Search for Radiative Decays of Cosmic Background Neutrino using Cosmic Infrared Background Energy Spectrum
Shin-Hong Kim, Ken-ichi Takemasa, Yuji Takeuchi, Shuji Matsuura
aa r X i v : . [ h e p - ph ] D ec Search for Radiative Decays of Cosmic BackgroundNeutrino using Cosmic Infrared Background EnergySpectrum
Shin-Hong Kim , Ken-ichi Takemasa , Yuji Takeuchi , and Shuji Matsuura Graduate school of Pure and Applied Sciences, University of Tsukuba,Tsukuba, Ibaraki,305-8571, Japan Institute of Space and Astronautical Science, JAXA, Sagamihara, Kanagawa, 252-5210, Japan
AbstractWe propose to search for the neutrino radiative decay by fitting a photon energy spec-trum of the cosmic infrared background to a sum of the photon energy spectrum fromthe neutrino radiative decay and a continuum. By comparing the present cosmic infraredbackground energy spectrum observed by AKARI and Spitzer to the photon energy spec-trum expected from neutrino radiative decay with a maximum likelihood method, weobatined a lifetime lower limit of 3 . × to 3 . × years at 95% confidence level forthe third generation neutrino ν in the ν mass range between 50 meV/ c and 150 meV/ c under the present constraints by the neutrino oscillation measurements. In the left-rightsymmetric model, the minimum lifetime of ν is predicted to be 1 . × years for m of50 meV/ c . We studied the feasibility of the observation of the neutrino radiative decaywith a lifetime of 1 . × years, by measuring a continuous energy spectrum of thecosmic infrared background. 1 Introduction
The difference between the mass-squares of different-generation neutrinos has been mea-sured by atmospheric neutrino oscillation experiments with Super-Kamiokande [1, 2],neutrino beam experiments with K2K [3] and MINOS [4, 5], solar neutrino oscillationexperiments with Super-Kamiokande [6] and SNO [7, 8] and a nuclear reactor oscillationexperiment with KamLAND [9, 10], but the neutrino mass itself has not been measuredyet. Detection of neutrino radiative decay enables us to measure a quantity independentof the difference between the mass-squares of different-generation neutrinos. Thus wecan determine the neutrino mass itself from these two independent measurements, theneutrino oscillation and the neutrino radiative decay.As the neutrino lifetime is so long as to be much larger than the age of the universe,the most promising method is to observe the decay of the cosmic background neutrino.Detection of this radiative decay means a discovery of the cosmic background neutrinopredicted by standard cosmology.The cosmic background neutrino has a temperature of 1.9K and a particle density ρ of 110 cm − per generation.Atmospheric neutrino data with Super-Kamiokande and neutrino beam data with K2Kand MINOS gives the mass-square difference between ν and ν , ∆ m of (2 . ± . × − eV [11] and the mixing angle of sin θ > ν and ν of ∆ m = (7 .
59 + 0 . / − . × − eV [11] and the mixing angle of sin θ = 0 . ± .
03 [11].We search for the neutrino radiative decay under these constraints on the mass-squaredifferences and the mixing angles between the neutrino generations. For this search, wemake a fit of the photon energy spectrum of Cosmic Infrared Background (CIB) to a sumof a neutrino decay photon energy spectrum and a continuum spectrum.In the left-right symmetric model, we make a feasibility study of the neutrino decaysearch in the CIB energy spectrum measurement.
In this paper we report the analysis results on the normal hierarchy case where the ν isthe heaviest neutrino and decay into ν or ν as ν → ν ( or ν ) + γ .In the ν rest frame, the decay photon energy E is related to the neutrino masses by E = m − m m .Since the term m − m was measured by the neutrino oscillation experiments, wecan determine m by measuring this E . The plot of m versus m is shown in Fig. 1.2he decay photon energy E is given as a function of m with the neutrino oscillationmeasurement constraint as shown in Fig. 2. When we consider the m range between 50meV/ c and 150 meV/ c , E ranges from 25 meV to 8 meV in the far-infrared region.Taking into account the redshift of the decay photon energy, the observed photonenergy E γ is given by E γ = E z ,where z is a redshift. As the lifetime become longer because the neutrino is movingaway, the decay rate of neutrino R is given by R = τ (1+ z ) , where τ is a neutrino lifetimeat the rest frame. Thus the decay photon flux per unit solid angle is given by dN γ dSdtd Ω = ρ πτ (1+ z ) dr ,where r is a distance between a neutrino decay point and a telescope with a detectionarea dS, and ρ is a density of the cosmic background neutrino of 110 cm − . Assuming aflat universe, dr is related with dz bydr = cH [(1 + z ) Ω M + Ω Λ ] − . dz ,where H is a Hubble constant of ( 74 ± − Mpc − , and Ω M and Ω Λ are thematter density and the cosmological constant which were measured to be [11]Ω M = 0 . ± . Λ = 0 . ± . M + Ω Λ = 1 . ± . M + Ω Λ = 1, we obtain thefollowing distribution of the decay photon flux dN γ dSdt per unit solid angle and unit energy : dN γ dSdtd Ω dE γ = ρc πτH E γ [( E E γ ) Ω M + Ω Λ ] − . .If we use the energy flux per unit solid angle I defined by I ≡ d ( N γ × E γ ) dSdtd Ω ,we obtain the energy flux per unit solid angle and unit energy given by dIdE γ = ρc πτH [( E E γ ) Ω M + Ω Λ ] − . .Using E γ = hν , ν dIdν = ρc πτH hν [( E hν ) Ω M + Ω Λ ] − . .This spectrum is smeared by the neutrino motion at 1.9K, but this effect is negligiblysmall. The photon energy spreads due to this neutrino motion are 0.6% and 1.5% in rmsfor the photon energies of 25 meV and 10 meV, respectively. The Cosmic Infrared Background (CIB) continuum in photon energy spectrum is themost serious foreground against this neutrino radiative decay signal because the sharp3dge of the signal spectrum is located between 8 meV and 25 meV in our search region.There have been studies where the neutrino lifetime limit was obtained using the CIBdata [12, 13]. However they did not use the photon energy spectrum expected from theneutrino radiative decay to estimate the neutrino lifetime limit but used only the totaldecay rate of neutrino. They did not use the AKARI CIB data which were not availableat that time.We perform a statistical test of the CIB data measured by COBE [14, 15] and AKARI[16] to estimate the neutrino lifetime limit. Since we do not have a sharp edge at highenergy end of the CIB energy spectrum, we set a lower limit of the heaviest neutrinolifetime. The CIB data measured by COBE and AKARI were directly compared with thephoton energy spectrum expected from the neutrino radiative decay neglecting the CIBcontinuum with a maximum likelihood method. In this comparison, we neglected the CIBcontinuum in order to estimate the neutrino lifetime limit in the worst case which givesthe lowest lifetime limit. The curve with a maximum likelihood is shown together withthe likelihood as a function of ν lifetime for m = 50 meV/ c and m = 10 meV/ c inFig 3. The arrow point in this figure gives us a lower limit of ν lifetime at 95% confidencelevel. We performed this procedure for various ν masses to obtain a lower limit of the ν lifetime at 95% confidence level as a function of ν mass as shown in Fig. 4. Theyrange from 1 . × to 2 . × years in the ν mass range between 50 meV/ c and150 meV/ c .Recent deep galaxy surveys with infrared satellites, AKARI [16], Spitzer [17] andHershel [18] have revealed that more than a half of the CIB energy originates from externalgalaxies. So we performed the analysis to obtain stronger constraint on the neutrinolifetime taking the integrated flux of galaxies into account. We subtracted the contributionof the distant galaxies as source points [17] from the CIB measured by AKARI as shownin Table 1. Since there were no measured values of the contributions at wavelengths of60, 90 and 140 µ m, we interpolated the measured values at wavelengths of 24, 70 and160 µ m. Thus we obatined the CIB after subtracting the contribution of distant galaxies.These corrected CIB data give a constraint on the neutrino lifetime as the most stringentlower limits.With the AKARI CIB data after subtracting the contributions of distant galaxiesas point sources, we performed a statistical test of the spectrum to obtain the neutrinolifetime limit, motivated by the fact that such corrected AKARI CIB data has much lesscontributions of distant galaxies than the COBE CIB data. The corrected AKARI CIBdata were compared to the photon energy spectrum expected from the neutrino radiativedecay with a maximum likelihood method. The curve with a maximum likelihood isshown together with the likelihood as a function of ν lifetime for m = 50 meV/ c and m = 10 meV/ c in Fig 5. An arrow point in this figure gives us a lower limit of ν lifetimeat 95% confidence level. We performed this procedure for various ν masses to obtain alower limit of the ν lifetime at 95% confidence level as a function of ν mass as shown inFig. 6. They range from 3.1 × to 3 . × years in the ν mass range between 504eV/ c and 150 meV/ c . L × SU(2) R × U(1) Model
In the standard model, the heaviest neutrino lifetime is predicted to be 10 year for ν with a mass of 50 meV/ c [19, 20, 21, 22]. It is too long to be measured by the presentmethod.In the left-right symmetric model, the lifetime is predicted to be much shorter thanin the standard model. The left-right symmetric SU(2) L × SU(2) R × U(1) model has twocharged weak bosons, or the left-handed weak boson W L and the right-handed weak boson W R which are mixed with a mixing angle ζ into two mass eigenstates W and W as follows[21, 22]: W = W L cos ζ - W R sin ζW = W L sin ζ + W R cos ζ In this model, the lifetime of ν is given by τ − = αG F π ( m − m m ) | U | | U | [ ( m + m ) m τ M W (1 + M W M W ) + 4 m τ (1 − M W M W ) sin ζ ], where α is a fine structure constant, G F is a Fermi coupling constant, m τ , M W and M W are masses of τ , W and W , respectively [21, 22]. U ij is the (i, j)-th element of theMaki-Nakagawa-Sakata mixing matrix [23] and we took | U | = 1 / √ | U | = 1 / √ W R is M R > ζ = 0. The upper limit of the mixing angle between W L and W R is sin ζ < m with M W of 0.715TeV, sin ζ of 0.013 and ∆ m of(2 . ± . × − eV in Fig. 7.For m of 50 meV/ c , the lifetime is calculated to be 1 . × years under the aboveconditions in left-right symmetric model. The present lifetime limit is shorter than thisprediction by a factor of 2 × − .We can improve the sensitivity of the search for neutrino radiative decay by measuringthe continuous energy spectrum of the Cosmic Infrared Background (CIB). We fit thecontinuous spectrum with a sum of the CIB continuum and the neutrino decay photonspectrum to search for a sharp edge of the neutrino decay photon spectrum.To estimate the energy resolution requirement, we performed the simulation study ofthe neutrino radiative decay assuming the following conditions: • The present CIB continuum is dominated by other sources than the neutrino ra-diative decay. This CIB spectrum is represented by a Planck distribution plus a5uadratic function. • m = 50 meV/ c and m = 10 meV/ c . • τ = 1 . × years.We simulated the CIB detection experiments with a 20cm-diameter telescope with aviewing angle of 0.1 degrees and energy resolutions of 0 to 5 % by 1 % step. With 100%detection efficiency and 10-hour data taking, we have the photon energy spectrum for theCIB and the neutrino radiative decay as shown in Fig. 8. The CIB continuum was fittedto a function of the Planck distribution plus a quadratic function. Then we calculated theenergy derivative of the photon energy spectrum for a sum of the CIB continuum and theneutrino radiative decay as shown in Fig. 8. In this negative energy derivative plot, thesharp edge of the energy spectrum is identified as a clean peak. The excess is 6.7 σ andwe can see the clear signal peak in the distribution if the energy resolution is less than2%.We search for the neutrino radiative decay in the m range between 50 meV/ c and150 meV/ c which corresponds to the photon energy range between 25 meV and 8 meVwith this experiment. Thus the photon energy range to be measured is between 5 meV( λ = 250 µ m ) and 35 meV ( λ = 35 µ m). In this photon energy range, the frequencyof photon coming in this telescope is expected to be around 5 MHz. As we will use 400pixels as a photon detector, the photon rate per pixel is around 12 kHz/pixel.By this simulation study, we found that the required energy resolution is less than2% at 25 meV. With this resolution, we estimated 5 σ observation lifetime with 10-hourrunning of this telescope from the differential CIB energy spectrum including the radiativedecay of the cosmic background neutrino for the m range between 50 meV/ c and 150meV/ c with ∆ m of 2 . × − eV . The 5 σ observation lifetime ranges from 2 . × to 3 . × years as shown in Fig. 7. Spectral emission features of the dusts in galaxiesat redshifts of 1, when a large fraction of the CIB energy was generated [17], may producea structure in the spectral energy distribution (SED) of CIB, similar to the neutrinodecay photon SED. However, SEDs of such distant galaxies in the energy range where theneutrino decay photon is expected to be observed, have not been well explored. Furtherstudy of the SED of distant galaxies with future, large-aperture, infrared telescope suchas JAXA’s SPICA (Space Infrared Telescope for Cosmology and Astrophysics) mission[24] is important to mitigate the spectral contamination of the neutrino decay photon.The present measured CIB spectrum includes the point-sources of distant galaxies andthe zodiacal light foreground ambiguity. By using small pixels with small viewing anglesuch as 0.005 degrees, we will be able to distinguish the distant galaxy point sources fromthe CIB spectrum. In the future project EXZIT ( Exo-Zodiacal Infrared Telescope ) [25]which will observe the CIB outside of Jupiter orbit, we will decrease the effect of thezodiacal emission significantly, and will have much less ambiguity of the zodiacal lightforeground. 6 Conclusion
We propose to search for the neutrino radiative decay by fitting a photon energy spec-trum of the cosmic infrared background to a sum of the photon energy spectrum fromthe neutrino radiative decay and a continuum. By comparing the present cosmic infraredbackground energy spectrum observed by AKARI and Spitzer to the photon energy spec-trum expected from neutrino radiative decay with a maximum likelihood method, weobatined a lower limit of netrino lifetime of 3.1 × to 3.8 × years at 95 % confi-dence level for ν in the mass range between 50 meV/ c and 150 meV/ c under the presentconstraints by neutrino oscillation measurements.In the left-right symmetric model, the lifetime is predicted to be much shorter than inthe standard model. The present mass limit of the right-handed weak boson W R is m R > W L and W R is sin ζ < ν is predicted to be 1 . × years for m of 50 meV/ c .The present lifetime limit is shorter than this prediction by a factor of 2 × − .By measuring the continuous energy spectrum of the cosmic infrared background in thephoton energy region between 5 meV ( λ = 250 µ m) and 35 meV ( λ = 35 µ m), we canexpect 5 σ observation of the radiative decay of neutrino with a lifetime of 1 . × years. Acknowlegements
We thank M. Yamauchi and Y. Okada at KEK for discussions regarding the neu-trino decay and its lifetime calculation. This work was supported by the Ministry ofEducation, Science, Sports and Culture of Japan. Part of this work was supported byKAKENHI(19540250 and 21111004).
References [1] Y. Fukuda, T. Hayakawa, E. Ichihara, K. Inoue, K. Ishihara, H. Ishino, Y. Itow, T.Kajita, J. Kameda, S. Kasuga, K. Kobayashi, Y. Kobayashi, Y. Koshio, M. Miura, M.Nakahata, S. Nakayama, A. Okada, K. Okumura, N. Sakurai, M. Shiozawa, Y. Suzuki,Y. Takeuchi, Y. Totsuka, S. Yamada, M. Earl, A. Habig, E. Kearns, M. D. Messier, K.Scholberg, J. L. Stone, L. R. Sulak, C. W. Walter, M. Goldhaber, T. Barszczxak, D.Casper, W. Gajewski, P. G. Halverson, J. Hsu, W. R. Kropp, L. R. Price, F. Reines,M. Smy, H. W. Sobel, M. R. Vagins, K. S. Ganezer, W. E. Keig, R. W. Ellsworth, S.Tasaka, J. W. Flanagan, A. Kibayashi, J. G. Learned, S. Matsuno, V. J. Stenger, D.Takemori, T. Ishii, J. Kanzaki, T. Kobayashi, S. Mine, K. Nakamura, K. Nishikawa,Y. Oyama, A. Sakai, M. Sakuda, O. Sasaki, S. Echigo, M. Kohama, A. T. Suzuki, T. J.Haines, E. Blaufuss, B. K. Kim, R. Sanford, R. Svoboda, M. L. Chen, Z. Conner, J. A.Goodman, G. W. Sullivan, J. Hill, C. K. Jung, K. Martens, C. Mauger, C. McGrew,7. Sharkey, B. Viren, C. Yanagisawa, W. Doki, K. Miyano, H. Okazawa, C. Saji,M. Takahata, Y. Nagashima, M. Takita, T. Yamaguchi, M. Yoshida, S. B. Kim, M.Etoh, K. Fujita, A. Hasegawa, T. Hasegawa, S. Hatakeyama, T. Iwamoto, M. Koga,T. Maruyama, H. Ogawa, J. Shirai, A. Suzuki, F. Tsushima, M. Koshiba, M. Nemoto,K. Nishijima, T. Futagami, Y. Hayato, Y. Kanaya, K. Kaneyuki, Y. Watanabe, D.Kielczewska, R. A. Doyle, J. S. George, A. L. Stachyra, L. L. Wai, R. J. Wilkes, andK. K. Young (Super Kamiokande Collaboration): Phys. Rev. Lett. 81 (1998) 1562.[2] Y. Ashie, J. Hosaka, K. Ishihara, Y. Itow, J. Kameda, Y. Koshio, A. Minamino, C.Mitsuda, M. Miura, S. Moriyama, M. Nakahata, T. Namba, R. Nambu, Y. Obayashi,M. Shiozawa, Y. Suzuki, Y. Takeuchi, K. Taki, S. Yamada, M. Ishitsuka, T. Kajita, K.Kaneyuki, S. Nakayama, A. Okada, K. Okumura, T. Ooyabu, C. Saji, Y. Takenaga,S. Desai, E. Kearns, S. Likhoded, J. L. Stone, L. R. Sulak, C. W. Walter, W. Wang,M. Goldhaber, D. Casper, J. P. Cravens, W. Gajewski, W. R. Kropp, D. W. Liu, S.Mine, M. B. Smy, H. W. Sobel, C. W. Sterner, M. R. Vagins, K. S. Ganezer, J. Hill,W. E. Keig, J. S. Jang, J. Y. Kim, I. T. Lim, R. W. Ellsworth, S. Tasaka, G. Guillian,A. Kibayashi, J. G. Learned, S. Matsuno, D. Takemori, M. D. Messier, Y. Hayato,A. K. Ichikawa, T. Ishida, T. Ishii, T. Iwashita, T. Kobayashi, T. Maruyama, K.Nakamura, K. Nitta, Y. Oyama, M. Sakuda, Y. Totsuka, A. T. Suzuki, M. Hasegawa,K. Hayashi, T. Inagaki, I. Kato, H. Maesaka, T. Morita, T. Nakaya, K. Nishikawa, T.Sasaki, S. Ueda, S. Yamamoto, T. J. Haines, S. Dazeley, S. Hatakeyama, R. Svoboda,E. Blaufuss, J. A. Goodman, G. W. Sullivan, D. Turcan, K. Scholberg, A. Habig,Y. Fukuda, C. K. Jung, T. Kato, K. Kobayashi, M. Malek, C. Mauger, C. McGrew,A. Sarrat, E. Sharkey, C. Yanagisawa, T. Toshito, K. Miyano, N. Tamura, J. Ishii,Y. Kuno, Y. Nagashima, M. Takita, M. Yoshida, S. B. Kim, J. Yoo, H. Okazawa,T. Ishizuka, Y. Choi, H. K. Seo, Y. Gando, T. Hasegawa, K. Inoue, J. Shirai, A.Suzuki, M. Koshiba, Y. Nakajima, K. Nishijima, T. Harada, H. Ishino, R. Nishimura,Y. Watanabe, D. Kielczewska, J. Zalipska, H. G. Berns, R. Gran, K. K. Shiraishi, A.Stachyra, K. Washburn, and R. J. Wilkes (Super Kamiokande Collaboration): Phys.Rev. Lett. 93 (2004) 101801.[3] M. H. Ahn, E. Aliu, S. Andringa, S. Aoki, Y. Aoyama, J. Argyriades, K. Asakura, R.Ashie, F. Berghaus, H. G. Berns, H. Bhang, A. Blondel, S. Borghi, J. Bouchez, S. C.Boyd, J. Burguet-Castell, D. Casper, J. Catala, C. Cavata, A. Cervera, S. M. Chen, K.O. Cho, J. H. Choi, U. Dore, S. Echigo, X. Espinal, M. Fechner, E. Fernandez, K. Fujii,Y. Fujii, S. Fukuda, Y. Fukuda, J. Gomez-Cadenas, R. Gran, T. Hara, M. Hasegawa,T. Hasegawa, K. Hayashi, Y. Hayato, R. L. Helmer, I. Higuchi, J. Hill, K. Hiraide,E. Hirose, J. Hosaka, A. K. Ichikawa, M. Ieiri, M. Iinuma, A. Ikeda, T. Inagaki, T.Ishida, K. Ishihara, H. Ishii, T. Ishii, H. Ishino, M. Ishitsuka, Y. Itow, T. Iwashita, H.I. Jang, J. S. Jang, E. J. Jeon, I. S. Jeong, K. K. Joo, G. Jover, C. K. Jung, T. Kajita,J. Kameda, K. Kaneyuki, B. H. Kang, I. Kato, Y. Kato, E. Kearns, D. Kerr, C. O.Kim, M. Khabibullin, A. Khotjantsev, D. Kielczewska, B. J. Kim, H. I. Kim, J. H.8im, J. Y. Kim, S. B. Kim, M. Kitamura, P. Kitching, K. Kobayashi, T. Kobayashi,M. Kohama, A. Konaka, Y. Koshio, W. Kropp, J. Kubota, Yu. Kudenko, G. Kume,Y. Kuno, Y. Kurimoto, T. Kutter, J. Learned, S. Likhoded, I. T. Lim, S. H. Lim, P. F.Loverre, L. Ludovici, H. Maesaka, J. Mallet, C. Mariani, K. Martens, T. Maruyama, S.Matsuno, V. Matveev, C. Mauger, K. B. McConnel Mahn, C. McGrew, S. Mikheyev,M. Minakawa, A. Minamino, S. Mine, O. Mineev, C. Mitsuda, G. Mitsuka, M. Miura,Y. Moriguchi, T. Morita, S. Moriyama, T. Nakadaira, M. Nakahata, K. Nakamura,I. Nakano, F. Nakata, T. Nakaya, S. Nakayama, T. Namba, R. Nambu, S. Nawang,K. Nishikawa, H. Nishino, S. Nishiyama, K. Nitta, S. Noda, H. Noumi, F. Nova, P.Novella, Y. Obayashi, A. Okada, K. Okumura, M. Okumura, M. Onchi, T. Ooyabu, S.M. Oser, T. Otaki, Y. Oyama, M. Y. Pac, H. Park, F. Pierre, A. Rodriguez, C. Saji, A.Sakai, M. Sakuda, N. Sakurai, F. Sanchez, A. Sarrat, T. Sasaki, H. Sato, K. Sato, K.Scholberg, R. Schroeter, M. Sekiguchi, E. Seo, E. Sharkey, A. Shima, M. Shiozawa, K.Shiraishi, G. Sitjes, M. Smy, H. So, H. Sobel, M. Sorel, J. Stone, L. Sulak, Y. Suga, A.Suzuki, Y. Suzuki, Y. Suzuki, M. Tada, T. Takahashi, M. Takasaki, M. Takatsuki, Y.Takenaga, K. Takenaka, H. Takeuchi, Y. Takeuchi, K. Taki, Y. Takubo, N. Tamura,H. Tanaka, K. Tanaka, M. Tanaka, Y. Tanaka, K. Tashiro, R. Terri, S. T. Jampens,A. Tornero-Lopez, T. Toshito, Y. Totsuka, S. Ueda, M. Vagins, L. Whitehead, C. W.Walter, W. Wang, R. J. Wilkes, S. Yamada, Y. Yamada, S. Yamamoto, Y. Yamanoi,C. Yanagisawa, N. Yershov, H. Yokoyama, M. Yokoyama, J. Yoo, M. Yoshida, and J.Zalipska (K2K Collaboration): Phys. Rev. D74 (2006) 072003.[4] D. G. Michael, P. Adamson, T. Alexopoulos, W. W. M. Allison, G. J. Alner, K.Anderson, C. Andreopoulos, M. Andrews, R. Andrews, K. E. Arms, R. Armstrong, C.Arroyo, D. J. Auty, S. Avvakumov, D. S. Ayres, B. Baller, B. Barish, M. A. Barker, P.D. Barnes, Jr., G. Barr, W. L. Barrett, E. Beall, B. R. Becker, A. Belias, T. Bergfeld,R. H. Bernstein, D. Bhattacharya, M. Bishai, A. Blake, V. Bocean, B. Bock, G. J.Bock, J. Boehm, D. J. Boehnlein, D. Bogert, P. M. Border, C. Bower, S. Boyd, E.Buckley-Geer, C. Bungau, A. Byon-Wagner, A. Cabrera, J. D. Chapman, T. R. Chase,D. Cherdack, S. K. Chernichenko, S. Childress, B. C. Choudhary, J. H. Cobb, J. D.Cossairt, H. Courant, D. A. Crane, A. J. Culling, J. W. Dawson, J. K. de Jong, D.M. DeMuth, A. De Santo, M. Dierckxsens, M. V. Diwan, M. Dorman, G. Drake, D.Drakoulakos, R. Ducar, T. Durkin, A. R. Erwin, C. O. Escobar, J. J. Evans, O. D.Fackler, E. Falk Harris, G. J. Feldman, N. Felt, T. H. Fields, R. Ford, M. V. Frohne,H. R. Gallagher, M. Gebhard, G. A. Giurgiu, A. Godley, J. Gogos, M. C. Goodman,Yu. Gornushkin, P. Gouffon, R. Gran, E. Grashorn, N. Grossman, J. J. Grudzinski,K. Grzelak, V. Guarino, A. Habig, R. Halsall, J. Hanson, D. Harris, P. G. Harris, J.Hartnell, E. P. Hartouni, R. Hatcher, K. Heller, N. Hill, Y. Ho, A. Holin, C. Howcroft,J. Hylen, M. Ignatenko, D. Indurthy, G. M. Irwin, M. Ishitsuka, D. E. Jaffe, C. James,L. Jenner, D. Jensen, T. Joffe-Minor, T. Kafka, H. J. Kang, S. M. S. Kasahara, J.Kilmer, H. Kim, M. S. Kim, G. Koizumi, S. Kopp, M. Kordosky, D. J. Koskinen, M.9ostin, S. K. Kotelnikov, D. A. Krakauer, A. Kreymer, S. Kumaratunga, A. S. Ladran,K. Lang, C. Laughton, A. Lebedev, R. Lee, W. Y. Lee, M. A. Libkind, J. Ling, J.Liu, P. J. Litchfield, R. P. Litchfield, N. P. Longley, P. Lucas, W. Luebke, S. Madani,E. Maher, V. Makeev, W. A. Mann, A. Marchionni, A. D. Marino, M. L. Marshak, J.S. Marshall, N. Mayer, J. McDonald, A. M. McGowan, J. R. Meier, G. I. Merzon, M.D. Messier, R. H. Milburn, J. L. Miller, W. H. Miller, S. R. Mishra, A. Mislivec, P.S. Miyagawa, C. D. Moore, J. Morfi’n, R. Morse, L. Mualem, S. Mufson, S. Murgia,M. J. Murtagh, J. Musser, D. Naples, C. Nelson, J. K. Nelson, H. B. Newman, F.Nezrick, R. J. Nichol, T. C. Nicholls, J. P. Ochoa-Ricoux, J. Oliver, W. P. Oliver,V. A. Onuchin, T. Osiecki, R. Ospanov, J. Paley, V. Paolone, A. Para, T. Patzak,Z. Pavlovic, G. F. Pearce, N. Pearson, C. W. Peck, C. Perry, E. A. Peterson, D. A.Petyt, H. Ping, R. Piteira, R. Pittam, A. Pla-Dalmau, R. K. Plunkett, L. E. Price,M. Proga, D. R. Pushka, D. Rahman, R. A. Rameika, T. M. Raufer, A. L. Read, B.Rebel, J. Reichenbacher, D. E. Reyna, C. Rosenfeld, H. A. Rubin, K. Ruddick, V. A.Ryabov, R. Saakyan, M. C. Sanchez, N. Saoulidou, J. Schneps, P. V. Schoessow, P.Schreiner, R. Schwienhorst, V. K. Semenov, S.-M. Seun, P. Shanahan, P. D. Shield, W.Smart, V. Smirnitsky, C. Smith, P. N. Smith, A. Sousa, B. Speakman, P. Stamoulis,A. Stefanik, P. Sullivan, J. M. Swan, P. A. Symes, N. Tagg, R. L. Talaga, A. Terekhov,E. Tetteh-Lartey, J. Thomas, J. Thompson, M. A. Thomson, J. L. Thron, G. Tinti,R. Trendler, J. Trevor, I. Trostin, V. A. Tsarev, G. Tzanakos, J. Urheim, P. Vahle,M. Vakili, K. Vaziri, C. Velissaris, V. Verebryusov, B. Viren, L. Wai, C. P. Ward, D.R. Ward, M. Watabe, A. Weber, R. C. Webb, A. Wehmann, N. West, C. White, R. F.White, S. G. Wojcicki, D. M. Wright, Q. K. Wu, W. G. Yan, T. Yang, F. X. Yumiceva,J. C. Yun, H. Zheng, M. Zois, and R. Zwaska1 (MINOS Collaboration): Phys. Rev.Lett. 97 (2006) 191801.[5] P. Adamson, C. Andreopoulos, K. E. Arms, R. Armstrong, D. J. Auty, D. S. Ayres,B. Baller, P. D. Barnes, Jr., G. Barr, W. L. Barrett, B. R. Becker, A. Belias, R.H. Bernstein, D. Bhattacharya, M. Bishai, A. Blake, G. J. Bock, J. Boehm, D. J.Boehnlein, D. Bogert, C. Bower, E. Buckley-Geer, S. Cavanaugh, J. D. Chapman, D.Cherdack, S. Childress, B. C. Choudhary, J. H. Cobb, S. J. Coleman, A. J. Culling, J.K. de Jong, M. Dierckxsens, M. V. Diwan, M. Dorman, S. A. Dytman, C. O. Escobar,J. J. Evans, E. Falk Harris, G. J. Feldman, M. V. Frohne, H. R. Gallagher, A. Godley,M. C. Goodman, P. Gouffon, R. Gran, E. W. Grashorn, N. Grossman, K. Grzelak,A. Habig, D. Harris, P. G. Harris, J. Hartnell, R. Hatcher, K. Heller, A. Himmel, A.Holin, J. Hylen, G. M. Irwin, M. Ishitsuka, D. E. Jaffe, C. James, D. Jensen, T. Kafka,S. M. S. Kasahara, J. J. Kim, M. S. Kim, G. Koizumi, S. Kopp, M. Kordosky, D. J.Koskinen, S. K. Kotelnikov, A. Kreymer, S. Kumaratunga, K. Lang, J. Ling, P. J.Litchfield, R. P. Litchfield, L. Loiacono, P. Lucas, J. Ma, W. A. Mann, A. Marchionni,M. L. Marshak, J. S. Marshall, N. Mayer, A. M. McGowan, J. R. Meier, G. I. Merzon,M. D. Messier, C. J. Metelko, D. G. Michael, J. L. Miller, W. H. Miller, S. R. Mishra,10. D. Moore, J. Morfi’n, L. Mualem, S. Mufson, S. Murgia, J. Musser, D. Naples, J. K.Nelson, H. B. Newman, R. J. Nichol, T. C. Nicholls, J. P. Ochoa-Ricoux, W. P. Oliver,R. Ospanov, J. Paley, V. Paolone, A. Para, T. Patzak, Z. Pavlovic’, G. Pawloski, G.F. Pearce, C. W. Peck, E. A. Peterson, D. A. Petyt, R. Pittam, R. K. Plunkett, A.Rahaman, R. A. Rameika, T. M. Raufer, B. Rebel, J. Reichenbacher, P. A. Rodrigues,C. Rosenfeld, H. A. Rubin, K. Ruddick, V. A. Ryabov, M. C. Sanchez, N. Saoulidou,J. Schneps, P. Schreiner, S.-M. Seun, P. Shanahan, W. Smart, C. Smith, A. Sousa, B.Speakman, P. Stamoulis, M. Strait, P. Symes, N. Tagg, R. L. Talaga, M. A. Tavera,J. Thomas, J. Thompson, M. A. Thomson, J. L. Thron, G. Tinti, I. Trostin, V. A.Tsarev, G. Tzanakos, J. Urheim, P. Vahle, B. Viren, C. P. Ward, D. R. Ward, M.Watabe, A. Weber, R. C. Webb, A. Wehmann, N. West, C. White, S. G. Wojcicki,D. M. Wright, T. Yang, M. Zois, K. Zhang, and R. Zwaska (MINOS Collaboration):Phys. Rev. Lett. 101 (2008) 131802.[6] S. Fukuda, Y. Fukuda, M. Ishitsuka, Y. Itow, T. Kajita, J. Kameda, K. Kaneyuki,K. Kobayashi, Y. Koshio, M. Miura, S. Moriyama, M. Nakahata, S. Nakayama, T.Namba, A. Okada, N. Sakurai, M. Shiozawa, Y. Suzuki, H. Takeuchi, Y. Takeuchi,Y. Totsuka, S. Yamada, S. Desai, M. Earl, E. Kearns, M.D. Messier, 1, J.L. Stone,L.R. Sulak, C.W. Walter, M. Goldhaber, T. Barszczak, D. Casper, W. Gajewski,W.R. Kropp, S. Mine, D.W. Liu, M.B. Smy, H.W. Sobel, M.R. Vagins, A. Gago, K.S.Ganezer, W.E. Keig, R.W. Ellsworth, S. Tasaka, A. Kibayashi, J.G. Learned, S. Mat-suno, D. Takemori, Y. Hayato, T. Ishii, T. Kobayashi, T. Maruyama, K. Nakamura, Y.Obayashi, Y. Oyama, M. Sakuda, M. Yoshida, M. Kohama, T. Iwashita, A.T. Suzuki,A. Ichikawa, T. Inagaki, I. Kato, T. Nakaya, K. Nishikawa, T.J. Haines, d, S. Dazeley,S. Hatakeyama, R. Svoboda, E. Blaufuss, M.L. Chen, J.A. Goodman, G. Guillian,G.W. Sullivan, D. Turc, K. Scholberg, A. Habig, M. Ackermann, J. Hill, C.K. Jung,M. Malek, K. Martens, C. Mauger, C. McGrew, E. Sharkey, B. Viren, C. Yanagisawa,T. Toshito, C. Mitsuda, K. Miyano, C. Saji, T. Shibata, Y. Kajiyama, Y. Nagashima,K. Nitta, M. Takita, H.I. Kim, S.B. Kim, J. Yoo, H. Okazawa, T. Ishizuka, M. Etoh,Y. Gando, T. Hasegawa, K. Inoue, K. Ishihara, J. Shirai, A. Suzuki, M. Koshiba, Y.Hatakeyama, Y. Ichikawa, M. Koike, K. Nishijima, H. Ishino, M. Morii, R. Nishimura,Y. Watanabe, D. Kielczewska, H.G. Berns, S.C. Boyd, A.L. Stachyra, and R.J. Wilkes(Super Kamiokande Collaboration): Phys. Lett. B539 (2002) 179.[7] Q. R. Ahmad, R. C. Allen, T. C. Andersen, J. D. Anglin, G. Bu”hler, J. C. Barton,E. W. Beier, M. Bercovitch, J. Bigu, S. Biller, R. A. Black, I. Blevis, R. J. Boardman,J. Boger, E. Bonvin, M. G. Boulay, M. G. Bowler, T. J. Bowles, S. J. Brice, M. C.Browne, T. V. Bullard, T. H. Burritt, K. Cameron, J. Cameron, Y. D. Chan, M.Chen, H. H. Chen, X. Chen, M. C. Chon, B. T. Cleveland, E. T. H. Clifford, J. H. M.Cowan, D. F. Cowen, G. A. Cox, Y. Dai, X. Dai, F. Dalnoki-Veress, W. F. Davidson,P. J. Doe, G. Doucas, M. R. Dragowsky, C. A. Duba, F. A. Duncan, J. Dunmore, E.D. Earle, S. R. Elliott, H. C. Evans, G. T. Ewan, J. Farine, H. Fergani, A. P. Ferraris,11. J. Ford, M. M. Fowler, K. Frame, E. D. Frank, W. Frati, J. V. Germani, S. Gil,A. Goldschmidt, D. R. Grant, R. L. Hahn, A. L. Hallin, E. D. Hallman, A. Hamer,A. A. Hamian, R. U. Haq, C. K. Hargrove, P. J. Harvey, R. Hazama, R. Heaton, K.M. Heeger, W. J. Heintzelman, J. Heise, R. L. Helmer, J. D. Hepburn, H. Heron, J.Hewett, A. Hime, M. Howe, J. G. Hykawy, M. C. P. Isaac, P. Jagam, N. A. Jelley,C. Jillings, G. Jonkmans, J. Karn, P. T. Keener, K. Kirch, J. R. Klein, A. B. Knox,R. J. Komar, R. Kouzes, T. Kutter, C. C. M. Kyba, J. Law, I. T. Lawson, M. Lay,H. W. Lee, K. T. Lesko, J. R. Leslie, I. Levine, W. Locke, M. M. Lowry, S. Luoma,J. Lyon, S. Majerus, H. B. Mak, A. D. Marino, N. McCauley, A. B. McDonald, D.S. McDonald, K. McFarlane, G. McGregor, W. McLatchie, R. Meijer Drees, H. Mes,C. Mifflin, G. G. Miller, G. Milton, B. A. Moffat, M. Moorhead, C. W. Nally, M. S.Neubauer, F. M. Newcomer, H. S. Ng, A. J. Noble, E. B. Norman, V. M. Novikov,M. O’Neill, C. E. Okada, R. W. Ollerhead, M. Omori, J. L. Orrell, S. M. Oser, A.W. P. Poon, T. J. Radcliffe, A. Roberge, B. C. Robertson, R. G. H. Robertson, J. K.Rowley, V. L. Rusu, E. Saettler, K. K. Schaffer, A. Schuelke, M. H. Schwendener, H.Seifert, M. Shatkay, J. J. Simpson, D. Sinclair, P. Skensved, A. R. Smith, M. W. E.Smith, N. Starinsky, T. D. Steiger, R. G. Stokstad, R. S. Storey, B. Sur, R. Tafirout,N. Tagg, N. W. Tanner, R. K. Taplin, M. Thorman, P. Thornewell, P. T. Trent, Y. I.Tserkovnyak, R. Van Berg, R. G. Van de Water, C. J. Virtue, C. E. Waltham, J.-X.Wang, D. L. Wark, N. West, J. B. Wilhelmy, J. F. Wilkerson, J. Wilson, P. Wittich, J.M. Wouters, and M. Yeh (SNO Collaboration): Phys. Rev. Lett. 87 (2001) 071301.[8] Q. R. Ahmad, R. C. Allen, T. C. Andersen, J. D.Anglin, J. C. Barton, E. W. Beier,M. Bercovitch, J. Bigu, S. D. Biller, R. A. Black, I. Blevis, R. J. Boardman, J. Boger,E. Bonvin, M. G. Boulay, M. G. Bowler, T. J. Bowles, S. J. Brice, M. C. Browne, T.V. Bullard, G. Bu”hler, J. Cameron, Y. D. Chan, H. H. Chen, M. Chen, X. Chen, B.T. Cleveland, E. T. H. Clifford, J. H. M. Cowan, D. F. Cowen, G. A. Cox, X. Dai,F. Dalnoki-Veress, W. F. Davidson, P. J. Doe, G. Doucas, M. R. Dragowsky, C. A.Duba, F. A. Duncan, M. Dunford, J. A. Dunmore, E. D. Earle, S. R. Elliott, H. C.Evans, G. T. Ewan, J. Farine, H. Fergani, A. P. Ferraris, R. J. Ford, J. A. Formaggio,M. M. Fowler, K. Frame, E. D. Frank, W. Frati, N. Gagnon, J. V. Germani, S. Gil,K. Graham, D. R. Grant, R. L. Hahn, A. L. Hallin, E. D. Hallman, A. S. Hamer, A.A. Hamian, W. B. Handler, R. U. Haq, C. K. Hargrove, P. J. Harvey, R. Hazama, K.M. Heeger, W. J. Heintzelman, J. Heise, R. L. Helmer, J. D. Hepburn, H. Heron, J.Hewett, A. Hime, M. Howe, J. G. Hykawy, M. C. P. Isaac, P. Jagam, N. A. Jelley,C. Jillings, G. Jonkmans, K. Kazkaz, P. T. Keener, J. R. Klein, A. B. Knox, R. J.Komar, R. Kouzes, T. Kutter, C. C. M. Kyba, J. Law, I. T. Lawson, M. Lay, H. W.Lee, K. T. Lesko, J. R. Leslie, I. Levine, W. Locke, S. Luoma, J. Lyon, S. Majerus, H.B. Mak, J. Maneira, J. Manor, A. D. Marino, N. McCauley, A. B. McDonald, D. S.McDonald, K. McFarlane, G. McGregor, R. Meijer Drees, C. Mifflin, G. G. Miller, G.Milton, B. A. Moffat, M. Moorhead, C. W. Nally, M. S. Neubauer, F. M. Newcomer,12. S. Ng, A. J. Noble, E. B. Norman, V. M. Novikov, M. O’Neill, C. E. Okada, R.W. Ollerhead, M. Omori, J. L. Orrell, S. M. Oser, A. W. P. Poon, T. J. Radcliffe, A.Roberge, B. C. Robertson, R. G. H. Robertson, S. S. E. Rosendahl, J. K. Rowley, V.L. Rusu, E. Saettler, K. K. Schaffer, M. H. Schwendener, A. Schu”lke, H. Seifert, M.Shatkay, J. J. Simpson, C. J. Sims, D. Sinclair, P. Skensved, A. R. Smith, M. W. E.Smith, T. Spreitzer, N. Starinsky, T. D. Steiger, R. G. Stokstad, L. C. Stonehill, R.S. Storey, B. Sur, R. Tafirout, N. Tagg, N. W. Tanner, R. K. Taplin, M. Thorman, P.M. Thornewell, P. T. Trent, Y. I. Tserkovnyak, R. Van Berg, R. G. Van de Water, C.J. Virtue, C. E. Waltham, J.-X. Wang, D. L. Wark, N. West, J. B. Wilhelmy, J. F.Wilkerson, J. R. Wilson, P. Wittich , J. M. Wouters, and M. Yeh (SNO Collaboration):Phys. Rev. Lett. 89 (2002) 011301.[9] K. Eguchi, S. Enomoto, K. Furuno, J. Goldman, H. Hanada, H. Ikeda, K. Ikeda, K.Inoue, K. Ishihara, W. Itoh, T. Iwamoto, T. Kawaguchi, T. Kawashima, H. Kinoshita,Y. Kishimoto, M. Koga, Y. Koseki, T. Maeda, T. Mitsui, M. Motoki, K. Nakajima,M. Nakajima, T. Nakajima, H. Ogawa, K. Owada, T. Sakabe, I. Shimizu, J. Shirai, F.Suekane, A. Suzuki, K. Tada, O. Tajima, T. Takayama, K. Tamae, H. Watanabe, J.Busenitz, Z. Djurcic, K. McKinny, D.-M. Mei, A. Piepke, E. Yakushev, E. Berger, Y.D. Chan, M. P. Decowski, D. A. Dwyer, S. J. Freedman, Y. Fu, B. K. Fujikawa, K. M.Heeger, K. T. Lesko, K.-B. Luk, H. Murayama, D. R. Nygren, C. E. Okada, A. W. P.Poon, H. M. Steiner, L. A. Winslow, G. A. Horton-Smith, R. D. McKeown, J. Ritter,B. Tipton, P. Vogel, C. E. Lane, T. Miletic, W. Gorham, G. Guillian, J. G. Learned,J. Maricic, S. Matsuno, S. Pakvasa, S. Dazeley, S. Hatakeyama, M. Murakami, R. C.Svoboda, B. D. Dieterle, M. DiMauro, J. Detwiler, G. Gratta, K. Ishii, N. Tolich, Y.Uchida, M. Batygov, W. Bugg, H. Cohn, Y. Efremenko, Y. Kamyshkov, A. Kozlov,Y. Nakamura, L. De Braeckeleer, C. R. Gould, H. J. Karwowski, D. M. Markoff, J. A.Messimore, K. Nakamura, R. M. Rohm, W. Tornow, A. R. Young, and Y.-F. Wang(KamLAND Collaboration): Phys. Rev. Lett. 90 (2003) 021802.[10] T. Araki, K. Eguchi, S. Enomoto, K. Furuno, K. Ichimura, H. Ikeda, K. Inoue,K. Ishihara, T. Iwamoto, T. Kawashima, Y. Kishimoto, M. Koga, Y. Koseki, T.Maeda, T. Mitsui, M. Motoki, K. Nakajima, H. Ogawa, K. Owada, J.-S. Ricol, I.Shimizu, J. Shirai, F. Suekane, A. Suzuki, K. Tada, O. Tajima, K. Tamae, Y. Tsuda,H. Watanabe, J. Busenitz, T. Classen, Z. Djurcic, G. Keefer, K. McKinny, D.-M. Mei,A. Piepke, E. Yakushev, B. E. Berger, Y. D. Chan, M. P. Decowski, D. A. Dwyer,S. J. Freedman, Y. Fu, B. K. Fujikawa, J. Goldman, F. Gray, K. M. Heeger, K. T.Lesko, K.-B. Luk, H. Murayama, A. W. P. Poon, H. M. Steiner, L. A. Winslow, G. A.Horton-Smith, C. Mauger, R. D. McKeown, P. Vogel, C. E. Lane, T. Miletic, P. W.Gorham, G. Guillian, J. G. Learned, J. Maricic, S. Matsuno, S. Pakvasa, S. Dazeley,S. Hatakeyama, A. Rojas, R. Svoboda, B. D. Dieterle, J. Detwiler, G. Gratta, K.Ishii, N. Tolich, Y. Uchida, M. Batygov, W. Bugg, Y. Efremenko, Y. Kamyshkov, A.Kozlov, Y. Nakamura, C. R. Gould, H. J. Karwowski, D. M. Markoff, J. A. Messimore,13. Nakamura, R. M. Rohm, W. Tornow, R. Wendell, A. R. Young, M.-J. Chen, Y.-F.Wang, and F. Piquemal (KamLAND Collaboration): Phys. Rev. Lett. 94 (2005)081801.[11] K. Nakamura, K. Hagiwara, K. Hikasa, H. Murayama, M. Tanabashi, T. Watari, C.Amsler, M. Antonelli, D.M. Asner, H. Baer, H.R. Band, R.M. Barnett, T. Basaglia,E. Bergren, J. Beringer, G. Bernardi, W. Bertl, H. Bichsel, O. Biebel, E. Blucher,S. Blusk, R.N. Cahn, M. Carena, A. Ceccucci, D. Chakraborty, M.-C. Chen, R.S.Chivukula, G. Cowan, O. Dahl, G. D’Ambrosio, T. Damour, D. de Florian, A. deGouvea, T. DeGrand, G. Dissertori, B. Dobrescu, M. Doser, M. Drees, D.A. Edwards,S. Eidelman, J. Erler, V.V. Ezhela, W. Fetscher, B.D. Fields, B. Foster, T.K. Gaisser,L. Garren, H.-J. Gerber, G. Gerbier, T. Gherghetta, G.F. Giudice, S. Golwala, M.Goodman, C. Grab, A.V. Gritsan, J.-F. Grivaz, D.E. Groom, M. Gru”newald, A.Gurtu, T. Gutsche, H.E. Haber, C. Hagmann, K.G. Hayes, M. Heffner, B. Heltsley,J.J. Herna’ndez-Rey, A. Ho”cker, J. Holder, J. Huston, J.D. Jackson, K.F. Johnson,T. Junk, A. Karle, D. Karlen, B. Kayser, D. Kirkby, S.R. Klein, C. Kolda, R.V.Kowalewski, B. Krusche, Yu.V. Kuyanov, Y. Kwon, O. Lahav, P. Langacker, A. Liddle,Z. Ligeti, C.-J. Lin, T.M. Liss, L. Littenberg, K.S. Lugovsky, S.B. Lugovsky, J. Lys,H. Mahlke, T. Mannel, A.V. Manohar, W.J. Marciano, A.D. Martin, A. Masoni, D.Milstead, R. Miquel, K. Mo”nig, M. Narain, P. Nason, S. Navas, P. Nevski, Y. Nir,K.A. Olive, L. Pape, C. Patrignani, J.A. Peacock, S.T. Petcov, A. Piepke, G. Punzi,A. Quadt, S. Raby, G. Raffelt, B.N. Ratcliff, P. Richardson, S. Roesler, S. Rolli, A.Romaniouk, L.J. Rosenberg, J.L. Rosner, C.T. Sachrajda, Y. Sakai, G.P. Salam, S.Sarkar, F. Sauli, O. Schneider, K. Scholberg, D. Scott, W.G. Seligman, M.H. Shaevitz,M. Silari, T. Sjo”strand, J.G. Smith, G.F. Smoot, S. Spanier, H. Spieler, A. Stahl, T.Stanev, S.L. Stone, T. Sumiyoshi, M.J. Syphers, J. Terning, M. Titov, N.P. Tkachenko,N.A. To”rnqvist, D. Tovey, T.G. Trippe, G. Valencia, K. van Bibber, G. Venanzoni,M.G. Vincter, P. Vogel, A. Vogt, W. Walkowiak, C.W. Walter, D.R. Ward, B.R.Webber, G. Weiglein, E.J. Weinberg, J.D. Wells, A. Wheeler, L.R. Wiencke, C.G.Wohl, L. Wolfenstein, J. Womersley, C.L. Woody, R.L. Workman, A. Yamamoto, W.-M. Yao, O.V. Zenin, J. Zhang, R.-Y. Zhu and P.A. Zyla (Particle Data Group): J.Phys. G 37 (2010) 075021.[12] M. T. Ressell and M. S. Turner: Comm. Astrophys. 14 (1990) 323.[13] A. Mirizzi, D. Montanino and P. D. Serpico: Phys. Rev. D76 (2007) 053007.[14] M. G. Hauser, R. G. Arendt, T. Kelsall, E. Dwek, N. Odegard, J. L. Weiland, H. T.Freudenreich, W. T. Reach, R. F. Silverberg, S. H. Moseley, Y. C. Pei, P. Lubin, J.C. Mather, R. A. Shafer, G. F. Smoot, R. Weiss, D. T. Wilkinson and E. L. Wright:Astrophys. J. 508 (1998) 25.[15] D. P. Finkbeiner, M. Davis and D. J. Schlegel: Astrophys. J. 544 (2000) 81.1416] S. Matsuura, M. Shirahata, M. Kawada, T. T. Takeuchi, D. Burgarella, D. L.Clements, W. S. Jeong, H. Hanami, S. A. Khan, H. Matsuhara, T. Nakagawa, S.Oyabu, C. P. Pearson, A. Pollo, S. Serjeant, T. Takagi and G. White: Astrophys. J.737 (2011) 2.[17] H. Dole, G. Lagache, J. L. Puget, K. I. Caputi, N. Fernandez-Conde, E. Le Floc’h,C. Papovich, P. G. Perez-Gonzalez, G. H. Rieke and M. Blaylock: Astron. Astrophys.451 (2006) 417-429.[18] S. Berta, B. Magnelli, D. Lutz, B. Altieri, H. Aussel, P. Andreani, O. Bauer, A.Bongiovanni, A. Cava, J. Cepa, A. Cimatti, E. Daddi, H. Dominguez, D. Elbaz, H.Feuchtgruber, N. M. Fo”rster Schreiber, R. Genzel, C. Gruppioni, R. Katterloher, G.Magdis, R. Maiolino, R. Nordon, A. M. Pe’rez Garci’a, A. Poglitsch, P. Popesso, F.Pozzi, L. Riguccini, G. Rodighiero, A. Saintonge, P. Santini, M. Sanchez-portal, L.Shao, E. Sturm, L. J. Tacconi, I. Valtchanov, M. Wetzstein and E. Wieprecht: Astron.Astrophys. 518 (2010) L30.[19] P. B. Pal and L. Wolfenstein: Phys. Rev. D25 (1982) 766.[20] K. Sato and M. Kobayashi: Prog. Theor. Phys. 58 (1977) 1775.[21] R. E. Schrock: Nucl. Phys. B206 (1982) 359.[22] M. A. B. Beg and W. J. Marciano: Phys. Rev. D17 (1978) 1395.[23] Z. Maki, M. Nakagawa and S. Sakata: Prog. Theor. Phys. 28 (1962) 870.[24] T. Nakagawa: American Astronomical Society, AAS Meeting (eV) m0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 ( e V ) m Figure 1: Relation between m and m . The solid band shows the 1 σ constraint bythe neutrino oscillation measurements (∆ m of (2 . ± . × − eV ). Three curvescorrespond to various neutrino decay photon energies of 25meV (dashed), 20meV (dotted)and 15meV(dot-dashed). (Color online) 16 (eV) m60 80 100 120 140 160 -3 × ( e V ) E -3 × Figure 2: Relation between E and m . The solid band shows the 1 σ constraint by theneutrino oscillation measurements (∆ m of (2 . ± . × − eV ).17 (cid:10) eV) γ E -3 -2 ) - s r - ( n W m ν d I / d ν ) -1 year -12 (10 -1 τ li ke li hood Figure 3: Top plot shows the CIB data measured by COBE (dark square) and AKARI(dark circle) fitted to the photon energy spectrum expected from the neutrino radiativedecay for m = 50 meV/ c and m = 10 meV/ c with a maximum likelihood method.The curve shows the best fit. Bottom plot shows the likelihood as a function of the ν lifetime. An arrow points to a lower limit of the neutrino lifetime at 95 % confidence level.18 (eV) m0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 li f e t i m e li m i t ( yea r ) × Figure 4: Lower limits of the neutrino lifetime at 95 % confidence level as a function of m obtained with the CIB data measured by COBE and AKARI.19 (eV) γ E -3 -2 ) - s r - ( n W m ν d I/ d ν
10 ) -1 year -12 (10 -1 τ li ke li hood Figure 5: Top plot shows the AKARI CIB data after subtracting the contributionof distant galaxies as point sources (dark circle) fitted to the photon energy spectrumexpected from the neutrino radiative decay for m = 50 meV/ c and m = 10 meV/ c with a maximum likelihood method. The curve shows the best fit. Bottom plot showsthe likelihood as a function of ν lifetime. An arrow points to a lower limit of the neutrinolifetime at 95 % confidence level. 20 (eV) m0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 li f e t i m e li m i t ( yea r ) × Figure 6: Lower limits of the neutrino lifetime at 95 % confidence level as a function of m obtained with the CIB data measured by AKARI after subtracting the contributionof distant galaxies. 21 (eV) m0.06 0.08 0.1 0.12 0.14 0.16 li f e t i m e ( yea r ) Figure 7: Expected lifetime minimum in the left-right symmetric model as a functionof m . The solid band shows the 1 σ constraint by the neutrino oscillation measurements(∆ m of (2 . ± . × − eV ). The sensitivity of 5 σ observation with the proposedmeasurement is shown by dark circles. 22 eV ] (cid:491) E0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 ] - [ e V (cid:491) / d E (cid:491) d N CIB fit curvePhoton energy spectrumResolution 0% -> <- Resolution 5% ] - [ e V γ N / d E d ×
0% 1% ] - [ e V γ N / d E d × ] - [ e V γ N / d E d -50510152025 ×
2% 3% ] - [ e V γ N / d E d -5051015 × Figure 8: The top plot shows the photon energy spectra of the CIB and the neutrinoradiative decay with various energy resolutions from 0 % to 5 % by 1 % step. TheCIB continuum is fitted to a sum of a function of the Planck distribution and a quadraticfunction. The bottom plot is the negative energy derivative of the photon energy spectrumfor a sum of the CIB continuum and the neutrino radiative decay for energy resolutionsof 0, 1, 2 and 3 %. (Color online) 23avelength CIB a contribution of CIB CIBdistant galaxies b after subtarction c after subtraction d ( µ m) (MJy sr − ) (MJy sr − ) (MJy sr − ) (nW m − sr − )24 0.017 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± a The CIB measured by AKARI in unit of MJy sr − . b The contribution of distant galaxies to the CIB measured by Spitzer in unit of MJy sr − .The numbers in parentheses were obtained by a linear interpolation. c The CIB measured by AKARI after subtracting the contribution of distant galaxies inunit of MJy sr − . d The CIB measured by AKARI after subtracting the contribution of distant galaxies inunit of nW m − sr −1