systems running at ≳20 cm 2 /h per emulsion layer were developed to cope with the emulsion analysis load [112][113][114][115][116][117][118][119][120][121].In a brick the spatial and angular resolutions are <1 m and ∼2 mrad.So far OPERA found three ]  → ]  candidate events (Figure 14) [122][123][124].In Figure 14(a) tracks 1-6 originate from the primary interaction vertex, and track 7 is a prompt neutral particle, and track 4 has a kink topology compatible with a -lepton decay. 1 and  2 in Figure 14(b) are -rays from the secondary vertex; their invariant total mass is compatible with  0 → 2 decay.Track 8 is from a  − .The invariant mass of the  0 and of the  − is compatible with that of (770) mass.The decay of the short track is thus compatible with  − →  − ]  .The second and third event are shown in Figures 14(b) and 14(c).From these results the evidence for ]  → ]  appearance can be established at the 3.4 level [123,124].The analysis of events is ongoing; the final result of ]  appearance search is expected by the end of 2014.
The OPERA search for ]  → ]  limited the window region for the LSND anomaly [125].
The ICARUS T600 detector is an innovative TPC liquid argon detector which ran on the CNGS beam, in Hall B of LNGS.One event recorded by T600 is shown in Figure 15.ICARUS performed a search for ]  to ]  limiting the window of open options for the LSND anomaly [129,130].
The T2K (from Tokai to Kamioka) experiment is a second generation long baseline experiment, which uses a 2.5 ∘ offaxis neutrino beam produced by 30 GeV protons at the Japan Proton Accelerator Research Complex (J-PARC) [131].The neutrino beam is sent to the SK detector, 295 km away; because of the kinematics of pion decay it emerges as a narrow beam peaked at 600 MeV.The schematic view of the neutrino beam line is sketched in Figure 16(a).A sophisticated near  detector complex (ND280) was built at a distance of 280 m from the target.It includes the on-axis monitor INGRID and an off-axis detector, a spectrometer with a magnetic field of 0.2 T which includes a  0 detector, a projection chamber system, two scintillation detectors, a 4 electromagnetic calorimeter, and a muon range detector.A single -like beam event detected in the SK detector is shown in Figure 16(b).28 ]  → ]  candidate events were detected and compared to an expected background of 4.6 ± 0.4 events.The excess events at SK correspond to a 90% confidence interval of 0.034 < sin 2 2 13 < 0.190 for normal hierarchy [132][133][134][135], and now it has a 7.5 significance for ]  → ]  [96].
The NO]A experiment, which will run using an upgraded NuMI beam, is in an advanced construction phase.A proton beam power of ∼0.7 MW is planned, with  ] ∼ 2 GeV and a baseline of 810 km, 14 mrad off-axis.The detector will be a 15 kt "totally active" tracking liquid scintillator, scheduled to be partly operational by the end of 2013.It will be placed at ground level in Northern Minnesota.The close detector will be a 220 t replica of the far detector, placed 14 mrad off-axis at ∼1 km from the target.The main NO]A physics aims include the study of ]  disappearance and ]  appearance with a precision about one order of magnitude better than at present [136].
5.1.The LSND Δ 2 Scale.In the 90s at the Los Alamos Laboratory in New Mexico the 800 MeV proton linear accelerator was used to produce a ]  beam with energies up to 300 MeV (from muon decays at rest) incident on the Liquid Scintillator Neutrino Detector (LSND), designed primarily to search for ]  → ]  oscillations.A 3.8 sigma excess of ]  candidate events was observed and interpreted as due to neutrino oscillations with a small mixing angle and a relatively large Δ 2 in the 0.2-10 eV 2 range [137,138].The results do not fit in the conventional 3 neutrino mixing scheme and require at least a fourth neutrino (sterile neutrino).
The KARMEN [139] reactor experiment partly ruled out the LSND results leaving a small region, 0.2-2 eV 2 , still compatible with the LSND oscillation signal.
The MiniBooNE experiment was designed to provide a test of the LSND signal.It used the Fermilab Booster neutrino beam generated from 8 GeV protons incident on a Be target.The center of MiniBooNE was 541 m from the production target.The near neutrino target was mineral oil in which relativistic particles created both Cherenkov and scintillation Figure 16: Sketch (a) of the T2K beam line, showing the primary proton beam line, the target station, the decay volume, the beam dump, the muon monitors, and the near on-axis and off-axis neutrino detectors.On (b) a single ring ]  event in the SK detector.light.The experiment did not confirm the LSND results but found an excess of electron-like events in the neutrino energy range below 475 MeV [140].The source of the excess remains unexplained, although several hypotheses were put forward [141,142].MiniBooNE reported on an updated search in antineutrino mode: an excess of ]  events for energies above 475 MeV was observed.The fit allowed regions for ]  → ]  oscillations in the 0.1 to 1 eV 2 Δ 2 range are consistent with the allowed region reported by LSND.
The search for sterile neutrinos is very active.The SM already provides right-handed neutrinos, which are "sterile" with respect to gauge bosons of the electroweak sector.Experimental searches concern light sterile neutrinos ( ] ∼ 1 eV), which could mix with active neutrinos and oscillate at short baselines.
In addition to the LSND and MiniBooNE results, which involve electron (anti)neutrino appearance in ]  , ]  beams, other anomalies in disappearance mode were found to fit the same sterile neutrino scenario at the eV scale.The so-called "gallium anomaly" refers to the ]  deficit in radioactive source calibration tests, at the gallium solar neutrino experiments SAGE and GALLEX [143].A reevaluation of ]  flux from reactors exceeded the measured value by ∼6% ("reactor anomaly") [144].A recent reanalysis stresses that uncertainties may be larger than the anomaly [145].When interpreted in terms of active to sterile neutrino oscillations, both gallium and reactor anomalies lead to oscillation parameters compatible with LSND and MiniBooNE results.It should be noted that the no-oscillation hypothesis is rejected at about 6, even if most of the statistical power is driven by LSND: removing LSND from the analysis, the oscillation significance drops to about 2 [146].Moreover it was found that the ]  disappearance channel is compatible with no oscillations in contradiction to what is expected, thus generating a tension with respect to previous results.The ]  disappearance channel in this Δ 2 region will be explored using atmospheric neutrinos in large acceptance detectors such as neutrino telescopes [147].In the near future the SOX experiment will test the reactor and gallium anomalies by detecting neutrinos and antineutrinos from MCi sources, with Borexino [148].
Among the various ideas to tackle the sterile neutrino problem the SPSC-P-347 proposal (ICARUS-NESSiE) at CERN would be a complete experimental setup to solve this issue.The project would exploit the ICARUS T600 detector as a far detector in a new low energy ]  beam line at the CERN SPS.In addition a 150 t LAr detector clone could be placed at 460 m from the target position to provide the unoscillated pattern.Two magnetic spectrometers would be placed downstream of the two LAr-TPC detectors to complement and enlarge the physics reach of the experiment.The LAr-TPC technology allows identifying and reconstructing ]  interactions.Muon neutrinos could be also identified even if charge reconstruction would be performed only at a statistical level with a large discrimination power.The spectrometers could complement and improve the muon neutrino sector by extending the measurable spectrum and performing charge identification at the 1% level on an event-by-event basis.The ICARUS-NESSiE proposal could span a large fraction of the parameter space in a limited time window simultaneously facing the ]  appearance and ]  disappearance channels and also providing a measurement of NC rates which are considered reliable signals of sterile neutrino existence 152].

Neutrino Oscillations and New Physics
Mechanisms other than flavor transitions have been tested as alternative or subdominant processes to explain atmospheric ]  data (i.e., violation of the equivalence principle, of Lorentz invariance, and of CPT symmetry) [153].The most relevant feature of these scenarios is the departure of the energy dependence of the oscillation length.
Lorentz Invariance Violation (LIV).MACRO and SK upthrough-going muon data were used to search for subdominant oscillations a possible LIV: in this case there could be mixing between flavor and velocity eigenstates.Limits were placed in the Lorentz violation parameter |ΔV| < 6⋅10 −24 at sin 2 V = 0 and |ΔV| < 4 × 10 −26 at sin 2 V = ±1 [154].In the context of a Standard Model Extension (SME) quantum strings could introduce nonlocality that could break Lorentz and/or CPT invariance.The neutrino oscillation probability may depend on the direction of the neutrino propagation; this effect would manifest, in experiments with both neutrino source and detector fixed on Earth, as a sidereal modulation in the number of detected neutrinos.This was searched for by the MINOS near detector without finding any effect: in the context of SME one could set limits on the magnitude of the Lorentz and CPT violating terms at the level of 10 −4 -10 −2 of the maximum expected, assuming a suppression of the signature by a factor of 10 −17 [155].More stringent limits may be obtained by neutrino telescopes; see Section 8.
Neutrino Decay.Using SK data Fogli et al. [79,80] have shown that the neutrino decay hypothesis fails to reproduce the observed zenith angle distribution of atmospheric neutrinos.MINOS excluded neutrino decay at 7 standard deviations studying the / ] distribution [104].
The radiative decay modes allowed for massive neutrinos are ] 2 → ] 1 + and ] 3 → ] 2,1 + [62].A direct experimental limit comes from the 2006 total solar eclipse in the Libya Sahara desert [63].For the ] 2 → ] 1 +  radiative decay the 95% CL lower lifetime limits are in the range 10 s ÷10 9 s for neutrino masses 10 −4 eV <  1 < 0.1 eV [63].A similar limit was obtained for the ] 3 → ] 2,1 +  decay, but the limit is tentative since it depends on the mixing angle  13 which was not known at that time.
Extra Dimensions.In models where the standard 1 + 3 dimensional world ("brane") is embedded in a larger 1 + 3 +  dimensional spacetime ("bulk")-with  being the number of extra dimensions-and SM left-handed neutrinos are frozen within the brane while right-handed neutrino singlets can propagate in the bulk.They give rise to perturbations that can alter the "standard" oscillation pattern of active neutrinos.By combining the results from KamLAND and MINOS a limit ≲1m was obtained on the size of the larger hidden dimension [156].
Lepton Flavor Violation.Neutrino oscillations arise from flavor mixing in the leptonic sector.In the SM the violation would be minimal and lead to a very small branching ratios for processes which violate lepton flavor, like  →  decay.Supersymmetric (SUSY) theories could give rise to lepton flavor violations through radiative corrections which could increase the branching ratio.This could happen also for electric dipole moments, for example, of the neutron and of the muon.The MEG collaboration published limits on the search for  + →  +  decay: <5.7 × 10 −13 (90% CL) [157].

Cross Section and Particle Production Measurements
After 1998 it was realized that the existing measurements of hadron production concerned mainly very forward angles and high momenta and were not adequate for the proper atmospheric neutrino simulations and for conventional and advanced neutrino beams.In 2000 the HARP experiment at the CERN-SPS pioneered systematic hadron production measurements over the full acceptance in angle and in momentum.It used proton and pion beams on different target materials [158].It produced the pion data needed for the K2K and MiniBooNE experiments.New neutrino cross-section measurements were also made by the K2K near detector (∼1.2 GeV), MiniBooNE (∼800 MeV), SciBooNE (∼800 MeV) [159,160], MIPP (from 1 to 120 GeV), NA61/SHINE experiment at the CERN-SPS [161,162], and T2K [163].
The MINERvA experiment in the NuMI beam-line at Fermilab is a fine-grained detector which will provide neutrino scattering data in the ∼1-20 GeV region [164][165][166][167].

Neutrino Telescopes and Atmospheric Neutrinos
Large size neutrino telescopes were built mainly to shed light on the most violent and energetic phenomena in the universe using high energy neutrinos as astrophysical probes.
High energy neutrinos with hundreds of GeV may come from nonthermal astrophysical sources [168].Multi-GeV neutrinos may also come from the interior of celestial bodies, like the sun, some planets, and the center of our galaxy where annihilation of weakly interactive massive particles (WIMPs) could take place.These searches require large detectors, like the Baikal detector in lake water [169], Amanda [170] and IceCube [171][172][173] in South Pole ice, and ANTARES in the Mediterranean sea [174][175][176]; a multi-km 3 detector is planned for the Mediterranean sea (Km3NeT) [177].The observation of neutrinos is based on the Cherenkov light induced by upgoing muons produced in high energy CC ]  interactions (to reduce the background from atmospheric muons, neutrino telescopes look downward).Large arrays of PMTs cover huge volumes of ice or sea water.
The cosmic very high energy neutrino flux is expected to decrease with energy as  −2 .Atmospheric neutrinos are a background with an energy dependence of  −3.7 .The possibility to perform neutrino oscillation studies is related to the energy threshold for detecting lower energy atmospheric neutrinos.If the spacing between neutrino telescope strings is reduced (as in the IceCube Deep Core array), the energy threshold is ∼20 GeV.It could be as low as few GeV in the future Km3NeT-ORCA and IceCube-PINGU inner cores.This opens the possibility to perform high statistics oscillation analyses up to ∼1 TeV, above which the Earth starts to become opaque to neutrinos.The IceCube present Inner Core allowed a first measurement of the atmospheric ]  oscillations which yielded in a 2-] flavor formalism: Δ 2 23 = (2.3 +0.6 −0.5 ) × 10 −3 eV 2 and sin 2 (2 23 ) > 0.73.The no-oscillation hypothesis is rejected [178][179][180][181].The ANTARES experiment obtained a measurement of |Δ 2  23 | of limited accuracy, |Δ 2 23 | = (3.1 ± 0.9) × 10 −3 eV 2 , but it checks the status of the apparatus and underlines the potential for future physics [174][175][176].
Figure 17 shows the atmospheric ]  energy spectrum in the range 0.1-400 TeV, measured by the IceCube, ANTARES, and AMANDA-II neutrino telescopes, using different energy estimators and different unfolding methods.The data are compared with the MC Bartol flux and with the more elaborate Bartol + Martin, Bartol + Enberg calculations.Within large systematic errors, the results from different experiments are compatible with each other and with the theoretical MC predictions [182][183][184].The data do not confirm nor reject the presence of prompt components.
Neutrino telescopes have searched for Lorentz invariance violations.IceCube, operating in a 40-string configuration, searched for a periodic variation in right ascension, a possible consequence of LIV preferred frame.No such directiondependent variation was found, and, due to the unique high energy reach of IceCube, it was possible to improve constraints on certain LIV oscillation by about three orders of magnitude with respect to other experiments [178][179][180][181]. Very large neutrino telescopes could also yield more precise direct and indirect results on dark matter (WIMPs) and on the searches for various exotic particles.

Conclusions and Perspectives
The standard model of particle physics obtained important confirmations in all experiments at LEP, SLC ( +  − ), HERA ( + ), and Fermilab () colliders, and a Higgs boson-like particle has been seen at the CERN LHC, but the SM needs further confirmations.
Neutrino oscillations provided a first indication for physics beyond the standard model.Globally the variations and the differences among the values from different experiments are small and well within their systematic errors.The variations are negligible compared to those reported in the early experiments on weak interactions and early atmospheric ] experiments.
In the three-active-neutrino frameworks one would like to solve the so-called "eightfold" degeneracy.Assuming the measured value of  13 and running in ]/] mode there are two different sets of parameters ( 13 ,   ) producing the same oscillation probabilities.These "clone solutions" are doubled by the unknown sign of Δ 2 23 (normal or inverted hierarchy) and redoubled by the  23 octant degeneracy, that is, the sign of ( 23 − /4).The problem may be solved by performing complete 3 neutrino analyses and by considering combinations of different baselines and energies [185,186].
Several groups worldwide are investigating future neutrino beams of higher intensity and purity: superbeams, betabeams, and neutrino factories [187,188].High intensity ]  beams (superbeams) from high intensity proton accelerators are based on the improvements of existing proton accelerator complexes.Beta-beams could be produced from radioactive ion beams, taking advantage of the technological progress in this field.The beta decays of unstable ions would lead to pure sources of ]  and ]  beams, which could be used to study ]  → ]  oscillations.High energy muon colliders have been studied for several purposes, in particular to obtain electron and muon neutrino beams from muon decays.The goal is to make high energy and high intensity muon storage rings which could be used as neutrino factories.It was proposed that simultaneous  − and  + decays could lead to important tests of CP violation in the leptonic sector [186,188,189].
The recent measurements of  13 ≃ 9 ∘ , together with the plans for upgraded higher intensity neutrino beams and new large refined detectors, open the door to a new golden age for neutrino physics, where one could obtain important information on neutrino masses and neutrino hierarchy, establish if  23 is maximal or, if it is not, in which octant it lies, and make important tests of CP violation in the leptonic sector.
New large neutrino telescopes may improve the knowledge on dark matter, on supernovae neutrinos, and on the measurements of some parameters of atmospheric neutrino oscillations.Do sterile neutrinos exist?Are sterile neutrinos the explanation of existing experimental data which cannot be reconciled with the standard mixing scenario?
The search for new physics beyond the SM will be one of the main fields of research at the LHC.Supersymmetry is still one of the theoretically favored models and this could shed light on dark matter.Other topics such as compositeness, technicolor, and extra dimensions could be searched for at the new energy frontier.LHC may also yield information on neutrinos [190]. Photon

Figure 1 : 3 1
Figure 1: Masses of leptons, of quarks, and of the Higgs boson and neutrino mass splittings in the solar and atmospheric sectors.The dots for ] masses indicate mass upper limits.∑ 3 1  ] ≃ 0.3 eV gives the upper limit on the sum of neutrino masses from cosmological observations (see text).

3. 2 .Figure 3 :
Figure 3: Cross section (a) and global view (b) of the MACRO detector.In the left figure are also shown the observed neutrino-induced event topologies.

Figure 4 :
Figure 4: Reduction factor in the number of upgoing muons for different Δ 2 23 values for a muon detection threshold of 1 GeV (MC studies).Note the shape dependence vs the Δ 2 23 values.

4 sr − 1 s − 1 )Figure 5 :
Figure 5: (a) MACRO up-through-going muons compared with oscillated and nonoscillated predictions of different MCs [68].(b) Measured zenith distributions for the IU low energy events.The black points are data; the shaded region is the MC predictions with no oscillations.The full line is for ]  ↔ ]  oscillations with maximal mixing and Δ 2 = 2.3 × 10 −3 eV 2 .

Figure 6 :Figure 7 :
Figure 6: (a) The MACRO ratio between the data in two angular bins (black point on gray line) and comparison with MC ]  ↔ ] sterile oscillations.(b) 90% CL allowed regions for the ]  ↔ ]  oscillations up to year 2004.

Figure 8 :
Figure 8: Zenith angle distributions from the SK detector (data from SK I + SK II + SK III) [77].

Figure 10 :
Figure 10: (a) Reconstructed energy spectrum for 58 one-ring events detected by K2K.The dashed blue line is for MC no oscillations; solid red line is the MC oscillation best fit.Both MC histograms are normalized to the data.(b) Comparison of K2K results with the SK atmospheric neutrino measurement [102, 103].

Figure 12 :
Figure 12: Sketch of the 730 km neutrino path from CERN to Gran Sasso and the GPS selection of events.

Figure 13 :
Figure 13: Schematic of the OPERA experiment in Hall C at Gran Sasso.

Figure 15 :
Figure 15: One CNGS event recorded in the ICARUS T600 detector.

Table 1 :
Nuclear reactor experiments Daya Bay, Reno, and Double Chooz.For each experiment the location, the number of nuclear reactors, the overall thermal power, the near/far detector distances, and the approximate depth of near/far detectors are given.Note that Daya Bay has two separate reactor core sites and therefore two near/far distances.

Table 2 :
Main parameters and results of some relevant atmospheric neutrino experiments.

Table 3 :
Main parameters of past, present, and future long-baseline neutrino oscillation experiments.