Neutrino Oscillations

Frontiers of Cosmic Ray Science 75

Yoichiro Suzuki, Kamioka Observatory Institute for Cosmic Ray Research,The University of Tokyo Higashi-Mozumi, Kamioka-chou, Yoshiki-gun, Gifu 506-1205, Japan [email protected]

Abstract

The neutrino oscillation is now established to be a leading effect of the solar and atmosphric neutrino flavour conversion. The atmospheric neutrino oscillation is mostly due to νµ → ντ and the solar neutrino oscillation is mostly due to νe → νµ, ντ . The observations of nutrino oscilaitons were also confirmed by the terrestrial experiments using man-made neutrinos from reactors and an accelerator. The precise measurements by the future oscillation experiments may lead us to the physic beyond the standard senario of the neutrino oscillations.

1. Introduction

The mixing matrix of the three neutrinos are writen by the unitary matrix Uα,i:       ν U U U ν  e   e1 e2 e3   1   νµ  =  Uµ1 Uµ2 Uµ3  =  ν2  . ντ Uτ1 Uτ2 Uτ3 ν3 The unitary matrix is composed of the three rotations:       −iδ 10 0 c13 0 s13e c12 s12 0       U =  0 c23 s23   010  −s12 c12 0  , −iδ 0 −s23 c23 s13e 0 c13 001 where sij = sin θij and cij = cos θij. The ﬁrst term is mostly responsible to the atmospheric neutrino oscillations and the last term is to the solar neutrino oscillations. The time evolution of neutrinos in three ﬂavour scheme will be written as 3 ∗ −iEkt |να >t= Uαke |νk > k=1 pp. 75–92 c 2004 by Universal Academy Press, Inc. 76

3 −iEkt ∗ = Uβke Uαk|νβ >. β k=1

Then the transition probability να → νβ becomes,

3 ∗ −i∆2 /2E 2 P |δ U U e k1 − | . να→νβ = αβ + βk αk[ 1] k=2

2 2 The transition probability depends upon ∆m12,∆m13, θ12, θ23, θ13 and CP vio- lating phase δ. By the knowledge from the oscillation experiments, we know, in either 2 2 2 −3 2 normal or inverse hierarchy, ∆m23 ∼ ∆m13 ∼ ∆matm ∼ (1.3 ∼ 3.0) × 10 eV , 2 2 −4 2 2 2 2 and ∆m12 ∼ ∆msol ∼ (6 ∼ 9) × 10 eV .∆sol and ∆atm ∆sol are the square mass diﬀerences to explain the solar and atmospheric neutrino oscillations in a two nutrino scheme. We also know from the reactor experiments[1][2] and from the SK atmospheric nutrino measurement that θ13 is small, the current limit is 2 2 2 −3 2 sin 2θ13 = |Ue3| < 0.05 for Deltam13 =2× 10 eV . This hierarchical mass structure and the smallness of s13 (c13 → 1) simliﬁes the neutrino mixing matrix to:   c s s e−iδ  12 12 13   −c23s12 c23c12 s23  .

s23s12 −s23c12 c23

(solar) Then the some of the matrix elements become simplified: |Ue1|∼cos θ12 ; (solar) (atm) (atm) |Ue2|∼sin θ12 and |Uµ3|∼sin θ23 ; |Uτ3|∼cos θ23 , and the atmospheric and solar neutrino oscillations can be treated independently. 2 Nevertherless, there is a effect of O(Ue3) for the solar neutrino oscillation, we need to keep it in mind. Also the low energy atmospheric neutrinos may have a small effect through ∆m12, but fortunately there is a cancelleration effect, and the intereference effect is small.

2. Solar Neutrinos

In June, 2001, the long standing solar neutrino problem has been ﬁnally solved by the combined results of Super-Kamiokande(SK)[3][4][5] and SNO[6]. SK is a 50 thousand ton imaging water Cherenkov detector which measures solar neutrinos through neutrino electron scattering; ν + e → ν + e. The total cross −43 2 section of eletron neutrinos on electron is 0.920×10 (Eν/10 MeV) cm and that −43 2 for mu or tau neutrinos is 0.157 × 10 (Eν/10 MeV) cm . SK has a sensitivity 77

to detect mu and tau neutrinos as well as electron neutrinos, but with the reduced sensitivity. The emission angle of the recoil electrons are limitted to the 2 forward region, θe ≤ 2me/E. This directionality enable us to extract the solar neutrino signal over the backgrounds with small systematic uncertainties. The recoil electron energy spectrum can also be measured. At the time of June, 2001, for the data obtained by the 1258 days of effective running time, SK obtained the flux of ’8B solar neutrinos’ to be 2.32 × 106 cm−2s−1 with 1% statistical and 3% systematic errors. SNO uses 1000 tons of D2O as a target and able to measure the charged current electron neutrino interactions and the neutral current interactions, sep- − arately through νe + d → e + p + p and νx + d → νx + p + n. The produced neutrons can be identified either by 1) n + d → T +6.25 MeVγ,2) n+35 Cl →36 Cl+8.6 MeVΣγ (Salt in water), and 3) n+3 He → p+T (Hellium3 Counters). SNO has published their first results on the charged current intera- tions in June 2001. The flux of the ’8B solar neutrinos’ is 1.75 × 106 cm−2s−1 with 4% statistical and 7% systematic errors. By comparing those two results and taking into account the difference in cross sections, the conclusive evidence that there are non-electron neutrino components in the solar neutrinos ovbserved on the Earth, was obtained. Those data also showed that the total flux of the solar 8B neutrinos produced in the Sun is 5.44 ± 0.99 × 106 cm−2s−1, which is consistent with the prediction from +1.01 6 −2 −1 the standard solar model of BP2000 [7] (5.05−0.81 × 10 cm s ) and about 65% of the solar neutrios has been converted to either mu or tau neutrinos on the way to the Earth. The results of the neutral current measurement of SNO[8][9] has further comfirmed the evidence of the solar neutrino oscillation. The neutral current result in 2002 (D2O) has shown directly the total solar neutrino flux is +0.44 +0.46 6 −2 −1 5.09−0.43(stat.)−0.43(syst.) × 10 cm s and the salt results in 2003[10] shows that the total flux is 5.21 ± 0.27(stat.) ± 0.38(syst.) × 106 cm−2s−1. Those numbers can be compared directly to the electron neutrino flux to verify neutrino oscillations.

2.1. Global analysis of the solar neutrino oscillation SK measures neutrinos above 4.5 MeV (K.E) and SNO measures those above 5 MeV, the high energy region of the solar neutrino spectrum. Homestake 37 experiment, which uses Cl as a target in a form of CCl4, measures the neutrino ﬂux above 814 keV. Their accumulated ﬂux value, since the biginning of the experiments in early 70’s, is 2.56 ± 0.23 SNU whereas the SSM of BP2000 +1.3 predicts 7.6−1.1 SNU. There are two exmeriments using Ga as a target. Those ex- 78

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-4 in eV 10 2 +Ga & Cl Rates m ∆ 10 -5

10 -6

10 -7

10 -8

10 -9

10-10

-11 SK/SNO Rates, SNO D/N and 10 SK Zenith Seasonal Spectrum ν →ν % e µ/τ (95 C.L.) 10-12 10-4 10-3 10-2 10-1 1 10 10 2 tan2(Θ)

Fig. 1. Global analysis of the solar neutrino oscillation. The outer allowed region is obtained by using SK and SNO data. The inner allowed region shows the results for all the solar neutrino data.

periment, called SAGE in Baksan Laboratory and GALLEX(GNO) in GranSasso 71 71 Laboratory, have started in early 90’s, The reaction νe + Ga → e + Ar has a lowest energy threshould of 235 KeV, sensitive to the neutrinos from the pp- +7 fusion reactions. The latest flux value is 71−6 SNU for SAGE and 71 ± 6 SNU for GALLEX+GNO, whereas the prediction is 128 SNU with an error of ∼7%. There are many global analyses on the solar neutrino oscillations. We, here, show, for example, the result done by the SK-Collaboration. The details of the methods will be found in reference[5]. Chlorine and Gallium experiments are included in the global analysis, but constraint by the flux predictions. But for the SK and SNO data, the absolute flux is not constraint. The result is shown in Fig. 1., the plot in tan2 θ vs ∆m2 (eV 2). The best fit parameters are (∆m2 =6.0 × 10−5 eV 2, tan2 θ =0.42). This parameters are in a region so called large mixing angle solutions (LMA) and the full mixing is excluded by 5.4σ[10]. By looking at the fitted parameters closely, there are a couple of things to be noted. The best fit parameters predict that the Chlorine rate is 2.98 SNU which is 1.9σ higer from the measured value, and the high flux value for hep- neutrinos more than 4 times larger than the SSM prediction is needed although the statistics is very low. These may be a statistical or a systematic effect, but 79

Fig. 2. Solar neutrino ﬂux measured by Super-kamiokande in 10 days time duration bins. The 7%, peak to peak, ﬂux variation due to the eccentricity of the earth was corrected.

need to keep watching. They may be a clue to sub-dominant eﬀects other than LMA.

2.2. Time variation of solar neutrinos SK measures the event time in high accurary with ∼15 events/day, which enable us to make a discussion of time variabilities, ranging from a day to years of the solar neutrino flux. The time variations, in a day or months, may arise from the variable magnetic field of the sun and the neutrino magnetic moments, although the required magnitude of the neutrino magnetic moments are rather large. We have divided data taken from May 31st, 1996 to July 15th, 2001, into bins. Each bin consists of the data for 10 days time durations. For each binned data, it may happen occationally that the detector was not 100% active. The mean live-time is calculated by taking into the acutual time of the data taking peorids. The 10 days binned data is shown in Fig. 2. and is corrected for the 1/R2 effect due to the eccentricity of the earth’s orbit. Lomb periodogram method was used to test the periodicities. Maximum power at f=0.0768 day−1 corresponding T=13.76 days, with a Lamb power of 7.51 (81.7% C.L.) was obtained. This peak can be explained by a statistical fluctuation and therefore, there is no strong short time variations in the solar neutrino data observed in Super-Kamiokande [11].

3. Terrestrial Experiments to Conﬁrm the Solar Neutrino Oscillation

The LMA solution can be tested by the terrestrial experiment using anti- neutrinos from nuclear power reactors. Suppose you take 5 MeV as a mean energy of neutrinos from the power reactors and 100 km as a distance, the experiment is sensitive to E/L =5× 10−5 eV 2. 80

1.4

1.2 KamLAND

1.0 expect 0.8 /N

obs

N 0.6

0.4

0.2

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101 102 103 104 105 Distance(m)

Fig. 3. The ﬂux result of KamLAND. Data points with the distance shorter than 103 m correspond to previous experiments.

KamLAND is a spherical detector containing 1,200 m3 of liquid scintilla- tors surrounded by mineral oil and viewd by 1280 17 inch PMT’s which provides about 20% photo cathode coverage of inner surface. The anti-electron neutrinos + from the reactors are detected through the reaction,ν ¯e + p → e + n. The neu- tron produced by the reaction is captured by a proton in the liquid scintillator and emits 2.2 MeV γ-ray. The threshold of the reaction is 1.8 MeV. The mean distance from reactors to the location of KamLAND in Kamioka mine is about 180 km. By effective 141.1 days of data, KamLAND[12] observed 54 events, where the expected number is 86.8±5.6 events. The ratio of the observation to the expectations is 0.661 ± 0.085 ± 0.041 as shown in Fig. 3. This shows a clear confirmation of the solar neutrino oscillations. We, however, should note that there are some differences between the solar neutrino experiments and the reactor experiment and therfore, a small mixture of the sub-leading effects may show up as a small but visibe effect in a precise comparison of the solar neutrino data and reactor data:

1. Solar neutrinos are νe and the reactor neutrinos areν ¯e, which is related to the CPT invariance;

2. The solar neutrino oscillations in the low energy region, say below 1 MeV 81

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2 10 2 10 KamLAND Rate & Spectrum hep-ph/0302230v2 (A. Ianni) in eV in eV 2 2 m m ∆ ∆

10 -4 10 -4 +Ga & Cl Rates

+Ga & Cl Rates

KamLAND Rate & Spectrum, SK/SNO Rates, SNO D/N and SK/SNO Rates, SNO D/N and SK Zenith Seasonal Spectrum SK Zenith Seasonal Spectrum ν →ν % ν →ν % e µ/τ (95 C.L.) e µ/τ (95 C.L.) 10 -5 10 -5 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 sin2(Θ) sin2(Θ)

Fig. 4. The allowed parameter Fig. 5. The allowed region for region by KamLAND and so- the combined analysis of all the lar neutrino experiments. The solar neutrino experiments and KamLAND region is obtained KamLAND. from A.Lanni et al. [13].

are dominated by vacuum oscillations, but in high energy region neutrinos convert adiabatically in the matter of the sun. There is no eﬀect by matter to the reactor neutrino oscillations;

3. The base-line is very long for the solar neutrinos and that for reactor neutrinos is relatively short, which may be related to the diﬀerent eﬀect for neurino decay if it exists;

4. There is a strong magnetic ﬁeld in the sun, but no considerable magnetic feild for the reactor neutrinos;

5. No phase information is important for the solar neutrino osillations, but the phase is crutial for the reactor neutrino oscillations; Therefore, precise measurements of both solar and reactor neutrinos, may provide a further comﬁrmation or may lead us to ﬁnd sub-leading phenomena beyond the standard scenario of LMA.

3.1. Combined solar neutrino and KamLAND analysis Though there are some dﬀerences in nature (see previous subsection) between the solar neutrino oscillation and the reactor neutrino oscillation, we may 82

1 0.9 0.8 0.7 tan2θ=0.42, ∆m2=6.0x10-5eV2 2θ 0.6 tan2 =0.44, -5 2 ∆m =7.2x10 eV 2θ 0.5 tan2 =0.52, -5 2 ∆m =6.3x10 eV 0.4 0.3 0.2 0.1 0 10-2 10-1 1 10 Eν in MeV

Fig. 6. The behavior of LMA solutions as a function of energy.

combine the results to extract the most stringent allowed regions for the sim- ple neutrino oscillation assumption. In Fig. 4. the allowed regions for solar and KamLAND experiment are separately shown and in Fig. 5. the results of the combined analysis is shown. The best ﬁt oscillation parameters for all the data are (∆m2 =7.2 × 10−5 eV 2, tan2 θ =0.44), which moves up slightly comparing to the results only from the solar neutrino data [5].

4. ∆m12 and sin θ12 in Future

The behavior of the LMA Solutions is shown in Fig. 6. The low energy solar neutrinos below 1∼2 MeV would not pass through the resonance scince the resonance condition is only satisfied at the place where the density becomes much higher than the core density of the sun. Therefore if the neutrino energy becomes lower than 1∼2 MeV, the transition probability start to approach to P =(1/2) sin2 2θ (vacuum oscillation). On the contrary, the neutrios with the energy larger than a few MeV, convert adiavatically in the sun, and the transition 2 2 2 2 2 probability, P = cos θV cos θm + sin θV sin θm, becomes P = sin θV as θm goes to π/2. The transition probabilities are mostly determined by the mixing angle in vacuum. Fuuture experiments would provide a further confirmation of the solar neutrino oscillations and a precise measurement of the oscillation parameters. And we obtain some hints of a sub-leading effect embeded in the oscillation phenomena. The most improtant tasks for the 8B-solar neutrino measurments are to positively observe the day/night flux difference and the spectrum rise in the low energy regions. Suppose the ’true’ oscillation parameters are the current best fit 83

ones, then we expect, 1∼2% daynight effect for SK and 2∼5% for SNO. For the LMA solutions we expect low energy rise in the spectrum of SK and SNO. For SK, this effect may be 10% if the energy threshold can get down to 4 MeV. The current energy threshold of SK is 4.5 MeV (total energy). For proving the global LMA behavior, the spectrum measurements of low energy solar neutrinos are of particular importance. Since the prediction of pp- neutrinos has small uncertainty, the mesurement of the pp-spectrum is particu- larly important to verify the LMA behavior. Other improtant measuremet is a flux of pep neutrinos, the energy of which is located in the transition region from vacuum to the adiavatic conversion. For LMA pp-neutrino flux would be reduced to 55∼58% and pep-neutrino to 51∼52%. Be-neutrino is also reduced to 52∼54%, but the uncertainty of the prediction is about 15%. For example, XMASS experiment [14] planned to mesure the pp-neutrino flux can make a precise mesurement of the θ12. This series of the measurements would provide a clue to understand the vacuum to matter transition of the solar neutrino oscilaltions in the sun and also to give us a hit for a sub-leading effect and a clue for the problem of low rate Cl experiment. Other important observation to be done in future is a precise energy spectrum measurement in KamLAND, which will provide a phase imformation of the neutrino oscillation.

5. Atmospheric Neutrinos

The definitive evidence of the neutrino oscillation has come from the observation of the zenith angle distribution of the atmospheric neutrinos [15] [16] [17]. The latest data of the atmospheric neutrinos are shown in Fig. 7. From a few hun- dred MeV fully contained events to TeV energy upward going muons, the clean zenith dependence which consistent with neutrino oscillation with the best fit parameters of ∆m2 =2.0 × 10−3 eV 2, sin2 2θ =1.0 are seen. For the best fit value, 2 2 χmin = 170.8/170d.o.f, whereas the null oscillation has χmin = 445.2/172d.o.f, which gives ∆χ2 = 274. Fig. 8. shows the allowed region of the neutrino oscillations. Also shown is the various allowed regions obtained by the different data subsamples which reveals the consistency among the data. Other experiments (MACRO [19] and SOUDAN-II [18]), which also meaure the atmospheric neutrinos also confirm the neutrino oscillation.

5.1. Sterile neutrinos in the atmospheric neutrino oscillations

In order to discriminate νµ → ντ oscillations from νµ → νs oscillations, the folowing two characteristic are utilized in the analysis. 1) Sterile neutrios, weak 84

µ 450 Sub-GeV e-like Sub-GeV -like 400 500 350 400 300 250 300 200 200

Number of Events 150 Number of Events 100 100 50 0 0 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 cosθ cosθ µ Multi-GeV e-like 350 Multi-GeV -like + PC 140 300 120 250 100 80 200 60 150 Number of Events 40 Number of Events 100 20 50 0 0 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 cosθ cosθ Sub-GeV Multi-ring Upward Stopping µ 50 ) 1.4 45 -1 sr 1.2 40 -1 s

35 -2 1

30 cm 0.8 25 -13 20 0.6

Number of Events 15 0.4

10 Flux(10 5 0.2 0 0 -1 -0.5 0 0.5 1 -1 -0.8 -0.6 -0.4 -0.2 0 cosθ cosθ Multi-GeV Multi-ring Upward Through Going µ ) 4 100 -1

sr 3.5 -1 s 3 80 -2

cm 2.5 60 -13 2 40 1.5 Number of Events 1 20 Flux(10 0.5 0 0 -1 -0.5 0 0.5 1 -1 -0.8 -0.6 -0.4 -0.2 0 cosθ cosθ Fig. 7. Zenith angle distributions of the atmospheric neutrinos of 1489 days of data. All the sub-samples are soncistent with the neutrino oscillation. 85 ) 2 (eV 2 m ∆

-2 10

Combine -3 10 Sub-GeV low Sub-GeV high Multi-GeV PC Multi-ring Up µ -4 10 0 0.2 0.4 0.6 0.8 1 1.2 sin22θ

Fig. 8. The allowed parameter regions. Also shown are the various allowed regions by sub-samples.

singlets, do not perform even neutral current interactions. 2) There is no matter eﬀect in the oscillation, νµ → ντ , but the νµ → νs oscillations are aﬀected by matter with a potential of (−1/2)Nn. A possibility of the 100% transition to the sterile state has been rejected [20]. A similar analysis method has been adopted, but for the transition of νµ → cos ξντ + sin ξνs oscillations. The ξ shows the mixing between ντ and νs. The results were obtained for the limit on sin2 ξ as a function of ∆m2.Forδm2 = 2 × 10−3 eV 2, SK collaboration has obtained sin2 ξ ≤ 0.26 (99% C.L.).

5.2. Appearance of ντ in atmospheric neutrinos It is not possible to identify τ apperance by event-by-event basis. We need to adopt a statistical analysis. The SK collaboartion has used three diﬀrent anaysis methods: 1) energy ﬂow analysis, 2) neutral network, and 3) likelihood method. For the likelihood method, events that enhances possible τ production are collected as an event sample. The multi-GeV and muti-ring events are selected and the requirment that the most energetic ring is e-like was imposed. Then we calculate the likelihood and apply further cuts to enhance τ and the events coming downwords are used as controll samples which does not contain any τ’s. In Fig. 9., the zenith angle distribution of the τ-enhances sample is shown. 86

200 Data Tau no Appearance Tau Appearance

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150

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0 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 CosΘ

Fig. 9. The zenith angle distribution of tau enhanced sample. The data is sonsistend with tau appearance and the number of taus are extracted from the ﬁgure.

The data is ﬁtted by the BG(without τ production) and τ expected distributions. 5 N − αN τ βNBG 2 χ2 data ( MC + MC) = σ cos θ

+19 was defined and α and β were fitted. The number of τ, thus botained was 48−20 +42 +12 events. If you correct for the efficiency, you get Nτ = 105−45 −17 events. We expect 86 tau production events for the data samples. Other analyses has given +35 +21 +44 similar results: Nτ (neural network)= 92−35 −16 events and Nτ (energy flow)= 79−40 events. Those numbers are consitent with the νµ → ντ oscillation.

5.3. Three ﬂavor analysis

In three ﬂavor analysis, we have useally assumed that ∆m12 = 0 and 2 ∆m13 =∆m23 and therefore the parameters to be determined are∆m13, θ23, and θ13. Since the solar neutrino mass diferecne ∆msol ∆m12 was now kown to be rather large, 6 ∼ 9 × 10−5 eV 2, the interference between the transitions through ∆m12 and ∆m13 must be considerd, although the electron appearance was very small due to the cancellaration from the original ratio of νµ:νe=2:1 and the full mixing of θ23. The eﬀects are calcurated for two typical parameters, one for no 2 −5 2 ∆m12 = 0(sin 2θ23 =1,Ue3 =0.2), and another for ∆m12 =7× 10 eV , 87

2 sin 2θ23 =1,Ue3 =0.2. The inteference eﬀects are then found to be around 2% in the neutrino energy below 400 MeV and in the higher energy range it is very small and negligible. The assumption of ∆m12 = 0 is still valid for the current accuracy of the data. In those assumptions and taking account the matter eﬀect 2 2 −3 2 properly, the limit, sin θ13 ≤ 0.16 (90% C.L.) at ∆m =3× 10 eV was obtained. The CHOOZ limit is 0.05 (90% C.L.).

5.4. What should we know further on atmospheric neutrinos

Although all the data are consistent with the νµ → ντ oscillations, there still be a possibility to explain the atmospheric neutrino anomary as othere eﬀects. The future observation of the direct oscillatory behavior in the L/E distribution and the conﬁrmation of the τ appearance made the oscillation senario more solid. Hope that in very near future, the SK collaboratin would provide those evidence.

6. Terrestrial Experments to Conﬁrm the Atmospheric Neutrino Os- cillations

K2K, the first earth-distance long baseline accelerator oscillation experiment from KEK to Kamioka, has published the first result in 2003 citeK2K- 1stResult-03. The base-line is 250 km and the mean νµ energy is 1.3 GeV. This distance and the typical beam energy comprize a characteristic oscillation probability of ∼0.3 for 2.5 × 10−3 eV 2 and sin2 2θ =1. The beam buckets are circulated every 2.2 second in the 12 GeV proton synchrotron at KEK and 1.2 µs long beam spill was transported to the production target. Pions produces are focused by the magnetic horn system and decays in the following 300 m long tunnel. Front detectors, 1kt water Cherenkov detectors, scintillation fiber detector, and muon range detector, placed at 300 m down stream of the production target, are used to monitor and normarize the neutrino interactions. The precise measuement of the beam spectrum was also done. The experiment has started in April, 1999. By using the data untill July, 2001 (K2K-I). The experiment has observed 56 fully contained events in the Super- Kamiokande detector for 4.8 × 1019 P.O.T.. The expercted number of events at +7.3 SK without neutrino oscillations is 80.6 ± 0.3(stat.)−8.0(syst.). Taking also the spectrum information, the null oscillation probability was obtained to be less than 1%. The result on the contour is shown in Fig. 10. citeK2K-1stResult-03. For the oscillation parameter of ∆m2 =2.8 × 10−3 eV 2 and sin2 2θ =1.0, you expect 54 events to be observed in SK. The result is consistent with the atmospheric neutrino oscillation. 88

Fig. 10. The 90% C.L. allowed region for the K2K experiment. The spectrum information and the ﬂux rate are used in the calculation. The allowed region for the atmospheric neutrino oscillation is also shown.

The tragetic accedent of SK, happend Nov-12, 2001, destroyed 6777 out of 11,146 inner photo-tubes (PMTs) used in the SK detector. SK has rebuilt by using about 50% of the available PMTs and resumed the experiment in December, 2002 (SK-II). K2K had also re-started in December, 2002 (K2K-II). The proposed beam to be used for the experiment is 1.0 × 1020 P.O.T., and we have already accumulated about 7.7 × 1019 P.O.T. by the end ov November, 2003. We expect to run until Spring of 2005 and expect to accumulate more than 1.0×1020 P.O.T.. The observation of the deﬁnitive energy spectrum distortion would be most valuable out come of K2K.

6.1. What is missing We should note that there are some differences between the atmospheric neutrinos and the K2K accelerator neutrinos. The atmospheric neutrinos are composed of νµ +¯νµ +νe +¯νe, whereas the man-made neutrinos at K2K are mostly νµ. The energy range of the atmosperic neutrios are very wide from 100 MeV to the order of TeV, but the neutrino energy of K2K is limited mostly in a range of 0.2 to 2.0 GeV. Ideally we need long-baseline oscillation experiments with different energies and at different distances and alsoν ¯µ disappearance experiment will provide further infromation. Looking into near future, The τ appearcnace experiment will clearify the oscillation mode and the electron appearance will give us the information on as-yet 89

undetermined mixing angle of θ13.

7. Beyond K2K

CERN Neutrino to Gran Sasso (CNGS) The CNGS [22] commission is expected in summer 2006. The CERN neutrino beam is aiming to Gran Sasso underground Laboartory, 730 km distance, to observe an appearance of τ events. ICARUS [23], 3000 tons of Liquid Ar. TPC is one of the detectors placed in the laboratory. The 300 ton prototype has been succesfull and 600 ton detector will be tested in Gran Sasso. OPERA [24] is a hybrid emulsion experiment consists of lead-nuclear emul- tion sadwich slabs. Total 900 tons are the target of neutrino interactions. The expected τ event rate for 5 years of operation @4.5 × 1019POT/yr is 4.3 for 1.6 × 10−3 eV 2 and 10.4 for 2.5 × 10−3 eV 2.

MINOS[25] The far detector, placed in SOUDAN mine, 735 km from Fermilab, has been completed and the new neutrino beam will commence in December, 2004. The physics run may start in 2005. The far detector is a 5.4 kt octagonal toroid interleaving with steel and scintillator counters. For the exposure of 10 ktyr (2 yr 20 2 ×3.84 ×10 POT/yr) you get the ∆m23 accuracy of ± 10% for the νµ disappearance, and you expect 8 electron appearance due to the νµ → νe oscillations for 2 2 2 |Ue3| =0.01 and δm =0.003 eV . Among the expected backgrounds of 38 events, 26 events come from neutral current interactiions.

T2K or J-PARCnu The T2K project has been approved as a 5 year construction program starting from April, 2004. The experiment will be expected to start in early 2009. Neutrino beam will be produced by protons accelerated by 50 GeV Proton Synchrotron to be constructed at JAERI, Tokai Villedge, 60 km north east of KEK. Phase I of the experiment uses 0.75 MW of the synchrotron power and SK as a far detector and is aiming to make a precise determination of the oscillation 2 parameters for νµ disappearance and to measure |Ue3| through the appearance of νµ → νe. Comparing the T2K experiment to the K2K experiment at KEK, the beam intensity would increase from 6×1012 ppp to 330×1012 ppp and the repitition rate would decrease from 0.45 to 0.275 Hz. The beam energy increases from 12 GeV to 50 GeV and the power from 5.2 kW to 750 kW. The total power in terms of the 90

interaction rate inceases about 100 times. By using the oﬀ-axis beam of 2 degree to adjust the peak beam energy to match the oscillation parameter, the accuracy of δ(sin2 2θ) ∼ 0.01 and δ(∆m2) ≤ 1 × 10−4 will be obtained in 5 year of running. 2 For the electron appearance, the sensitivity down to |Ue3| ∼ 0.0015 ∼ 0.002, about 1/20 of the CHOOZ limit, will be acheived.

NuMI Off-Axis For the NuMI-Off axis experiment [26], a 50 kt detector with low Z and high granularity will be placed at the distance of 700 to 900 km from the neutrino production target. The medium energy NuMI will be used to produce low energy off-axis narrow band beam with the energy ∼2 GeV. The beam produces fewer neutral current background and the energy is below τ threshold. A 5 year running of the experiment with 3.6×1020POT/yr for the 20kt fiducial volume, you get 400 2 oscillated electron production for |Ue3| =0.025 (∼CHOOZ limit), and 15 electron 2 events for |Ue3| =0.0025. The ultimate sensitivity (90% C.L.) will reach down to 2 |Ue3| =0.0007 (statistics only). The eariest possibility is in late 2007.

Reactor experiments for θ13 A reactor oscilation experiment with the baseline of O (1 km) has an oscillation probability 2 2 2 Pν¯e→ν¯e =1− sin 2θ13 sin (∆m13L/4E),

2 and is possible to measure directly θ13. There is no uncertainty due to sin θ23 as for the long baseline accelerator experiments. There are no matter effects and no CP violation effects. However, it is a difficult experiment since it must measure very small effect in a large number. If you aim to reach a sensitivity of sin2 2θ ≤ 0.01, then you need about 50 tons of detector which is 10 times larger than the CHOOZ detector. You also need larger power for the nuclear reactors. The two detectors are absolutely neccessary to reduce the systematic uncertainty to be less than 1%. The deeper site to reduce background is required.

There are a few possible sites considered. Kr2Det is a 2 detector experiment at Krasnoyarsk. The detectors are placed at 15 m and 1000 m. The depth of the far detector is 600m water equivalent. Total 20,000 events are expected. Diablo Canion at California coast has a mountain close to the coast. The detector can be place at 600 m w.e. depth. There are two 3.1 GW reactors. Kashiwazaki in Japan is another possible site. But the underground shaft must be built. There are 7 nuclear power stations, the largest in the world. Those reactor experiments aiming to measure θ13 are now very actively 91

investigated.

MiniBooNE The MiniBooNE experiment [27] has started in the last year and has accumulated already more than 20% of the data required. It uses 800 tons of mineral oil viewed by 1280 8 inch PMTs. Neutrinos are produced by the 8 GeV booster at Fermilab that provids 5 × 1020 POT/yr. The detector is located at 0.5 km down stream and the experiment will look for the νµ → νe oscillations in the higher mass-diﬀerence region to test the LSND anomaly, which has suggested the oscillation at the parameter near ∆m2 ∼ 1 eV 2 and sin2 2θ ∼ 3×10−3. In order to accomodate solar and atmospheric neutrino oscillations and LSND anomaly as a neutrino oscillation, you require either sterile neutrinos, non-standard interactions or CPT violation. The ﬁrst results will be announced in 2005.

8. Beyond the Horizon of θ13

2 2 If sin 2θ13 > 0.01, then there is a chance that sin 2θ13 can be observed by near future experiments. The positively deﬁnd θ13 would lead us to a new area where we can study the lepton sector in detail including a possible CP Vioration. For exmample, phase II experiment of J-PARCnu would provide a good chance 2 to discover CPV for a CPV phase range of 10 to 40 deg for sin 2θ13=0.02. In order to reach to this level, we need to do very good experiment to discover positive θ13. And we need a good detector and a good beam in future discovery [28].

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[23] more information on http://www.aquila.infn.it/icarus/

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