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Neutrino Experiments: Review of Recent Results
Nuclear Physics B (Proc. Suppl.) 144 (2005) 286–296 www.elsevierphysics.com
Neutrino Experiments: Review of Recent Results Junpei Shiraia (for the KamLAND Collaboration) a
Research Center for Neutrino Science, Tohoku University, Aoba-ku, Sendai-shi, 980-8578, Japan Great progress has been made recently in neutrino experiments. Especially the solar, reactor, atmospheric and accelerator experimets all confirmed strong evidence indicating neutrino oscillation, and precise measurements on the neutrino mass and mixing angles are going on. In this brief review a history of the solar and reactor experiments are described and then latest results from KamLAND reactor experiment, and related neutrino oscillation experiments, mainly devoting to non-accelerator experiments, are presented. Then a present status of the neutrinoless double β-decay and the planned direct neutrino mass experiments are described.
1. Introduction Neutrino oscillation experiments have a long history of more than 30 years in which continuous efforts have been made to clarify the characteristics of neutrino. Among them the most fundamental one is to study the mass which, in the standard theory of elementary particles, is assumed to be zero. Since the weak flavor eigenstates do not necessarily coincide with the mass eigenstates, a neutrino in a flavor eigenstate is in general a linear combination of the mass eigenstates with different masses. It is expressed as 3 |να >= i=1 Uαi |νi >, (1) where |να > is a flavor eigenstate, |ν i > the mass eigenstates and U αi are elements of the 3 × 3 PMNS(Pontecorvo-Maki-Nakagawa-Sakata) [1] mixing matrix. If neutrinos have finite masses, the mixing results in periodic flavor transformation of a neutrino, which is called neutrino oscillation. In a 2-flavor scheme of the neutrino oscillation the survival probability of a flavor (α), P(να → να ) or transformation probability to other flavor (β) P (να → νβ ) is expressed as P (να → να ) = 1 − P (να → νβ ) = 1−sin2 2θ sin2 (∆M 2 L/4Eν ),
(2)
0920-5632/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2005.02.039
where L is a flight distance and E ν is the neutrino energy. θ and ∆M 2 are the mixing angle and the mass squared difference of the two mass eigenstates, respectively, and they are parameters determined only experimentally by measuring the neutrino flux, energy spectra and the time variation, etc. Clear evidences of reduction of the neutrino flux and the change of the spectrum from the orginal flux have been accumulated in the solar, reactor, atmospheric, and accelerator neutrino experiments. They establish or strongly support the neutrino oscillation, and corresponding ∆M 2 ’s and the mixing anlges are determined. In this paper a brief history and the present status of the studies on neutrino oscillation, and planned experiments on neutrinos are reviewed being mainly devoted to non-accelerator experiments. A history of the solar neutrino experiments and reactor experiments are described and new results of KamLAND reactor neutrino experiment and atmospheric neutrino rsults from Super-Kamiokande (Super-K) are presented. Then, a discussion is made on planned experiments for measuring the third mixing angle (θ13 ) in comparison with the long baseline accelerator experiments. Finally, the status of the neutrinoless double β-decay experiments and direct neutrino mass measurements are described.
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2. Solar Neutrino Experiments; a Brief History There has been a long-standing puzzle in solar neutrino experiments called the solar neutrino problem; the observed solar neutrino fluxes are significantly less than the prediction. The problem originated from a challenge by R.Davis [2] in late 1960’s aiming to confirm the neutrino generating process of the thermo-nuclear fusion in the center of the sun, 4p+2e− → 4 He+2νe +26.73 MeV−E ν ,
(3)
where Eν is the neutrino energy. The experiment measured the flux by νe +35 Cl→ 37 Ar+e− (Eν ≥814 keV) using a 615 ton tetrachloroethelene (C2 Cl4 ) in Homestake mine in USA. The data [3] showed significantly smaller flux of only about 30% of the prediction. Fig. 1 shows the solar neutrino flux predicted by the standard solar model (SSM) [4].
Figure 1. Solar neutrino flux predicted by the standard solar model (SSM) [4].
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The deficit was confirmed in late 1980’s and 1990’s by Kamiokande experiment [5] in Kamioka mine in Japan. With a 3000 ton water Cherenkov detector with a threshold energy of 7 MeV they made a real time measurement of the 8 B neutrino flux by the elastic scattering (ν + e − → ν + e− ). The directional information of the recoil electrons showed that the neutrinos really come from the sun, while the measured flux is only 55% of the prediction. Another confirmation was made in 1990’s by GALLEX [6] and GNO [7] at Gran Sasso in Italy and SAGE [8] at Baksan in Russia. They all used reaction of νe +71 Ga→71 Ge+e− (Eν ≥233 keV) to measure the dominant flux (called pp neutrino) of the solar neutrino. They all showed that the observed flux were 50-60% of the prediction. These experiments have established the flux deficit and the problem subsisted through many checks both in experimental and theoretical sides. An idea was proposed to explain the discrepancy that the neutrino has a finite mass and changes the original flavor (ν e ) to another one(s) during the long flight to the earth. Since all the solar neutrino experiments were sensitive only or dominantly to νe , the neutrinos with non-νe flavors can escape the detection. The scenario is called neutrino oscillation and described by two parameters; the mixing angle θ and the mass squared difference (∆M 2 ). There were several allowed regions of oscillation parameters depending on the assumed mechanisms; oscillation in vacuum (VAC), and the matter-enhanced oscillation (MSW effect [10]) in the sun and the earth (LMA, SMA and LOW). They scattered large area in a ∆M 2 − tan2 θ plane with ∆M 2 from 10−12 to 10−3 eV2 and tan2 θ from 10−3 to ∼ 1. A precise 8 B neutrino flux measurement by the Super-Kamiokande 50 kton water Cherenkov detector in Kamioka mine started in 1996. They detected the νe elastic scattering and confirmed the 8 B flux deficit [13] with much higher statistics and improved threshold (5 MeV) from Kamiokande, and measured the energy spectrum, the seasonal variation of the flux and Day-time and Night-time flux difference. In 2001, SNO detector in Sudbury in Canada using 1 kton heavy water (D 2 O) Cherenkov
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detector observed the evidence of the flavor change [11]. They measured the 8 B solar neutrino flux by using three processes; νe + d → p + p + e− [CC],
(4)
ν + d → n + p + ν [NC],
(5)
−
−
ν +e → ν +e [ES],
(6)
where [CC] is the charged current process which occurs only by νe , while [NC] is the neutral current process which is equally sensitive to the three active flavors (ν e , νµ and ντ ) and the νe elastic scattering [ES] is mainly sensitive to ν e but with a reduced sensitivity to νµ and ντ . It is noted that in the first SNO results a high statistics νe sacttering data [13] from Super-K was used in the analysis. Fig. 2 shows the SNO results of [12]. It is clear that the total active neutrino flux agrees well with the prediction of the SSM [4] while the νe component is significantly smaller than the total flux and consistent with the previous solar neutrino experiments. The observed flavor change of the neutrino suggested that the solar neutrino problem is explained by the neutrino oscillation. Fig. 3 shows the allowed region of oscillation parameters [14] by assuming 2-flavor neutrino oscillation obtained by the solar experiments. Combination of all the solar experiments supported the LMA solution with a region of ∆M 2 = (3 − 22)×10 −5 eV2 and sin2 2θ = 0.72 − 0.97 at 95% C.L. However, it is not clear that the neutrino oscillation is the real mechanism of the solar neutrino problem because other possible processes like neutrino decay or a flavor change by Spin-Flavor precession in the magnetic field in the sun were not completely excluded. Moreover, none of the solar experiments can uniquely determine the solution due to the rate only measurements and/or the uncertainties of the parameters in the matter oscillation and unknown conditions in the interior of the sun. It is therefore definitely needed to solve the problem by another experiment with much less uncertainty in the conditions.
Figure 2. Results from SNO experiment [12]. Summed flux of νµ and ντ components (Φµτ ) versus that of νe component (Φe ) is presented by three bands obtaind by corresponding neutrino reactions. Total active neutrino flux obtained by the neutral current reaction is in good agreement with the SSM prediction. The ellipses at the intercept are 68%, 95% and 99% joint probability contours for Φe and Φµτ .
3. Reactor Neutrino KamLAND
Experiments
and
Another trend of neutrino oscillation search has been made by experiments using nuclear reactors which date back to an experiment by F.Reines in 1950’s to discover the neutrino. A nuclear reactor provides pure anti-electron neutrinos (¯ ν e ’s) because the fission products are neutron rich nuclei and they β − decay and emit ν¯e ’s. The neutrino flux is calculated better than 2% uncertainty by using the reactor information of the initial fuel components, the thermal power and burn-up of the fission elements which are dominated by 235 U, 239 Pu, 238 U and 241 Pu. In average ∼ 6 ν¯e ’s are emitted and ∼200 MeV of energy are released per fission. The flux decreases with an energy and extends up to around 8.5
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Sensitivity to the neutrino oscillation is determined by the products of the baseline, target mass and the ν¯e flux, if backgrounds are sufficiently suppressed. Experiments with baselines ranging from a few ten meters to ∼1 km were carried out until 1990’s. However, they found no deviation in the flux and the spectral shape from the expectation assuming no oscillation. A reactor ν¯e experiment with a bseline of ∼100 km can check the LMA solution (∆M 2 ∼ 10−5 eV2 ) to the solar neutrino problem under the assumption of CPT invariance, if sufficiently intense ν¯e flux is provided and a detector with a large target volume placed in a very low background is realized.
Figure 3. Allowed oscillation parameter regions (95% C.L.) in a 2-flavor neutrino framework from the all solar neutrino experiments. Four solutions to the solar neutrino problem are indicated [14].
MeV. The neutrino spectrum from each fissile element is well known from experiments measuring electron spectra emitted from fission products of 235 U, 239 Pu and 241 Pu produced by thermal neutrons and from calculation for daughter nuclei of 238 U fissioned by fast neutrons [15]. The ν¯e is detected by using the inverse β − decay reaction, ν¯e p→ e+ n, with 1.8 MeV threshold of Eν¯e . The cross section is precisely known within 0.2% and increases with Eν¯e . Since the recoil neutron energy is negligibly small, E ν¯e is obtained by the energy of the positron signal (kinetic plus annihilation energies) which is E ν¯e −0.8 MeV.
Figure 4. KamLAND detector.
KamLAND(Kamioka Liquid scintillator AntiN eutrino Detector) is a 1000 ton liquid scintillator neutrino experiment located in 1000 m un-
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derground in Kamioka mine in Japan [16], where the Kamiokande detector used to be. Study of the reactor neutrino oscillation is a primary goal of the first stage. There are 53 power reactors in Japan. More than half of them are locating at 175±35 km from KamLAND and are generating 70 GW thermal power which amounts to ∼7% of the total reactor power in the world. Expected ν¯e flux at KamLAND is 106 /s/cm2 without oscillation. So, KamLAND is located in the best place for carrying out the long baseline reactor experiment. Fig. 4 shows the detector. The central part is the liquid scintillator filled in a transparent plastic balloon of 13 m in diameter and suspended in non-scintillating oil. It is viewed by 1325 17-inch and 554 20-inch photo-multiplier tubes (PMTs) to measure the energy and position of an event in the liquid scintillator with a trigger threshold of 200 17-inch PMT hits corresponding to ∼0.7 MeV, and a resolution of 6.2%/ E[M eV ] . The central part is contained in a stainless-steel spherical tank of 18 m in diameter. The outside of the tank is a 3200 ton water Cherenkov detector equipped with 225 20-inch PMTs to identify cosmic-ray muons which penetrates the detector in every ∼3 sec and serves as a radiation shield against γ rays and neutrons from the surrounding rock. The energy calibration is made by γ-ray sources along the central vertical axis. Neutron capture events and β decays of unstable nuclei produced uniformly in the detector by cosmic ray muons are also utilized for the calibration. ν¯e detection is made by ν¯e p→ e+ n reaction, where prompt e+ signal (Eprompt , kinetic plus annihilation energies) and a delayed neutron capture signal of 2.2 MeV γ emitted in ∼210 µs later than the prompt one are detected. The combination of the space and time correlation of the prompt and delayed signals and the delayed energy information greatly reduce accidental backgrounds from residual radioactivities and external γ rays. The ν¯e energy is obtained by Eprompt +0.8 MeV. In the reactor ν¯e analysis, Eν¯e >3.4 MeV is selected to remove possible contribution of geoν¯e ’s from β decays of 238 U and 232 Th series in
the earth. The experiment started in 2002 and the first results [16] based on a data sample of 162 ton·yr in the same year showed a clear evidence of reactor ν¯e disappearance for the first time at 99.95% C.L.; 54 ν¯e events are observed with an expected background of ∼ 1 event, while 86.8±5.6 ν¯e events are expected from no-oscillation assumption. The results strongly suggested the neutrino oscillation and the 2-flavor neutrino oscillation analysis exclude all the solutions to the solar neutrino problem other than the LMA from the rate only analysis under the assumption of the CPT invariance. Combined rate plus spectral shape analysis further restricted the LMA region to two narrow bands of ∆M 2 and provided the best fit values; ∆m2 = 6.9 × 10 −5 eV2 and sin2 2θ = 1.0. A new results [17] from KamLAND has come from 766.3 ton·yr data sample which is 4.7 times larger than the first reactor results by longer data taking period and improved analysis method using an enlarged fidutial volume. Fig. 5 shows the observed E prompt spectrum above the analysis threshold of 2.6 MeV. A clear deficit of the flux and the spectral distortion compared to the no-oscillation spectrum can be seen. The observed number of ν¯e candidates above the analysis threshold (E prompt > 2.6 MeV) is 258 events compared to the expectation of 365±24 events in the absence of neutrino oscillation. Including a newly found background from 13 C(n, α)16 O, total backgrounds expected above the analysis threshold are 17.8±7.3 events, and survival probability of ν¯e is obtained as 0.658±0.044(stat)±0.047(syst). The reactor neutrino disappearance is again confirmed with an improved significance of 99.998%. Moreover, the observed spectral shape shows a clear distortion which is well explained by an oscillation but disagrees with a scaled nooscillation spectrum with 99.6% significance. An oscillatory behaviour of the data can be seen by an L0 /Eν¯e plot as shown in Fig. 6. In the figure alternative hypotheses, the decay and decoherence are shown. They reproduce the data much poorer than oscillation and are excluded at 99.3% and 98.2% C.L., respectively.
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1.4
2.6 MeV prompt analysis threshold
KamLAND data best-fit oscillation best-fit decay best-fit decoherence
1.2
Ratio
1 0.8 0.6 0.4 0.2 0
20
30
40
50
60
70
80
L 0/E ν (km/MeV) e
Figure 5. Energy spectrum of the prompt e + signal Eprompt (= Eν¯e − 0.8 MeV) of ν¯e p → e+ n candidates above the analysis threshold of Eprompt > 2.6 MeV observed in a new 766.3 ton·yr data sample of KamLAND [17] (dots with error bars). Histograms show the accidental and the 13 C(α, n)16 O backgrounds, and the expectation of no-oscillation and the best-fit oscillation spectrum with the systematic error.
So, KamLAND has found for the first time not only the reduction of the ν¯e flux but also the ν¯e spectral distortion which is a decisive evidence for the neutrino oscillation. The rate plus shape analysis with two-flavor neutrino determine the −5 oscillation parameters as ∆M 2 = 7.9+0.6 −0.5 × 10 2 2 eV and tan θ = 0.46 which are presented in Fig. 7. Under the CPT invariance the solar neutrino problem was finally resolved. Combined with the solar experiments the most precise pa−5 rameters are provided as ∆M 2 = 7.9+0.6 −0.5 × 10 +0.10 2 2 eV and tan θ = 0.40−0.07 . 4. Atmospheric and Accelerator νµ Experiments It was an atmospheric neutrino experiments by Super-K in 1998 that showed the first evidence of the neutrino oscillation which means the finite mass of the neutrino [18]. The observed large zenith-angle-dependent deficit of ν µ (and
Figure 6. Ratio of the observed to the nooscillation expectation of the ν¯e spectrum versus L0 /E at KamLAND [17], where L 0 is taken as 180 km. The best-fit of the oscillation is shown by a solid histogram. The two curves show the best fit by hypotheses of decay and decoherence.
ν¯µ ) while non-observation of an increase in ν e (and ν¯e ) strongly indicate νµ → ντ transformation with a large mixing angle of sin 2 2θatm > 0.82 2 and 5 × 10−4 < ∆Matm < 6 × 10−3 eV2 at 90% C.L. Recently Super-K reported analysis on the zenith angle distribution of the atmospheric ν µ events of a large data sample (SK-I; 1496 days from 1996 to 2001) [19], and the L/E spectrum for the events with high L/E resolution from the data sample [20]. Fig. 8 shows the L/E spectrum. A structure can be seen at 500 km/GeV which is consistent with neutrino oscillation, while other hypotheses of the neutrino decay and decoherence are disfavored with 3.4σ and 3.8σ, respectively. Combined with the results on the zenith angle distribution of the atmospheric ν µ data of SK-I and the recent results of the K2K long baseline (250 km from the KEK to Kamioka) accelerator νµ experiment [21] which has indicated neutrino oscillation by observed reduction of ν µ flux together with a distortion of the energy spectrum, the 2-flavor neutrino oscillation parameters 2 are obtained as 1.02 and of sin2 2θatm and ∆Matm −3 2 2.4×10 eV , respectively.
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Figure 7. New results from KamLAND reactor neutrino analysis [17]. Excluded regions (at 95% C.L.) by the rate and allowed regions by the rate plus spectral shape are shown together with the LMA region obtained by the solar neutrino experiments.
In three neutrino mixing this fact and the solar 2 2 ≈ ∆M23 ≈ and reactor results show that ∆M atm 2 2 2 ∆M13 ∆M ≈ ∆M12 , and the mixing angles are quite large; sin 2 2θatm ≈ sin2 2θ23 ≈ 1 and that sin2 2θ ≈ sin2 2θ12 ≈ 1. 5. θ13 Measurement From the oscillation studies for ν µ (¯ νµ ) and νe (¯ νe ) by solar, reactor and atmospheric and accelerator experiments, the mixing angles θ 23 and 2 2 θ12 , and corresponding ∆M 23 and ∆M12 have been determined. The next challenge is to measure θ13 and CP violation phase (δ) which are the remaining parameters of the PMNS mixing matrix. Future long baseline accelerator experiments [23] are planning to determine θ 13 and δ by carrying out the measurements of P (ν µ → νe ) and P (¯ νµ → ν¯e ). However, in these experiments
Figure 8. L/E plot from the recent studies of Super-K atmospheric muon data [20]. Vertical axis is the ratio of the data to the Monte Carlo events without neutrino oscillation (points) as a function of the reconstructed L/E. The solid line is the best-fit by νµ → ντ oscillation, while the dashed and dotted lines are the best-fit by neutrino decay and decoherence.
the observability of δ is controlled by θ 13 by a combination of sin 2θ13 × sin δ. This means that CP violation effect would not be observed if sin 2θ13 is very small. Therefore, θ 13 measurement is very important to be considered in designing the future accelerator neutrino experiments. The reactor ν¯e experiment can make a great contribution to the θ13 measurement. The survival probability of ν¯e is expressed as P (¯ νe → ν¯e ) = 1 − c413 sin2 2θ12 sin2 ∆12 − s212 sin2 2θ13 sin2 ∆32 −c212 sin2 2θ13 sin2 ∆31 , (7) where cij ≡ cos θij , sij ≡ sin θij and ∆ij ≡ (Mi2 − Mj2 )L/4Eν . Since ∆32 ≈ ∆31 ≈ 30∆21 , taking a baseline L at around 1 km makes the fac-
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tors sin2 ∆32 ≈ sin2 ∆31 close to 1 while the factor sin2 ∆12 is negligibly small. Then, the above equation simply becomes P (¯ νe → ν¯e ) = 1 − sin2 2θ13 sin2 ∆31 .
(8)
This makes possible a pure θ 13 measurement in the reactor experiment. On the contrary, in an accelerator experiment of studying νµ → νe appearance, transformation probability P (νµ → νe ) is expressed as P (νµ → νe ) = sin2 2θ13 s223 sin2 ∆32 2 2 −(π/2)(∆M12 /∆M23 )c13 sin 2θ12 sin 2θ23
× sin 2θ13 sin δ.
(9)
If the second term of Eq.(9) is safely neglected compared to the first term, then by taking L to make sin2 ∆32 ∼ 1, the experiment can measure the sin2 2θ13 from the first term. However, there is an intrinsic uncertainty in determination of sin2 2θ13 because of the two values of s223 (= sin2 θ23 ) which is equal to (1 ± 1 − sin2 2θ23 )/2. For example, the present lower limit of sin2 2θ23 = 0.95 by Super-K gives s223 = 0.61 and 0.39 which makes a large uncertainty of sin2 2θ13 . The situation is shown in Fig. 9 [22] by the two conical bands. Besides, we have no knowledge about the value of sinδ in the second term of Eq.(9) and the coefficient of the sin 2θ13 sin δ is ∼0.04, the term could make a non-negligible contribution to the uncertainty depending on the value of P (νµ → νe ) as shown also in Fig. 9. Therefore, P (¯ ν µ → ν¯e ) measurement would also be needed to determine sin 2 2θ13 , because the expression of P (¯ ν µ → ν¯e ) is the same as P (νµ → νe ) except for the different sign of the corresponding term in Eq.(9) containing sin δ. Reactor experiment for θ 13 measurement could therefore provide a crucial step towards the future CP violation studies in accelerator experiments. The present limit on θ13 is given as sin2 2θ13 < 0.12 by CHOOZ reactor experiment [24]. There are several planned experiments using reactors [25] [26] [27] [28] [29]. In Japan
Figure 9. Appearance probability P (ν µ → νe ) vs. sin2 2θ13 for sin2 2θ13 = 0.92 [22]. The matter effect is neglected. Two bands correspond to the two sin2 θ23 values, and the width of the bands is due to the unknown value of sin δ.
KASKA experiment [22] is planned in Kashiwazaki where the world’s largest power station is located and intense ν¯e flux from reactors with 24.3 GW thermal power can be used for the experiment. One far detector at ∼1.8 km and two near detectors at ∼ 350 m from the two groups of 7 reactor units and placed under 200 m and 70 m underground, respectively will measure the flux from the reactors. Each detector uses 8 ton Gd-loaded liquid scintillator viewed by 400 8-inch PMTs. The total systematic error is 0.5∼1% and 60,000 events/3yr is expected in the far detector to achieve the sensitivity of sin2 2θ13 =0.017 to 0.026. 6. Search for Neutrinoless Double β-Decay Neutrinoless double β-decay (0νββ) is a nuclear decay process, (A, Z) → (A, Z +2)+e− +e− ,
(10)
which is a total lepton number violation process (∆L = 2) and takes place if the neutrino is a massive Majorana particle (ν = ν¯).
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0ν −1 ) ) The decay rate of 0νββ process ( (T 1/2 is connected to the effective Majorana mass (| < Mββ > |) by 0ν −1 (T1/2 ) = G0ν |M 0ν |2 | < Mββ > |2 ,
(11)
where G0ν is the phase space factor. M 0ν is the nuclear matrix element and theoretically derived but with a large uncertainty. The effective Majorana mass is expressed by 3 × 3 mixing matrix elements U αi as 3 2 | < Mββ > | = | i=1 Uei mi | = |M1 c212 c213 + M2 s212 c213 e2iβ + M3 s213 c213 e2i(γ−δ) |, (12) where β and γ are Majorana CP phases. So, study of 0νββ decay is very important because not only we can know whether it is Majorana or Dirac particle but we can get the information about the mass pattern and the absolute mass scale of the neutrino; whether it is M1 ∼ M2 < M3 (called Normal Hierarchy), M1 ∼ M2 > M3 (Inverted Hierarchy) or M 1 ∼ M2 ∼ M3 (Degenerate), depending on the mass scale. They are fundamental properties of neutrino which cannot be determined by neutrino oscillation experiments alone. Fig. 10 shows the relation [30] between | < Mββ > | and the lightest neutrino mass from the present knowledge obtained by neutrino oscilla2 = tion experiments. Since we know that ∆M 12 2 2 2 2 2 2 , M2 − M1 ≈ ∆M ∆M23 ≈ ∆M13 ≈ ∆Matm 2 2 and the mixing angles sin 2θ and sin 2θatm are close to 1, region of | < M ββ > | is restricted to the bands depending on the mass patern of the neutrino. An experiment with a sensitivity of | < Mββ > | ∼ 0.01 eV could therefore discriminate the mass pattern and constrain the absolute scale of the neutrino mass. Experimentally 0νββ signal could appear as a peak of the 2β spectrum at the Q-value and above the 2νββ-decay process, νe +¯ νe . (A, Z) → (A, Z+2)+e− +e− +¯
(13)
Figure 10. Relation between the effective mass | < Mββ > | and the lightest neutrino mass [30].
Lots of challenging experiments to 0νββ are planned or under preparation to attain the sensitivity by selecting the nucleus and detection 0ν . G0ν is methods to optimize G0ν times T1/2 roughly proportional to the5th power of the Q0ν ) ∝ (a /A) M t/(B∆E), where value and (T1/2 a, and A are the isotopic abundance (enrichment), detection efficiency and atomic weight of the nucleus. M, B, t and ∆E are the total mass of the material containing the nucleus, the background rate, the data taking period and the energy resolution. Planned experiments are going to use techniques of cryogenics (for 76 Ge, 113 Cd, 123 Te and 116 Cd), tracking (for 150 Nd, 100 Mo, 82 Se and 136 Xe) and scintillation (for 48 Ca, 116 Cd, 160 Gd and 136 Xe). They are aiming at sensitivities of | < Mββ > | to 100 ∼ 10 meV in several years of data taking. A recent claim [31] by Heidelberg-Moscow experiment to have discovered 0νββ decay using
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enriched 76 Ge detector as a 4.2σ effect corresponding to T 0ν1/2 = (0.69 − 4.18) × 10 25 yr and Mν = (0.24 − 0.58) eV could be confirmed or refuted by coming experiments with such high sensitivities.
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tion of the β ray which is connected to the gaseous tritium source through a transport system of superconducting solenoids. The detector R&D is underway to achieve the sensitivity of M ν ∼ 0.2 eV. 8. Summary
7. Direct Neutrino Mass Measurement The direct neutrino mass experiment uses only kinematics of the charged particles in a weak decay process to see the missing mass of the neutrino. It does not depend on any theory and/or hypothses of the process. The most stringent upper bound on the neutrino mass has been obtained by experiments which measure the electron spectrum of the β − decay. It is given by the simple decay kinematics and expressed as N (E) = KF (E, Z)pET [(E0 − E)2 − Mν2 ], (14) where K, p, E, ET are the normalization factor, the momentum, kinetic energy and total energy of the β ray and F (E, Z) is the Fermi function. The experiment searches for the effect of the finite mass of the neutrino (Mν ) which would appear at the endpoint energy E0 . The observed large flavor mixing of the neutrino might indicate that the properties of the neutrino can be around the same including the mass. If so, the neutrino mass might be quasidegenerate and could be checked by a search with sub-eV sensitivity. Due to a small E0 (18.6 keV), super-allowed transition and the well known spectrum of the final daughter molecules, experiments using tritium β decay, 3 H →3 He + e− + ν¯e have provided the most stringent limits on M ν . Recent experiments at Troitsk [32] and Mainz [33] provide the upper limits (at 95% C.L.) of < 2.5 eV and < 2.8 eV, respectively. A planned experiment, KATRIN at Karlsruhe in Germany [34], is a large acceptance and high resolution experiment to measure the tritium β spectrum using gaseous tritium. Based on the techniques developed in the Troitsk and Mainz experiments the new experiment uses a large tank (10m in diameter) of the electrostatic spectrometer system to make adiabatic magnetic collima-
1) Recent neutrino experiments have established neutrino oscillation by observing the flux deficit, flavor change and spectral distortion; solar and reactor neutrino experiments for ν e and ν¯e , atmospheric neutrino and accelerator experiνµ ). ment for νµ (¯ 2) Neutrino mixing angles, θ 12 , θ23 , and the 2 2 squared mass differences, ∆M 12 and ∆M23 are being determined precisely by ongoing neutrino oscillation experiments. 3) Reactor θ13 measurement is crucial for the coming long baseline accelerator experiment aiming to measure CP-violating phase δ. 4) 0νββ experiment is crucial not only to know whether neutrino is Majorana particle or not, but constrain or determine the mass pattern and the absolute mass scale of the neutrino. Planned experiments with a | < Mββ > | sensitivity to ∼0.01 eV could make a great step in unerstanding characteristics of the neutrino. 5) Direct neutrino mass search with a mass sensitivity of sub-eV is very important to provide or constrain unambiguously the pattern and the aboslute mass sacle of the neutrino. 9. Acknowledgements The author would like to thank the organizing committee for having invited him to the conference and providing excellent hospitalities throughout the conference. REFERENCES 1. B.Pontecorvo,Zh.Eksp. Teor. Fiz. 33, 549 (1957) and 34, 247 (1958); Z.Maki, M.Nakagawa and S.Sakata, Prog.Theor. Phys. 28, 870 (1962). 2. D.Davis,Jr. et al., Phys.Rev.Lett.20, 1205 (1968). 3. B.T.Cleveland et al., Ap.J.496, 505 (1998).
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4. J.N.Bahcall, M.H.Pinsonneault and S.Basu, Astrophys.J.555, 990 (2001). 25. 5. K.S.Hirata et al., Phys.Rev.Lett.63, 16 (1989). 6. W.Hampel et al., Phys Lett.B447, 127 26. (1999). 7. M.Altmann et al., Phys.Lett.B490, 16 27. (2000). 28. 8. J.N.Abdurashitov et al., Sov.Phys.JETP 95, 181 (2002). 29. 9. S.Fukuda et al., Phys.Lett.B539, 179 (2002). 10. L.Wofenstein, Phys.Rev.D 17, 2369 30. (1978); S.P.Mikheyev and A.Yu.Smirnov, Sov.J.Nucl.Phys. 42, 913 (1985). 31. 11. Q.R.Ahmad et al., Phys.Rev.Lett. 87 071301 (2001). 32. 12. Q.R.Ahmad et al., Phys.Rev.Lett. 89 011301 (2002). 33. 13. S.Fukuda et al., Phys.Rev.Lett. 86, 5651 (2001). 34. 14. H.Murayama, http://hitoshi.berkeley.edu/neutrino/ 15. 235 U: K.Schreckenbach et al Phys. Lett. B160, 325 (1985); 239,241 Pu: A.A.Hahn et al., Phys. Lett. B218, 365 (1989); 238 U: P.Vogel et al., Phys. Rev. C24, 1543 (1981). 16. KamLAND Collaboration (K.Eguchi et al.), Phys.Rev.Lett.90, 021802 (2002). 17. KamLAND Collaboration (K.Eguchi et al.), hep-ex/0406035. 18. Y.Fukuda et al., Phys.Rev.Lett. 81, 1562 (1998). 19. E.Kearns, presented at ν2004 in Paris in Jun.14-19, 2004. 20. Y.Ashie et al.,Phys.Rev.Lett. 93, 101801 (2004). 21. M.H.Ahn et al., Phys.Rev.Lett. 90, 041801 (2003). 22. F.Suekane in: Proc. of the 4th Int. Workshop on Neutrino Oscillations and their Origin, edited by Y.Suzuki et al., (World Scientific, 2003), p.155; http://kaska.hep.sc.niigatau.ac.jp/ 23. See for example, Y.Hayato (T2K @J-PARK), M.Thompson (NuMI-MINOS) and D.Antiero /A.Bueno (CNGS-OPERA /ICARUS) presented at ν2004 in Paris in Jun.14-19, 2004. 24. The CHOOZ Collaboration (M.Apollonio et al.), Eur. Phys. J. C27, 331 (2003), hep-
ex/0301017. F.Ardellier et al., Letter of Intent for DoubleCHOOZ: http://doublechooz. in2p3.fr/ 0405032.pdf Braidwood http://mwtheta13.uchicago.edu; Diablo Canyon http://theta13.lbl.gv/ Y.Kozlov et al., hep-ph/0109277. Daya Bay http://www.physics.hku.hk/events/ workshops/neutrino/ Angra http://www.hep.anl.gov/minos/reactor13/ Angra/proposal.html P.Vogel and A.Piepke, Phys.Lett.B592, 447 (2004). H.V.Klapdor-Kleingrothaus et al., hepex/0404088. V.M.Lobashev et al., Phys.Lett.B 460, 227 (1999). Ch.Weinheimer et al., Phys.Lett.B 460, 219 (1999). KATRIN(Letter of Intent), A.Osipowicz et al., hep-ex/0109033.
Neutrino Experiments: Review of Recent Results Junpei Shiraia (for the KamLAND Collaboration) a
Research Center for Neutrino Science, Tohoku University, Aoba-ku, Sendai-shi, 980-8578, Japan Great progress has been made recently in neutrino experiments. Especially the solar, reactor, atmospheric and accelerator experimets all confirmed strong evidence indicating neutrino oscillation, and precise measurements on the neutrino mass and mixing angles are going on. In this brief review a history of the solar and reactor experiments are described and then latest results from KamLAND reactor experiment, and related neutrino oscillation experiments, mainly devoting to non-accelerator experiments, are presented. Then a present status of the neutrinoless double β-decay and the planned direct neutrino mass experiments are described.
1. Introduction Neutrino oscillation experiments have a long history of more than 30 years in which continuous efforts have been made to clarify the characteristics of neutrino. Among them the most fundamental one is to study the mass which, in the standard theory of elementary particles, is assumed to be zero. Since the weak flavor eigenstates do not necessarily coincide with the mass eigenstates, a neutrino in a flavor eigenstate is in general a linear combination of the mass eigenstates with different masses. It is expressed as 3 |να >= i=1 Uαi |νi >, (1) where |να > is a flavor eigenstate, |ν i > the mass eigenstates and U αi are elements of the 3 × 3 PMNS(Pontecorvo-Maki-Nakagawa-Sakata) [1] mixing matrix. If neutrinos have finite masses, the mixing results in periodic flavor transformation of a neutrino, which is called neutrino oscillation. In a 2-flavor scheme of the neutrino oscillation the survival probability of a flavor (α), P(να → να ) or transformation probability to other flavor (β) P (να → νβ ) is expressed as P (να → να ) = 1 − P (να → νβ ) = 1−sin2 2θ sin2 (∆M 2 L/4Eν ),
(2)
0920-5632/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2005.02.039
where L is a flight distance and E ν is the neutrino energy. θ and ∆M 2 are the mixing angle and the mass squared difference of the two mass eigenstates, respectively, and they are parameters determined only experimentally by measuring the neutrino flux, energy spectra and the time variation, etc. Clear evidences of reduction of the neutrino flux and the change of the spectrum from the orginal flux have been accumulated in the solar, reactor, atmospheric, and accelerator neutrino experiments. They establish or strongly support the neutrino oscillation, and corresponding ∆M 2 ’s and the mixing anlges are determined. In this paper a brief history and the present status of the studies on neutrino oscillation, and planned experiments on neutrinos are reviewed being mainly devoted to non-accelerator experiments. A history of the solar neutrino experiments and reactor experiments are described and new results of KamLAND reactor neutrino experiment and atmospheric neutrino rsults from Super-Kamiokande (Super-K) are presented. Then, a discussion is made on planned experiments for measuring the third mixing angle (θ13 ) in comparison with the long baseline accelerator experiments. Finally, the status of the neutrinoless double β-decay experiments and direct neutrino mass measurements are described.
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2. Solar Neutrino Experiments; a Brief History There has been a long-standing puzzle in solar neutrino experiments called the solar neutrino problem; the observed solar neutrino fluxes are significantly less than the prediction. The problem originated from a challenge by R.Davis [2] in late 1960’s aiming to confirm the neutrino generating process of the thermo-nuclear fusion in the center of the sun, 4p+2e− → 4 He+2νe +26.73 MeV−E ν ,
(3)
where Eν is the neutrino energy. The experiment measured the flux by νe +35 Cl→ 37 Ar+e− (Eν ≥814 keV) using a 615 ton tetrachloroethelene (C2 Cl4 ) in Homestake mine in USA. The data [3] showed significantly smaller flux of only about 30% of the prediction. Fig. 1 shows the solar neutrino flux predicted by the standard solar model (SSM) [4].
Figure 1. Solar neutrino flux predicted by the standard solar model (SSM) [4].
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The deficit was confirmed in late 1980’s and 1990’s by Kamiokande experiment [5] in Kamioka mine in Japan. With a 3000 ton water Cherenkov detector with a threshold energy of 7 MeV they made a real time measurement of the 8 B neutrino flux by the elastic scattering (ν + e − → ν + e− ). The directional information of the recoil electrons showed that the neutrinos really come from the sun, while the measured flux is only 55% of the prediction. Another confirmation was made in 1990’s by GALLEX [6] and GNO [7] at Gran Sasso in Italy and SAGE [8] at Baksan in Russia. They all used reaction of νe +71 Ga→71 Ge+e− (Eν ≥233 keV) to measure the dominant flux (called pp neutrino) of the solar neutrino. They all showed that the observed flux were 50-60% of the prediction. These experiments have established the flux deficit and the problem subsisted through many checks both in experimental and theoretical sides. An idea was proposed to explain the discrepancy that the neutrino has a finite mass and changes the original flavor (ν e ) to another one(s) during the long flight to the earth. Since all the solar neutrino experiments were sensitive only or dominantly to νe , the neutrinos with non-νe flavors can escape the detection. The scenario is called neutrino oscillation and described by two parameters; the mixing angle θ and the mass squared difference (∆M 2 ). There were several allowed regions of oscillation parameters depending on the assumed mechanisms; oscillation in vacuum (VAC), and the matter-enhanced oscillation (MSW effect [10]) in the sun and the earth (LMA, SMA and LOW). They scattered large area in a ∆M 2 − tan2 θ plane with ∆M 2 from 10−12 to 10−3 eV2 and tan2 θ from 10−3 to ∼ 1. A precise 8 B neutrino flux measurement by the Super-Kamiokande 50 kton water Cherenkov detector in Kamioka mine started in 1996. They detected the νe elastic scattering and confirmed the 8 B flux deficit [13] with much higher statistics and improved threshold (5 MeV) from Kamiokande, and measured the energy spectrum, the seasonal variation of the flux and Day-time and Night-time flux difference. In 2001, SNO detector in Sudbury in Canada using 1 kton heavy water (D 2 O) Cherenkov
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detector observed the evidence of the flavor change [11]. They measured the 8 B solar neutrino flux by using three processes; νe + d → p + p + e− [CC],
(4)
ν + d → n + p + ν [NC],
(5)
−
−
ν +e → ν +e [ES],
(6)
where [CC] is the charged current process which occurs only by νe , while [NC] is the neutral current process which is equally sensitive to the three active flavors (ν e , νµ and ντ ) and the νe elastic scattering [ES] is mainly sensitive to ν e but with a reduced sensitivity to νµ and ντ . It is noted that in the first SNO results a high statistics νe sacttering data [13] from Super-K was used in the analysis. Fig. 2 shows the SNO results of [12]. It is clear that the total active neutrino flux agrees well with the prediction of the SSM [4] while the νe component is significantly smaller than the total flux and consistent with the previous solar neutrino experiments. The observed flavor change of the neutrino suggested that the solar neutrino problem is explained by the neutrino oscillation. Fig. 3 shows the allowed region of oscillation parameters [14] by assuming 2-flavor neutrino oscillation obtained by the solar experiments. Combination of all the solar experiments supported the LMA solution with a region of ∆M 2 = (3 − 22)×10 −5 eV2 and sin2 2θ = 0.72 − 0.97 at 95% C.L. However, it is not clear that the neutrino oscillation is the real mechanism of the solar neutrino problem because other possible processes like neutrino decay or a flavor change by Spin-Flavor precession in the magnetic field in the sun were not completely excluded. Moreover, none of the solar experiments can uniquely determine the solution due to the rate only measurements and/or the uncertainties of the parameters in the matter oscillation and unknown conditions in the interior of the sun. It is therefore definitely needed to solve the problem by another experiment with much less uncertainty in the conditions.
Figure 2. Results from SNO experiment [12]. Summed flux of νµ and ντ components (Φµτ ) versus that of νe component (Φe ) is presented by three bands obtaind by corresponding neutrino reactions. Total active neutrino flux obtained by the neutral current reaction is in good agreement with the SSM prediction. The ellipses at the intercept are 68%, 95% and 99% joint probability contours for Φe and Φµτ .
3. Reactor Neutrino KamLAND
Experiments
and
Another trend of neutrino oscillation search has been made by experiments using nuclear reactors which date back to an experiment by F.Reines in 1950’s to discover the neutrino. A nuclear reactor provides pure anti-electron neutrinos (¯ ν e ’s) because the fission products are neutron rich nuclei and they β − decay and emit ν¯e ’s. The neutrino flux is calculated better than 2% uncertainty by using the reactor information of the initial fuel components, the thermal power and burn-up of the fission elements which are dominated by 235 U, 239 Pu, 238 U and 241 Pu. In average ∼ 6 ν¯e ’s are emitted and ∼200 MeV of energy are released per fission. The flux decreases with an energy and extends up to around 8.5
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Sensitivity to the neutrino oscillation is determined by the products of the baseline, target mass and the ν¯e flux, if backgrounds are sufficiently suppressed. Experiments with baselines ranging from a few ten meters to ∼1 km were carried out until 1990’s. However, they found no deviation in the flux and the spectral shape from the expectation assuming no oscillation. A reactor ν¯e experiment with a bseline of ∼100 km can check the LMA solution (∆M 2 ∼ 10−5 eV2 ) to the solar neutrino problem under the assumption of CPT invariance, if sufficiently intense ν¯e flux is provided and a detector with a large target volume placed in a very low background is realized.
Figure 3. Allowed oscillation parameter regions (95% C.L.) in a 2-flavor neutrino framework from the all solar neutrino experiments. Four solutions to the solar neutrino problem are indicated [14].
MeV. The neutrino spectrum from each fissile element is well known from experiments measuring electron spectra emitted from fission products of 235 U, 239 Pu and 241 Pu produced by thermal neutrons and from calculation for daughter nuclei of 238 U fissioned by fast neutrons [15]. The ν¯e is detected by using the inverse β − decay reaction, ν¯e p→ e+ n, with 1.8 MeV threshold of Eν¯e . The cross section is precisely known within 0.2% and increases with Eν¯e . Since the recoil neutron energy is negligibly small, E ν¯e is obtained by the energy of the positron signal (kinetic plus annihilation energies) which is E ν¯e −0.8 MeV.
Figure 4. KamLAND detector.
KamLAND(Kamioka Liquid scintillator AntiN eutrino Detector) is a 1000 ton liquid scintillator neutrino experiment located in 1000 m un-
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derground in Kamioka mine in Japan [16], where the Kamiokande detector used to be. Study of the reactor neutrino oscillation is a primary goal of the first stage. There are 53 power reactors in Japan. More than half of them are locating at 175±35 km from KamLAND and are generating 70 GW thermal power which amounts to ∼7% of the total reactor power in the world. Expected ν¯e flux at KamLAND is 106 /s/cm2 without oscillation. So, KamLAND is located in the best place for carrying out the long baseline reactor experiment. Fig. 4 shows the detector. The central part is the liquid scintillator filled in a transparent plastic balloon of 13 m in diameter and suspended in non-scintillating oil. It is viewed by 1325 17-inch and 554 20-inch photo-multiplier tubes (PMTs) to measure the energy and position of an event in the liquid scintillator with a trigger threshold of 200 17-inch PMT hits corresponding to ∼0.7 MeV, and a resolution of 6.2%/ E[M eV ] . The central part is contained in a stainless-steel spherical tank of 18 m in diameter. The outside of the tank is a 3200 ton water Cherenkov detector equipped with 225 20-inch PMTs to identify cosmic-ray muons which penetrates the detector in every ∼3 sec and serves as a radiation shield against γ rays and neutrons from the surrounding rock. The energy calibration is made by γ-ray sources along the central vertical axis. Neutron capture events and β decays of unstable nuclei produced uniformly in the detector by cosmic ray muons are also utilized for the calibration. ν¯e detection is made by ν¯e p→ e+ n reaction, where prompt e+ signal (Eprompt , kinetic plus annihilation energies) and a delayed neutron capture signal of 2.2 MeV γ emitted in ∼210 µs later than the prompt one are detected. The combination of the space and time correlation of the prompt and delayed signals and the delayed energy information greatly reduce accidental backgrounds from residual radioactivities and external γ rays. The ν¯e energy is obtained by Eprompt +0.8 MeV. In the reactor ν¯e analysis, Eν¯e >3.4 MeV is selected to remove possible contribution of geoν¯e ’s from β decays of 238 U and 232 Th series in
the earth. The experiment started in 2002 and the first results [16] based on a data sample of 162 ton·yr in the same year showed a clear evidence of reactor ν¯e disappearance for the first time at 99.95% C.L.; 54 ν¯e events are observed with an expected background of ∼ 1 event, while 86.8±5.6 ν¯e events are expected from no-oscillation assumption. The results strongly suggested the neutrino oscillation and the 2-flavor neutrino oscillation analysis exclude all the solutions to the solar neutrino problem other than the LMA from the rate only analysis under the assumption of the CPT invariance. Combined rate plus spectral shape analysis further restricted the LMA region to two narrow bands of ∆M 2 and provided the best fit values; ∆m2 = 6.9 × 10 −5 eV2 and sin2 2θ = 1.0. A new results [17] from KamLAND has come from 766.3 ton·yr data sample which is 4.7 times larger than the first reactor results by longer data taking period and improved analysis method using an enlarged fidutial volume. Fig. 5 shows the observed E prompt spectrum above the analysis threshold of 2.6 MeV. A clear deficit of the flux and the spectral distortion compared to the no-oscillation spectrum can be seen. The observed number of ν¯e candidates above the analysis threshold (E prompt > 2.6 MeV) is 258 events compared to the expectation of 365±24 events in the absence of neutrino oscillation. Including a newly found background from 13 C(n, α)16 O, total backgrounds expected above the analysis threshold are 17.8±7.3 events, and survival probability of ν¯e is obtained as 0.658±0.044(stat)±0.047(syst). The reactor neutrino disappearance is again confirmed with an improved significance of 99.998%. Moreover, the observed spectral shape shows a clear distortion which is well explained by an oscillation but disagrees with a scaled nooscillation spectrum with 99.6% significance. An oscillatory behaviour of the data can be seen by an L0 /Eν¯e plot as shown in Fig. 6. In the figure alternative hypotheses, the decay and decoherence are shown. They reproduce the data much poorer than oscillation and are excluded at 99.3% and 98.2% C.L., respectively.
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1.4
2.6 MeV prompt analysis threshold
KamLAND data best-fit oscillation best-fit decay best-fit decoherence
1.2
Ratio
1 0.8 0.6 0.4 0.2 0
20
30
40
50
60
70
80
L 0/E ν (km/MeV) e
Figure 5. Energy spectrum of the prompt e + signal Eprompt (= Eν¯e − 0.8 MeV) of ν¯e p → e+ n candidates above the analysis threshold of Eprompt > 2.6 MeV observed in a new 766.3 ton·yr data sample of KamLAND [17] (dots with error bars). Histograms show the accidental and the 13 C(α, n)16 O backgrounds, and the expectation of no-oscillation and the best-fit oscillation spectrum with the systematic error.
So, KamLAND has found for the first time not only the reduction of the ν¯e flux but also the ν¯e spectral distortion which is a decisive evidence for the neutrino oscillation. The rate plus shape analysis with two-flavor neutrino determine the −5 oscillation parameters as ∆M 2 = 7.9+0.6 −0.5 × 10 2 2 eV and tan θ = 0.46 which are presented in Fig. 7. Under the CPT invariance the solar neutrino problem was finally resolved. Combined with the solar experiments the most precise pa−5 rameters are provided as ∆M 2 = 7.9+0.6 −0.5 × 10 +0.10 2 2 eV and tan θ = 0.40−0.07 . 4. Atmospheric and Accelerator νµ Experiments It was an atmospheric neutrino experiments by Super-K in 1998 that showed the first evidence of the neutrino oscillation which means the finite mass of the neutrino [18]. The observed large zenith-angle-dependent deficit of ν µ (and
Figure 6. Ratio of the observed to the nooscillation expectation of the ν¯e spectrum versus L0 /E at KamLAND [17], where L 0 is taken as 180 km. The best-fit of the oscillation is shown by a solid histogram. The two curves show the best fit by hypotheses of decay and decoherence.
ν¯µ ) while non-observation of an increase in ν e (and ν¯e ) strongly indicate νµ → ντ transformation with a large mixing angle of sin 2 2θatm > 0.82 2 and 5 × 10−4 < ∆Matm < 6 × 10−3 eV2 at 90% C.L. Recently Super-K reported analysis on the zenith angle distribution of the atmospheric ν µ events of a large data sample (SK-I; 1496 days from 1996 to 2001) [19], and the L/E spectrum for the events with high L/E resolution from the data sample [20]. Fig. 8 shows the L/E spectrum. A structure can be seen at 500 km/GeV which is consistent with neutrino oscillation, while other hypotheses of the neutrino decay and decoherence are disfavored with 3.4σ and 3.8σ, respectively. Combined with the results on the zenith angle distribution of the atmospheric ν µ data of SK-I and the recent results of the K2K long baseline (250 km from the KEK to Kamioka) accelerator νµ experiment [21] which has indicated neutrino oscillation by observed reduction of ν µ flux together with a distortion of the energy spectrum, the 2-flavor neutrino oscillation parameters 2 are obtained as 1.02 and of sin2 2θatm and ∆Matm −3 2 2.4×10 eV , respectively.
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Figure 7. New results from KamLAND reactor neutrino analysis [17]. Excluded regions (at 95% C.L.) by the rate and allowed regions by the rate plus spectral shape are shown together with the LMA region obtained by the solar neutrino experiments.
In three neutrino mixing this fact and the solar 2 2 ≈ ∆M23 ≈ and reactor results show that ∆M atm 2 2 2 ∆M13 ∆M ≈ ∆M12 , and the mixing angles are quite large; sin 2 2θatm ≈ sin2 2θ23 ≈ 1 and that sin2 2θ ≈ sin2 2θ12 ≈ 1. 5. θ13 Measurement From the oscillation studies for ν µ (¯ νµ ) and νe (¯ νe ) by solar, reactor and atmospheric and accelerator experiments, the mixing angles θ 23 and 2 2 θ12 , and corresponding ∆M 23 and ∆M12 have been determined. The next challenge is to measure θ13 and CP violation phase (δ) which are the remaining parameters of the PMNS mixing matrix. Future long baseline accelerator experiments [23] are planning to determine θ 13 and δ by carrying out the measurements of P (ν µ → νe ) and P (¯ νµ → ν¯e ). However, in these experiments
Figure 8. L/E plot from the recent studies of Super-K atmospheric muon data [20]. Vertical axis is the ratio of the data to the Monte Carlo events without neutrino oscillation (points) as a function of the reconstructed L/E. The solid line is the best-fit by νµ → ντ oscillation, while the dashed and dotted lines are the best-fit by neutrino decay and decoherence.
the observability of δ is controlled by θ 13 by a combination of sin 2θ13 × sin δ. This means that CP violation effect would not be observed if sin 2θ13 is very small. Therefore, θ 13 measurement is very important to be considered in designing the future accelerator neutrino experiments. The reactor ν¯e experiment can make a great contribution to the θ13 measurement. The survival probability of ν¯e is expressed as P (¯ νe → ν¯e ) = 1 − c413 sin2 2θ12 sin2 ∆12 − s212 sin2 2θ13 sin2 ∆32 −c212 sin2 2θ13 sin2 ∆31 , (7) where cij ≡ cos θij , sij ≡ sin θij and ∆ij ≡ (Mi2 − Mj2 )L/4Eν . Since ∆32 ≈ ∆31 ≈ 30∆21 , taking a baseline L at around 1 km makes the fac-
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tors sin2 ∆32 ≈ sin2 ∆31 close to 1 while the factor sin2 ∆12 is negligibly small. Then, the above equation simply becomes P (¯ νe → ν¯e ) = 1 − sin2 2θ13 sin2 ∆31 .
(8)
This makes possible a pure θ 13 measurement in the reactor experiment. On the contrary, in an accelerator experiment of studying νµ → νe appearance, transformation probability P (νµ → νe ) is expressed as P (νµ → νe ) = sin2 2θ13 s223 sin2 ∆32 2 2 −(π/2)(∆M12 /∆M23 )c13 sin 2θ12 sin 2θ23
× sin 2θ13 sin δ.
(9)
If the second term of Eq.(9) is safely neglected compared to the first term, then by taking L to make sin2 ∆32 ∼ 1, the experiment can measure the sin2 2θ13 from the first term. However, there is an intrinsic uncertainty in determination of sin2 2θ13 because of the two values of s223 (= sin2 θ23 ) which is equal to (1 ± 1 − sin2 2θ23 )/2. For example, the present lower limit of sin2 2θ23 = 0.95 by Super-K gives s223 = 0.61 and 0.39 which makes a large uncertainty of sin2 2θ13 . The situation is shown in Fig. 9 [22] by the two conical bands. Besides, we have no knowledge about the value of sinδ in the second term of Eq.(9) and the coefficient of the sin 2θ13 sin δ is ∼0.04, the term could make a non-negligible contribution to the uncertainty depending on the value of P (νµ → νe ) as shown also in Fig. 9. Therefore, P (¯ ν µ → ν¯e ) measurement would also be needed to determine sin 2 2θ13 , because the expression of P (¯ ν µ → ν¯e ) is the same as P (νµ → νe ) except for the different sign of the corresponding term in Eq.(9) containing sin δ. Reactor experiment for θ 13 measurement could therefore provide a crucial step towards the future CP violation studies in accelerator experiments. The present limit on θ13 is given as sin2 2θ13 < 0.12 by CHOOZ reactor experiment [24]. There are several planned experiments using reactors [25] [26] [27] [28] [29]. In Japan
Figure 9. Appearance probability P (ν µ → νe ) vs. sin2 2θ13 for sin2 2θ13 = 0.92 [22]. The matter effect is neglected. Two bands correspond to the two sin2 θ23 values, and the width of the bands is due to the unknown value of sin δ.
KASKA experiment [22] is planned in Kashiwazaki where the world’s largest power station is located and intense ν¯e flux from reactors with 24.3 GW thermal power can be used for the experiment. One far detector at ∼1.8 km and two near detectors at ∼ 350 m from the two groups of 7 reactor units and placed under 200 m and 70 m underground, respectively will measure the flux from the reactors. Each detector uses 8 ton Gd-loaded liquid scintillator viewed by 400 8-inch PMTs. The total systematic error is 0.5∼1% and 60,000 events/3yr is expected in the far detector to achieve the sensitivity of sin2 2θ13 =0.017 to 0.026. 6. Search for Neutrinoless Double β-Decay Neutrinoless double β-decay (0νββ) is a nuclear decay process, (A, Z) → (A, Z +2)+e− +e− ,
(10)
which is a total lepton number violation process (∆L = 2) and takes place if the neutrino is a massive Majorana particle (ν = ν¯).
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0ν −1 ) ) The decay rate of 0νββ process ( (T 1/2 is connected to the effective Majorana mass (| < Mββ > |) by 0ν −1 (T1/2 ) = G0ν |M 0ν |2 | < Mββ > |2 ,
(11)
where G0ν is the phase space factor. M 0ν is the nuclear matrix element and theoretically derived but with a large uncertainty. The effective Majorana mass is expressed by 3 × 3 mixing matrix elements U αi as 3 2 | < Mββ > | = | i=1 Uei mi | = |M1 c212 c213 + M2 s212 c213 e2iβ + M3 s213 c213 e2i(γ−δ) |, (12) where β and γ are Majorana CP phases. So, study of 0νββ decay is very important because not only we can know whether it is Majorana or Dirac particle but we can get the information about the mass pattern and the absolute mass scale of the neutrino; whether it is M1 ∼ M2 < M3 (called Normal Hierarchy), M1 ∼ M2 > M3 (Inverted Hierarchy) or M 1 ∼ M2 ∼ M3 (Degenerate), depending on the mass scale. They are fundamental properties of neutrino which cannot be determined by neutrino oscillation experiments alone. Fig. 10 shows the relation [30] between | < Mββ > | and the lightest neutrino mass from the present knowledge obtained by neutrino oscilla2 = tion experiments. Since we know that ∆M 12 2 2 2 2 2 2 , M2 − M1 ≈ ∆M ∆M23 ≈ ∆M13 ≈ ∆Matm 2 2 and the mixing angles sin 2θ and sin 2θatm are close to 1, region of | < M ββ > | is restricted to the bands depending on the mass patern of the neutrino. An experiment with a sensitivity of | < Mββ > | ∼ 0.01 eV could therefore discriminate the mass pattern and constrain the absolute scale of the neutrino mass. Experimentally 0νββ signal could appear as a peak of the 2β spectrum at the Q-value and above the 2νββ-decay process, νe +¯ νe . (A, Z) → (A, Z+2)+e− +e− +¯
(13)
Figure 10. Relation between the effective mass | < Mββ > | and the lightest neutrino mass [30].
Lots of challenging experiments to 0νββ are planned or under preparation to attain the sensitivity by selecting the nucleus and detection 0ν . G0ν is methods to optimize G0ν times T1/2 roughly proportional to the5th power of the Q0ν ) ∝ (a /A) M t/(B∆E), where value and (T1/2 a, and A are the isotopic abundance (enrichment), detection efficiency and atomic weight of the nucleus. M, B, t and ∆E are the total mass of the material containing the nucleus, the background rate, the data taking period and the energy resolution. Planned experiments are going to use techniques of cryogenics (for 76 Ge, 113 Cd, 123 Te and 116 Cd), tracking (for 150 Nd, 100 Mo, 82 Se and 136 Xe) and scintillation (for 48 Ca, 116 Cd, 160 Gd and 136 Xe). They are aiming at sensitivities of | < Mββ > | to 100 ∼ 10 meV in several years of data taking. A recent claim [31] by Heidelberg-Moscow experiment to have discovered 0νββ decay using
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enriched 76 Ge detector as a 4.2σ effect corresponding to T 0ν1/2 = (0.69 − 4.18) × 10 25 yr and Mν = (0.24 − 0.58) eV could be confirmed or refuted by coming experiments with such high sensitivities.
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tion of the β ray which is connected to the gaseous tritium source through a transport system of superconducting solenoids. The detector R&D is underway to achieve the sensitivity of M ν ∼ 0.2 eV. 8. Summary
7. Direct Neutrino Mass Measurement The direct neutrino mass experiment uses only kinematics of the charged particles in a weak decay process to see the missing mass of the neutrino. It does not depend on any theory and/or hypothses of the process. The most stringent upper bound on the neutrino mass has been obtained by experiments which measure the electron spectrum of the β − decay. It is given by the simple decay kinematics and expressed as N (E) = KF (E, Z)pET [(E0 − E)2 − Mν2 ], (14) where K, p, E, ET are the normalization factor, the momentum, kinetic energy and total energy of the β ray and F (E, Z) is the Fermi function. The experiment searches for the effect of the finite mass of the neutrino (Mν ) which would appear at the endpoint energy E0 . The observed large flavor mixing of the neutrino might indicate that the properties of the neutrino can be around the same including the mass. If so, the neutrino mass might be quasidegenerate and could be checked by a search with sub-eV sensitivity. Due to a small E0 (18.6 keV), super-allowed transition and the well known spectrum of the final daughter molecules, experiments using tritium β decay, 3 H →3 He + e− + ν¯e have provided the most stringent limits on M ν . Recent experiments at Troitsk [32] and Mainz [33] provide the upper limits (at 95% C.L.) of < 2.5 eV and < 2.8 eV, respectively. A planned experiment, KATRIN at Karlsruhe in Germany [34], is a large acceptance and high resolution experiment to measure the tritium β spectrum using gaseous tritium. Based on the techniques developed in the Troitsk and Mainz experiments the new experiment uses a large tank (10m in diameter) of the electrostatic spectrometer system to make adiabatic magnetic collima-
1) Recent neutrino experiments have established neutrino oscillation by observing the flux deficit, flavor change and spectral distortion; solar and reactor neutrino experiments for ν e and ν¯e , atmospheric neutrino and accelerator experiνµ ). ment for νµ (¯ 2) Neutrino mixing angles, θ 12 , θ23 , and the 2 2 squared mass differences, ∆M 12 and ∆M23 are being determined precisely by ongoing neutrino oscillation experiments. 3) Reactor θ13 measurement is crucial for the coming long baseline accelerator experiment aiming to measure CP-violating phase δ. 4) 0νββ experiment is crucial not only to know whether neutrino is Majorana particle or not, but constrain or determine the mass pattern and the absolute mass scale of the neutrino. Planned experiments with a | < Mββ > | sensitivity to ∼0.01 eV could make a great step in unerstanding characteristics of the neutrino. 5) Direct neutrino mass search with a mass sensitivity of sub-eV is very important to provide or constrain unambiguously the pattern and the aboslute mass sacle of the neutrino. 9. Acknowledgements The author would like to thank the organizing committee for having invited him to the conference and providing excellent hospitalities throughout the conference. REFERENCES 1. B.Pontecorvo,Zh.Eksp. Teor. Fiz. 33, 549 (1957) and 34, 247 (1958); Z.Maki, M.Nakagawa and S.Sakata, Prog.Theor. Phys. 28, 870 (1962). 2. D.Davis,Jr. et al., Phys.Rev.Lett.20, 1205 (1968). 3. B.T.Cleveland et al., Ap.J.496, 505 (1998).
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