Journal of High Energy Physics

, 2014:104

Statistical tests of sterile neutrinos using cosmology and short-baseline data

  • Johannes Bergström
  • M. C. Gonzalez-Garcia
  • V. Niro
  • J. Salvado
Open Access
Article

Abstract

In this paper we revisit the question of the information which cosmology provides on the scenarios with sterile neutrinos invoked to describe the SBL anomalies using Bayesian statistical tests. We perform an analysis of the cosmological data in ΛCDM+r + νs cosmologies for different cosmological data combinations, and obtain the marginalized cosmological likelihood in terms of the two relevant parameters, the sterile neutrino mass ms and its contribution to the energy density of the early Universe ΔNeff. We then present an analysis to quantify at which level a model with one sterile neutrino is (dis)favoured with respect to a model with only three active neutrinos, using results from both short-baseline experiments and cosmology. We study the dependence of the results on the cosmological data considered, in particular on the inclusion of the recent BICEP2 results and the SZ cluster data from the Planck mission. We find that only when the cluster data is included the model with one extra sterile neutrino can become more favoured that the model with only the three active ones provided the sterile neutrino contribution to radiation density is suppressed with respect to the fully thermalized scenario. We have also quantified the level of (in)compatibility between the sterile neutrino masses implied by the cosmological and SBL results.

Keywords

Cosmology of Theories beyond the SM Neutrino Physics 

References

  1. [1]
    B. Pontecorvo, Neutrino experiments and the problem of conservation of leptonic charge, Sov. Phys. JETP 26 (1968) 984 [INSPIRE].ADSGoogle Scholar
  2. [2]
    V.N. Gribov and B. Pontecorvo, Neutrino astronomy and lepton charge, Phys. Lett. B 28 (1969) 493 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    M.C. Gonzalez-Garcia and M. Maltoni, Phenomenology with massive neutrinos, Phys. Rept. 460 (2008) 1 [arXiv:0704.1800] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    M.C. Gonzalez-Garcia, M. Maltoni, J. Salvado and T. Schwetz, Global fit to three neutrino mixing: critical look at present precision, JHEP 12 (2012) 123 [arXiv:1209.3023] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    K.N. Abazajian et al., Light sterile neutrinos: a white paper, arXiv:1204.5379 [INSPIRE].
  6. [6]
    LSND collaboration, A. Aguilar-Arevalo et al., Evidence for neutrino oscillations from the observation of anti-neutrino(electron) appearance in a anti-neutrino(muon) beam, Phys. Rev. D 64 (2001) 112007 [hep-ex/0104049] [INSPIRE].ADSGoogle Scholar
  7. [7]
    MiniBooNE collaboration, A.A. Aguilar-Arevalo et al., Event excess in the MiniBooNE search for \( {\overline{\nu}}_{\mu}\to {\overline{\nu}}_e \) oscillations, Phys. Rev. Lett. 105 (2010) 181801 [arXiv:1007.1150] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    MiniBooNE collaboration, A.A. Aguilar-Arevalo et al., Improved search for \( {\overline{\nu}}_{\mu}\to {\overline{\nu}}_e \) oscillations in the MiniBooNE experiment, Phys. Rev. Lett. 110 (2013) 161801 [arXiv:1207.4809] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    G. Mention et al., The reactor antineutrino anomaly, Phys. Rev. D 83 (2011) 073006 [arXiv:1101.2755] [INSPIRE].ADSGoogle Scholar
  10. [10]
    T. Mueller et al., Improved predictions of reactor antineutrino spectra, Phys. Rev. C 83 (2011) 054615 [arXiv:1101.2663] [INSPIRE].ADSGoogle Scholar
  11. [11]
    P. Huber, On the determination of anti-neutrino spectra from nuclear reactors, Phys. Rev. C 84 (2011) 024617 [Erratum ibid. C 85 (2012) 029901] [arXiv:1106.0687] [INSPIRE].
  12. [12]
    C. Giunti and M. Laveder, Statistical significance of the Gallium anomaly, Phys. Rev. C 83 (2011) 065504 [arXiv:1006.3244] [INSPIRE].ADSGoogle Scholar
  13. [13]
    C. Giunti, M. Laveder, Y.F. Li, Q.Y. Liu and H.W. Long, Update of short-baseline electron neutrino and antineutrino disappearance, Phys. Rev. D 86 (2012) 113014 [arXiv:1210.5715] [INSPIRE].ADSGoogle Scholar
  14. [14]
    M.A. Acero, C. Giunti and M. Laveder, Limits on ν e and \( {\overset{-}{nu}}_e \) disappearance from Gallium and reactor experiments, Phys. Rev. D 78 (2008) 073009 [arXiv:0711.4222] [INSPIRE].ADSGoogle Scholar
  15. [15]
    J. Kopp, M. Maltoni and T. Schwetz, Are there sterile neutrinos at the eV scale?, Phys. Rev. Lett. 107 (2011) 091801 [arXiv:1103.4570] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    C. Giunti and M. Laveder, 3 + 1 and 3 + 2 sterile neutrino fits, Phys. Rev. D 84 (2011) 073008 [arXiv:1107.1452] [INSPIRE].ADSGoogle Scholar
  17. [17]
    C. Giunti and M. Laveder, Status of 3 + 1 neutrino mixing, Phys. Rev. D 84 (2011) 093006 [arXiv:1109.4033] [INSPIRE].ADSGoogle Scholar
  18. [18]
    C. Giunti and M. Laveder, Implications of 3 + 1 short-baseline neutrino oscillations, Phys. Lett. B 706 (2011) 200 [arXiv:1111.1069] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    A. Donini, P. Hernández, J. Lopez-Pavon, M. Maltoni and T. Schwetz, The minimal 3 + 2 neutrino model versus oscillation anomalies, JHEP 07 (2012) 161 [arXiv:1205.5230] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    J.M. Conrad, C.M. Ignarra, G. Karagiorgi, M.H. Shaevitz and J. Spitz, Sterile neutrino fits to short baseline neutrino oscillation measurements, Adv. High Energy Phys. 2013 (2013) 163897 [arXiv:1207.4765] [INSPIRE].CrossRefGoogle Scholar
  21. [21]
    C. Giunti, M. Laveder, Y.F. Li and H.W. Long, Pragmatic view of short-baseline neutrino oscillations, Phys. Rev. D 88 (2013) 073008 [arXiv:1308.5288] [INSPIRE].ADSGoogle Scholar
  22. [22]
    G. Karagiorgi, M.H. Shaevitz and J.M. Conrad, Confronting the short-baseline oscillation anomalies with a single sterile neutrino and non-standard matter effects, arXiv:1202.1024 [INSPIRE].
  23. [23]
    J. Kopp, P.A.N. Machado, M. Maltoni and T. Schwetz, Sterile neutrino oscillations: the global picture, JHEP 05 (2013) 050 [arXiv:1303.3011] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    Particle Data Group collaboration, K. Nakamura et al., Review of particle physics, J. Phys. G 37 (2010) 075021 [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    G. Mangano et al., Relic neutrino decoupling including flavor oscillations, Nucl. Phys. B 729 (2005) 221 [hep-ph/0506164] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    N. Saviano et al., Multi-momentum and multi-flavour active-sterile neutrino oscillations in the early universe: role of neutrino asymmetries and effects on nucleosynthesis, Phys. Rev. D 87 (2013) 073006 [arXiv:1302.1200] [INSPIRE].ADSGoogle Scholar
  27. [27]
    A. Mirizzi et al., The strongest bounds on active-sterile neutrino mixing after Planck data, Phys. Lett. B 726 (2013) 8 [arXiv:1303.5368] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    M.C. Gonzalez-Garcia, M. Maltoni and J. Salvado, Robust cosmological bounds on neutrinos and their combination with oscillation results, JHEP 08 (2010) 117 [arXiv:1006.3795] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    M.A. Acero and J. Lesgourgues, Cosmological constraints on a light non-thermal sterile neutrino, Phys. Rev. D 79 (2009) 045026 [arXiv:0812.2249] [INSPIRE].ADSGoogle Scholar
  30. [30]
    J. Hamann, S. Hannestad, G.G. Raffelt, I. Tamborra and Y.Y.Y. Wong, Cosmology seeking friendship with sterile neutrinos, Phys. Rev. Lett. 105 (2010) 181301 [arXiv:1006.5276] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    E. Giusarma, M. Archidiacono, R. de Putter, A. Melchiorri and O. Mena, Sterile neutrino models and nonminimal cosmologies, Phys. Rev. D 85 (2012) 083522 [arXiv:1112.4661] [INSPIRE].ADSGoogle Scholar
  32. [32]
    M. Archidiacono, E. Calabrese and A. Melchiorri, The case for dark radiation, Phys. Rev. D 84 (2011) 123008 [arXiv:1109.2767] [INSPIRE].ADSGoogle Scholar
  33. [33]
    M. Archidiacono, N. Fornengo, C. Giunti and A. Melchiorri, Testing 3 + 1 and 3 + 2 neutrino mass models with cosmology and short baseline experiments, Phys. Rev. D 86 (2012) 065028 [arXiv:1207.6515] [INSPIRE].ADSGoogle Scholar
  34. [34]
    M.C. Gonzalez-Garcia, V. Niro and J. Salvado, Dark radiation and decaying matter, JHEP 04 (2013) 052 [arXiv:1212.1472] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    P. Di Bari, S.F. King and A. Merle, Dark radiation or warm dark matter from long lived particle decays in the light of Planck, Phys. Lett. B 724 (2013) 77 [arXiv:1303.6267] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    J. Hasenkamp and J. Kersten, Dark radiation from particle decay: cosmological constraints and opportunities, JCAP 08 (2013) 024 [arXiv:1212.4160] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    P. Graf and F.D. Steffen, Dark radiation and dark matter in supersymmetric axion models with high reheating temperature, JCAP 12 (2013) 047 [arXiv:1302.2143] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    Planck collaboration, P.A.R. Ade et al., Planck 2013 results. XVI. Cosmological parameters, Astron. Astrophys. (2014) [arXiv:1303.5076] [INSPIRE].
  39. [39]
    S. Das et al., The Atacama Cosmology Telescope: temperature and gravitational lensing power spectrum measurements from three seasons of data, JCAP 04 (2014) 014 [arXiv:1301.1037] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    R. Keisler et al., A measurement of the damping tail of the cosmic microwave background power spectrum with the South Pole Telescope, Astrophys. J. 743 (2011) 28 [arXiv:1105.3182] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    C.L. Reichardt et al., A measurement of secondary cosmic microwave background anisotropies with two years of South Pole Telescope observations, Astrophys. J. 755 (2012) 70 [arXiv:1111.0932] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    BICEP2 collaboration, P.A.R. Ade et al., Detection of B-mode polarization at degree angular scales by BICEP2, Phys. Rev. Lett. 112 (2014) 241101 [arXiv:1403.3985] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    L. Verde, S.M. Feeney, D.J. Mortlock and H.V. Peiris, (Lack of) cosmological evidence for dark radiation after Planck, JCAP 09 (2013) 013 [arXiv:1307.2904] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    M. Archidiacono et al., Light sterile neutrinos after BICEP-2, JCAP 06 (2014) 031 [arXiv:1404.1794] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    C. Dvorkin, M. Wyman, D.H. Rudd and W. Hu, Neutrinos help reconcile Planck measurements with both Early and Local Universe, Phys. Rev. D 90 (2014) 083503 [arXiv:1403.8049] [INSPIRE].ADSGoogle Scholar
  46. [46]
    J.-F. Zhang, Y.-H. Li and X. Zhang, Sterile neutrinos help reconcile the observational results of primordial gravitational waves from Planck and BICEP2, arXiv:1403.7028 [INSPIRE].
  47. [47]
    J.-F. Zhang, Y.-H. Li and X. Zhang, Cosmological constraints on neutrinos after BICEP2, Eur. Phys. J. C 74 (2014) 2954 [arXiv:1404.3598] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    F. Wu, Y. Li, Y. Lu and X. Chen, Cosmological parameter fittings with the BICEP2 data, Sci. China Phys. Mech. Astron. 57 (2014) 1449 [arXiv:1403.6462] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    B. Leistedt, H.V. Peiris and L. Verde, No new cosmological concordance with massive sterile neutrinos, Phys. Rev. Lett. 113 (2014) 041301 [arXiv:1404.5950] [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    E. Giusarma, E. Di Valentino, M. Lattanzi, A. Melchiorri and O. Mena, Relic neutrinos, thermal axions and cosmology in early 2014, Phys. Rev. D 90 (2014) 043507 [arXiv:1403.4852] [INSPIRE].ADSGoogle Scholar
  51. [51]
    R. Flauger, J.C. Hill and D.N. Spergel, Toward an understanding of foreground emission in the BICEP2 region, JCAP 08 (2014) 039 [arXiv:1405.7351] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    Planck collaboration, R. Adam et al., Planck intermediate results. XXX. The angular power spectrum of polarized dust emission at intermediate and high Galactic latitudes, arXiv:1409.5738 [INSPIRE].
  53. [53]
    J. Hamann, S. Hannestad, G.G. Raffelt and Y.Y.Y. Wong, Sterile neutrinos with eV masses in cosmology: how disfavoured exactly?, JCAP 09 (2011) 034 [arXiv:1108.4136] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    J.R. Kristiansen, Ø. Elgarøy, C. Giunti and M. Laveder, Cosmology with sterile neutrino masses from oscillation experiments, arXiv:1303.4654 [INSPIRE].
  55. [55]
    M. Archidiacono, N. Fornengo, C. Giunti, S. Hannestad and A. Melchiorri, Sterile neutrinos: cosmology versus short-baseline experiments, Phys. Rev. D 87 (2013) 125034 [arXiv:1302.6720] [INSPIRE].ADSGoogle Scholar
  56. [56]
    S. Gariazzo, C. Giunti and M. Laveder, Light sterile neutrinos in cosmology and short-baseline oscillation experiments, JHEP 11 (2013) 211 [arXiv:1309.3192] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    C.M. Ho and R.J. Scherrer, Sterile neutrinos and light dark matter save each other, Phys. Rev. D 87 (2013) 065016 [arXiv:1212.1689] [INSPIRE].ADSGoogle Scholar
  58. [58]
    G. Gelmini, S. Palomares-Ruiz and S. Pascoli, Low reheating temperature and the visible sterile neutrino, Phys. Rev. Lett. 93 (2004) 081302 [astro-ph/0403323] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    R. Foot and R.R. Volkas, Reconciling sterile neutrinos with big bang nucleosynthesis, Phys. Rev. Lett. 75 (1995) 4350 [hep-ph/9508275] [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    Y.-Z. Chu and M. Cirelli, Sterile neutrinos, lepton asymmetries, primordial elements: how much of each?, Phys. Rev. D 74 (2006) 085015 [astro-ph/0608206] [INSPIRE].ADSGoogle Scholar
  61. [61]
    L. Bento and Z. Berezhiani, Blocking active sterile neutrino oscillations in the early universe with a Majoron field, Phys. Rev. D 64 (2001) 115015 [hep-ph/0108064] [INSPIRE].ADSGoogle Scholar
  62. [62]
    B. Dasgupta and J. Kopp, Cosmologically safe eV-scale sterile neutrinos and improved dark matter structure, Phys. Rev. Lett. 112 (2014) 031803 [arXiv:1310.6337] [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    S. Hannestad, R.S. Hansen and T. Tram, How self-interactions can reconcile sterile neutrinos with cosmology, Phys. Rev. Lett. 112 (2014) 031802 [arXiv:1310.5926] [INSPIRE].ADSCrossRefGoogle Scholar
  64. [64]
    R. Trotta, Bayes in the sky: bayesian inference and model selection in cosmology, Contemp. Phys. 49 (2008) 71 [arXiv:0803.4089] [INSPIRE].ADSCrossRefGoogle Scholar
  65. [65]
    M. Hobson et. al., Bayesian methods in cosmology, Cambridge University Press, Cambridge U.K. (2010)Google Scholar
  66. [66]
    F. Feroz et al., Bayesian selection of sign(μ) within mSUGRA in global fits including WMAP5 results, JHEP 10 (2008) 064 [arXiv:0807.4512] [INSPIRE].ADSCrossRefGoogle Scholar
  67. [67]
    J. Bergström, Bayesian evidence for non-zero θ 13 and CP-violation in neutrino oscillations, JHEP 08 (2012) 163 [arXiv:1205.4404] [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    J. Bergström, Combining and comparing neutrinoless double beta decay experiments using different nuclei, JHEP 02 (2013) 093 [arXiv:1212.4484] [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    H. Jeffreys, Theory of probability, Oxford University Press, Oxford U.K. (1961).MATHGoogle Scholar
  70. [70]
    R.E. Kass and A.E. Raftery, Bayes factors, J. Am. Stat. Ass. 90 (1995) 773.CrossRefMATHGoogle Scholar
  71. [71]
    Planck collaboration, P.A.R. Ade et al., Planck intermediate results. XVI. Profile likelihoods for cosmological parameters, Astron. Astrophys. 566 (2014) A54 [arXiv:1311.1657] [INSPIRE].CrossRefGoogle Scholar
  72. [72]
    J.O. Berger, B. Liseo and R.L. Wolpert, Integrated likelihood methods for eliminating nuisance parameters, Stat. Sci. 14 (1999) 1.ADSCrossRefMATHMathSciNetGoogle Scholar
  73. [73]
    WMAP collaboration, C.L. Bennett et al., Nine-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: final maps and results, Astrophys. J. Suppl. 208 (2013) 20 [arXiv:1212.5225] [INSPIRE].ADSCrossRefGoogle Scholar
  74. [74]
    BOSS collaboration, L. Anderson et al., The clustering of galaxies in the SDSS-III baryon oscillation spectroscopic survey: baryon acoustic oscillations in the data release 10 and 11 galaxy samples, arXiv:1312.4877 [INSPIRE].
  75. [75]
    SDSS collaboration, W.J. Percival et al., Baryon acoustic oscillations in the Sloan Digital Sky Survey data release 7 galaxy sample, Mon. Not. Roy. Astron. Soc. 401 (2010) 2148 [arXiv:0907.1660] [INSPIRE].ADSCrossRefGoogle Scholar
  76. [76]
    N. Padmanabhan, X. Xu, D.J. Eisenstein, R. Scalzo, A.J. Cuesta et al., A 2 per cent distance to z = 0.35 by reconstructing baryon acoustic oscillationsI. Methods and application to the Sloan Digital Sky Survey, Mon. Not. Roy. Astron. Soc. 427 (2012) 2132 [arXiv:1202.0090] [INSPIRE].ADSCrossRefGoogle Scholar
  77. [77]
    F. Beutler et al., The 6dF galaxy survey: baryon acoustic oscillations and the local Hubble constant, Mon. Not. Roy. Astron. Soc. 416 (2011) 3017 [arXiv:1106.3366] [INSPIRE].ADSCrossRefGoogle Scholar
  78. [78]
    C. Blake et al., The WiggleZ dark energy survey: mapping the distance-redshift relation with baryon acoustic oscillations, Mon. Not. Roy. Astron. Soc. 418 (2011) 1707 [arXiv:1108.2635] [INSPIRE].ADSCrossRefGoogle Scholar
  79. [79]
    A.G. Riess et al., A 3% solution: determination of the Hubble constant with the Hubble Space Telescope and Wide Field Camera 3, Astrophys. J. 730 (2011) 119 [Erratum ibid. 732 (2011) 129] [arXiv:1103.2976] [INSPIRE].
  80. [80]
    Planck collaboration, P.A.R. Ade et al., Planck 2013 results. XX. Cosmology from Sunyaev-Zeldovich cluster counts, arXiv:1303.5080 [INSPIRE].
  81. [81]
    J. Benjamin et al., CFHTLenS tomographic weak lensing: quantifying accurate redshift distributions, arXiv:1212.3327 [INSPIRE].
  82. [82]
    C. Heymans et al., CFHTLenS tomographic weak lensing cosmological parameter constraints: mitigating the impact of intrinsic galaxy alignments, arXiv:1303.1808 [INSPIRE].
  83. [83]
    M. Kilbinger et al., CFHTLenS: combined probe cosmological model comparison using 2D weak gravitational lensing, Mon. Not. Roy. Astron. Soc. 430 (2013) 2200 [arXiv:1212.3338] [INSPIRE].ADSCrossRefGoogle Scholar
  84. [84]
    S. Dodelson and L.M. Widrow, Sterile-neutrinos as dark matter, Phys. Rev. Lett. 72 (1994) 17 [hep-ph/9303287] [INSPIRE].ADSCrossRefGoogle Scholar
  85. [85]
    A. Lewis and S. Bridle, Cosmological parameters from CMB and other data: a Monte Carlo approach, Phys. Rev. D 66 (2002) 103511 [astro-ph/0205436] [INSPIRE].ADSGoogle Scholar
  86. [86]
    A. Lewis, A. Challinor and A. Lasenby, Efficient computation of CMB anisotropies in closed FRW models, Astrophys. J. 538 (2000) 473 [astro-ph/9911177] [INSPIRE].ADSCrossRefGoogle Scholar
  87. [87]
    J.-F. Zhang, J.-J. Geng and X. Zhang, Neutrinos and dark energy after Planck and BICEP2: data consistency tests and cosmological parameter constraints, arXiv:1408.0481 [INSPIRE].
  88. [88]
    P. Marshall, N. Rajguru and A. Slosar, Bayesian evidence as a tool for comparing datasets, Phys. Rev. D 73 (2006) 067302 [astro-ph/0412535] [INSPIRE].ADSGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Johannes Bergström
    • 1
  • M. C. Gonzalez-Garcia
    • 2
    • 3
  • V. Niro
    • 1
  • J. Salvado
    • 4
  1. 1.Departament d’Estructura i Constituents de la Matèria and Institut de Ciencies del CosmosUniversitat de BarcelonaBarcelonaSpain
  2. 2.Institució Catalana de Recerca i Estudis Avançats (ICREA), Departament d’Estructura i Constituents de la Matèria and Institut de Ciencies del CosmosUniversitat de BarcelonaBarcelonaSpain
  3. 3.C.N. Yang Institute for Theoretical PhysicsState University of New York at Stony BrookStony BrookU.S.A.
  4. 4.Wisconsin IceCube Particle Astrophysics Center (WIPAC) and Department of PhysicsUniversity of WisconsinMadisonU.S.A.

Personalised recommendations