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A. Yu. Smirnov International Centre for Theoretical Physics, Trieste, Italy Latsis Symposium 2013, ``Nature at the Energy Frontiers’’ ETH Zurich, June 3 – 6, 2013

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Neutrinos and LHC Smallness is related to existence of new physics at high energy scales M new ~ (V EW ) 2 m GUT scale Leptogenesis Studying neutrino mass and mixing probe of new physics at these scales TeV scale mechanisms of neutrino mass generation ? Atmospheric neutrinos in Ice Cube E = 4 10 2 TeV ~ 10 10 - 10 16 GeV s = (1 TeV ) 2 Cosmic neutrinos ( ?) with E ~ 10 3 TeV

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Discovery of the 1-3 mixing All well established/ confirmed results are described by Discovery of cosmic neutrinos of high energies ? Reactor, Galllium LSND, MiniBooNE New solar neutrino anomaly Additional radiation in the Universe Connected ? 1 eV sterile neutrino: not a small perturbation of the 3 picture - Mass hierarchy - CP violation -absolute scale - nature (Majorana?) Theory beyond Weinberg operator?

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January 2012 August 2012 M.G Aarsten, et al. arXiv:1304.5356 [astro-ph.HE] E = 1.14 +/- 0.17 PeV E = 1.04 +/- 0.16 PeV Atmospheric neutrino background: 0.082 +/- 0.004 (stat) +0.041/–0.057(syst.) p-value 2.9 10 -2 (2.8 ) ``Hint’’ of cosmic neutrinos or Excess at lower energies 0.02 – 0.3 PeV 28 events (7 with muons) are observed ~ ~ 11 expected New physics with atmospheric neutrinos Centers of two cascades

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MSW-effect Oscillations Can be resonantly enhanced in matter Parametric efects

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In wide energy range: from 0.3 MeV to 30 GeV confirming standard oscillation picture with standard dispersion relations Daya Bay MINOS KAMLAND 15 years after discovery: routinely detect oscillation effects

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e 2 1 MASS 1 2 3 3 m 2 23 m 2 32 m 2 21 Inverted mass hierarchyNormal mass hierarchy ? m 2 32 = 2.4 x 10 -3 eV 2 m 2 21 = 7.5 x 10 -5 eV 2 Two large mixings (cyclic permutation) For antineutrinos spectra are different (distribution of the and - flavors in 1 and 2 ) due to possible CP-violation 1-3 mixing Symmetry: TBM?

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sin 2 13 0.0 0.010 0.020 0.030 0.040 RENO, 1 Fogli et al, 1 T2K 90% QLC Double Chooz, 1 Daya Bay, 1 breaking mass ratio Gonzalez-Garcia et al, 1

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sin 2 23 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 MINOS, 1 SK (NH), 90% Fogli et al, 1 SK (IH), 90% QLC Gonzalez-Garcia et al, 1

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symmetry

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``Naturalness’’ Absence of Fine tunning of mass matrix m 21 2 m 32 2 O(1) sin 2 13 ~ ½sin 2 C Quark- Lepton Complementarity GUT, family symmetry ~ ½cos 2 2 23 – symmetry violation The same 1-3 mixing with completely different implications 12 23 Mixing anarchy > 0.025 Self-complementarity ~ ¼ sin 2 12 sin 2 23 Analogy with quark mixing relation 13 = 2 1/2 ( - 23 ) 1/3 – |U e2 | 2 ~ sin 2 13

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Large scale structure of the Universe m < 0.23 eV (68 % CL) SDSS KATRIN m e eff < 2.2 0.2 eV (90% CL) Cosmology (Planck BAO) Oscillations m m 31 2 0.045 eV m2m3m2m3 m 21 2 m 32 2 ~ 0.18 Direct kinematic measurements (future) NH m 21 m 1 ~ = 1.6 10 -2 m 21 2 m 32 2 IH The weakest hierarchy Strong degeneracy symmetry

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m ee = k U ek 2 m k e i x p p n n e e m ee W W m ee = U e1 2 m 1 + U e2 2 m 2 e + U e3 2 m 3 e 76 Ge 76 Se + e + e Q ee = 2039 keV 5 detectors, 71.7 kg yr m ee = (0.29 – 0.35) eV Heidelberg-Moscow EXO-200 m ee < (0.14 – 0.38) eV Xe- Observatory 136 Xe

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m1m1 Heidelberg- Moscow GERDA II CUORE GERDA I NEMO GERDA II Cuoricino EXO-200 Upper bounds, boxes – uncertainties of NME S M Bilenky C Giunti arXiv:1203.5250 [hep-ph] EXO-200: m ee < (0.14 – 0.38) eV H-M: m ee = (0.29 – 0.35) eV KamLAND-Zen EXO and Kamland-Zen Almost exclude H-M (interpretation in terms of light Majorana neutrinos

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Phase I in absense of signal for 20 kg year: T 1/2 > 1.9 10 25 yr (90% CL) GERmanium Detector Array 3 range: (0.69 – 4.19) 10 25 yr T 1/2 = 1.19 10 25 yr Heidelberg- Moscow: Can confirm but not exclude completely Blind analysis, the box should be opened now Phase II: 37.5 kg y: 0.09 – 0.29 eV Phase III: 1 ton 0.01 eV

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In spite of 1-3 mixing determination… ~ 10 -9 – 10 19 GeV from symmetry and hierarchy far from real understanding this new physics? anarchy to Still at the cross-roads from eV to Planck Phenomenology: to a large extend elaborated Discovery of new physics BSM in some other sectors would have ….. Some interesting developments along different lines From minimalistic scenario of nuMSM to sophisticated structures at several new scales

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P. F. Harrison D. H. Perkins W. G. Scott U tbm = U 23 ( /4) U 12 - maximal 2-3 mixing - zero 1-3 mixing - no CP-violation U tbm = 2/3 1/3 0 - 1/6 1/3 - 1/2 - 1/6 1/3 1/2 2 is tri-maximally mixed 3 is bi-maximally mixed - sin 2 12 = 1/3 L. Wolfenstein Uncertainty related to sign of 2-3 mixing: 23 = Symmetry from mixing matrix In the first approximation 0.15 0.62 0.78

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S Mixing appears as a result of different ways of the flavor symmetry breaking in the neutrino and charged lepton (Yukawa) sectors. This leads to different residual symmetries GfGf GlGl G Residual symmetries of the mass matrices M M l 1 A4A4 T’ S4S4 T7T7 ? T S Symmetry transformatios in mass bases Generic symetries which do not depend on values of masses to get TBM Z 2 x Z 2 ZmZm S M S T = M In this framework bounds on mixing can be obtained without explicit model-building In flavor basis S iU

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( U PMNS S i U PMNS + T ) p = I D. Hernandez, A.S. 1204.0445 Explicitly (S iU T) p = I (S iU T) p = (W iU ) p = I The main relation: connects the mixing matrix and generating elements of the group in the mass basis Equivalent to Tr ( U PMNS S i U PMNS + T ) = a Tr (W iU ) = a a = j j j p = 1 j - three eigenvalues of W iU j = 1,2,3 Transformations should be taken in the basis where CC are diagonal In flavor basis

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Also S. F. Ge, D. A. Dicus, W. W. Repko, PRL 108 (2012) 041801 |U i | 2 = |U i | 2 |U i | 2 = For column of the mixing matrix: 1 – a 4 sin 2 ( k/m) k, m, p integers which determine symmetry group S4S4 D. Hernandez, A.S. = 103 0 k = 0 a = 0 If symmetry transformations S depend on specific mass spectrum, Relations include also masses and Majorana CP phases D. Hernandez, A Y S. 1304.7738 [hep-ph] sin 2 2 23 = sin = cos = m 2 /m 1 = 1

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u r, u b, u j, d r, d b, d j, e u r c, u b c, u j c, c d r c, d b c, d j c, e c RH-neutrino S S S S S S S S S S - Enhance mixing - Produce zero order structure - Randomness (if needed) S S S S S S S S S S S S S S S S S S S Hidden sector SO(10) GUT + … High scale mass seesaw Explains smallness of neutrino mass and difference of q- and l- mixings Possibly some Hidden sector at GUT - Planck scales Flavor symmetries at very high scales, above GUT? Old does not mean wrong

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Tests of the low (TeV) -scale mechanisms of neutrino mass generation R-parity violation Low scale Seesaw Of different types at LHC RH neutrinos at LHC Tests of BSM framework which can lead to the neutrino mass generation Tests of the physics framework SUSY, extraD … No good motivations Search for mediators of seesaw, accompanying particles Radiative mechanisms

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l Type-Ii l l j j x q q l N WRWR bi-leptons with the same-sign Senjanovic Keung WR*WR* q q 0 s (jj l) = m N 2 No missing energy Peaks at s (jj ll) = m W 2 Also opposite sign leptons

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nn P.S Bhupal Dev, et al, 1305.0056 [hep-ph]

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Mix with active neutrinos s No weak interactions: - singlets of the SM symmetry group Light RH-components of neutrinos may have Majorana masses maximal mixing? Sov. Phys. JETP 26 984 (1968) Pisa, 1913 Dear Dr. Alexei Yu. Smirnov, Please pay attention to our upcoming Special Issue on "Research in Sterility" which will be published in the "Advances in Sexual Medicine", an open access journal. We cordially invite you to submit your paper …

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LSND MiniBooNE Gallex,GNO SAGE G.Mention et al, arXiv: 1101.2755 P Huber m 41 2 = 1 - 2 eV 2

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e 2 1 4 mass m 2 31 m 2 21 3 m 2 41 s P ~ 4|U e4 | 2 |U 4 | 2 restricted by short baseline exp. BUGEY, CHOOZ, CDHS, NOMAD LSND/MiniBooNE: vacuum oscillations With new reactor data: m 41 2 = 1.78 eV 2 U e4 = 0.15 U 4 = 0.23 P ~ 4|U e4 | 2 (1 - |U e4 | 2 ) For reactor and source experiments - additional radiation in the universe - bound from LSS? ( 0.89 eV 2 )

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All positive evidences vs null results Tension between disappearance data and ν μ → ν e LSND-MiniBooNE signals J. Kopp, P. A. N. Machado, M. Maltoni, T. Schwetz, 1303.3011 [hep-ph] cosmology 0PERA OPERA, Collaboration 1303.3953 [hep-ex] Controversial situation

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N eff = 3.30 (95 % CL) + 0.54 - 0.51 N eff = 3.30 +/- 0.27 (68% CL) Inconclusive Effective number of neutrino species BBN N eff = 3.68 (68 % CL) + 0.80 - 0.70 Y. I. Izotov and T X Thuan Astrophys J 710 (2010) L67 After Planck Planck +WP+highL+BAO N eff = 3.62 (95 % CL) + 0.50 - 0.48 Planck +WP+highL + H 0

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NESSiE Neutrino Experiment with Spectrometers in Europe, Charged Current (CC) muon neutrino and antineutrino interactions. two magnetic spectrometers located in two sites:"Near" and "Far" from the proton target of the CERN-SPS beam. complemented by an ICARUS-like LAr target For (NC) and electron neutrino CC interactions reconstruction. arXiv: 1304.7127 [physics.ins-det] NUCIFER Very short baseline reactor experiment Source experiments SCRAAM OscSNS BooNE Accelerator SBL experiments MicroBooNE (LArTPC), Tens kilocurie source 50 kCi 144 Ce - 144 Pr (3 MeV) or 106 Ru - 106 Rh (3.54 MeV) MiniBooNE + SciBooNE BOREXINO, KamLAND, SNO+ M. Cribier et al, 1107.2335 [hep-ex]] SOX 51 Cr G Bellini et al 1304.7721

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H Nunokawa O L G Peres R Zukanovich-Funchal Phys. Lett B562 (2003) 279 S Choubey JHEP 0712 (2007) 014 - s oscillations with m 2 ~ 1 eV 2 are enhanced in matter of the Earth in energy range 0.5 – few TeV IceCube This distorts the energy spectrum and zenith angle distribution of the atmospheric muon neutrinos S Razzaque and AYS, 1104.1390, [hep-ph]

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Possible distortion of the zenith angle distribution due to sterile neutrinos Varying |U 0 | 2 < 3% stat. error no sterile IC79 Less than 5% puls A. Gross, 1301.4339 [hep-ex] CC interactions, muon tracks

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A Esmaili, AYS

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With 5% uncorrelated systematics

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e 2 1 0 mass m 2 31 m 2 21 3 m 2 dip s - additional radiation in the Universe if mixed in 3 Very light sterile neutrino - solar neutrino data Motivated by no problem with LSS (bound on neutrino mass) m 0 ~ 0.003 eV can be tested in atmospheric neutrinos with DC IceCube sin 2 2 ~ 10 -3 sin 2 2 ~ 10 -1 DE scale? M 2 M Planck M ~ 2 - 3 TeV

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pp 7 Be CNO 8 B e - survival probability from solar neutrino data vs LMA-MSW solution HOMESTAKE low rate. pep SNO SNO+

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m 0 ~ 0.003 eV M 2 M Planck m 0 = M ~ 2 - 3 TeV P. de Holanda, AYS

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L R Normal Mass hierarchy 3- 10 kev - warm dark matter - radiative decays X-rays Few 100 MeV - generate light mass of neutrinos - generate via oscillations lepton asymmetry in the Universe - can beproduced in B-decays (BR ~ 10 -10 ) split ~ few kev M. Shaposhnikov et al Phenomenology of sterile neutrinos BAU WDM Everything below EW scale small Yukawa couplings EW seesaw

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Neutrino mass hierarchy CP-violation deviation of 2-3 mixing from maximal Absolute mass scale Majorana nature Searches for - decay Checks of existence of sterile neutrinos Study of geo-neutrinos Solar neutrinos: DN - asymmetry, CNO, spectral upturn Detection of high energy cosmic neutrinos Neutrinos and cosmology: connections of neutrinos to the dark Universe Detection of Galactic SN neutrinos relic SN neutrinos Reconstruction of the mass and mixing spectrum Astrophysics Majorana phases

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Earth matter effect Energy spectrs NOvA Neutrino beam Fermilab-PINGU(W. Winter) Sterile neutrinos may help? NH IH nu antinu

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Strong suppression of the e peak NH e 3 in neutrino channels NH in antineutrino IH Shock wave effect in the antineutrino channel only NH in the neutrino channel only IH If the earth matter effect is observed for antineutrinos NH is established! Permutation of the electron and non-electron neutrino spectra Neutrino collective effects Time rise of the anti- e burst initial phase IH more in IH case, spectral splits at high energies IH P. Serpico et al Earth matter effects G Fuller et al B Dasgupta et al A.Dighe, A. S. C. Lunardini G. Fuller, et al R. Tomas et al

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The neutrino oscillation probability at baselines of 295 (left), 810 (middle), and 7500 km (right) as a function of the neutrino energy. The red (blue) band corresponds to the normal (inverted) mass hierarchy and the band width is obtained by varying the value of. The probabilities for look similar with the hierarchies interchanged. Note the different scales of the axes. M. Blennow and A Y Smirnov Advances in High Energy Physics Volume 2013 (2013), Article ID 972485

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WC, V = 0.99 Mt Fid. V = 0.56 Mt 99,000, 20 inch PMTs 20% photocoverage JPARC beam, off-axis Baseline 295 km Segmented scimtillator detector 14 kT NuMI beamoff-axis (14 mrad) baseline 810 km CP/MH/astro CP/MH/osc. parameters MH/astro ICAL Iron calorimeter scintillator MH: 2 - 3 in half space

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MEMPHYS: CERN - Fréjus tunnel. Two WC tanks 65 m (d) x 103 m (h) LBNO LBNE The LENA (Low-Energy Neutrino Astronomy) 50 kt of liquid scintillator (LSc) tank 32 m x 100 m height.

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Oscillation physics with Huge atmospheric neutrino detectors ANTARES DeepCore Oscillations at high energies 10 – 100 GeV in agreement with low energy data no oscillation effect at E > 100 GeV Ice Cube Oscillations 2.7

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M G Aarten et al [IceCube Collaboration] arXiv: 1305.3909

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ANTARES Ice Cube Precision IceCube Next Generation Upgrade Oscillation Research with Cosmics with the Abyss

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20 new strings (~60 DOMs each) in 30 MTon DeepCore volume Few GeV threshold in inner 10 Mton volume Existing IceCube strings Existing DeepCore strings New PINGU strings PINGU v6Denser array Energy resolution ~ 3 GeV125m 75m 26m 6 m vertical DC: h = 350 m d =250

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+ n + h muon track cascade E E h E = E + E h E h E 10 5 events/year E. Akhmedov, S. Razzaque, A. Y. S. arXiv: 1205.7071 S tot ~ s n 1/2

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~ 1/E 0.5 = 0.2E ~ 0.5/E 0.5 Smearing with Gaussian reconstruction functions characterized by (half) widths = A E = B (m p / E ) 1/2

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S tot = [ ij S ij 2 ] 1/2 Improvements of reconstruction of the neutrino angle leads to substantial increase of significance without degeneracy of parameters , GeV 2.3 7.8 E, GeV 10 – 20 20 – 50 Tyce De Young, March 2013 8.3 o 4.3 o 3, 14 o

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with experimental smearing E = (0.7 E ) 1/2 0 = 20 o y-integrated bad nu – nubar separation bad angular resolution Mathieu Ribordy, A. Y.S., 1303.0758 [hep-ph] Increases significance by 30 – 70 %

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sin 2 32, true = 0.42 sin 2 32, fit = 0.50

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Shape does not change the amplitude changes Large significance at low energies Difficult with PINGU but can be done with next update With E ~ 0.1 GeV

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The last mixing angle the 1-3 mixing is measured. Strong impact on phenomenology, theory and future experimental programs. Critical check of the 0 - decay observation claim Studies of atmospheric neutrinos may allow to establish mass hierarchy, measure oscillation parameters, perform searches for sterile neutrinos, non-standard interactions. The fastest, cheapest, reliable way? Theory: still at the cross-roads. The same 1-3 mixing from different relations with different implications. TBM, Flavor symmetries…? Sterile neutrinos: challenge for everything. Ice Cube can help IceCube: hint for detection of cosmic neutrinos of high energies or new physics in neutrino interactions? Race for thre neutrino mass hierarchy and CP has started New important developments (new phase) in the field can be related to Multi-megaton mass scale under ice,underwater detectors with low (~1 GeV) energy threshold (PINGU, ORCA)

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indirect connection Light active neutrinos Mechanism of neutrino mass generation new particles Mixing pattern Flavor symmetries ensure stability of DM particles play the role of DM right handed neutrinos Z2Z2 New neutrino states HDM Warm DM Direct connection of the Universe Dark Energy Neutrinos and gravitino as DM W. Buchmueller Everything from one

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P. F. Harrison D. H. Perkins W. G. Scott U tbm = U 23 ( /4) U 12 - maximal 2-3 mixing - zero 1-3 mixing - no CP-violation U tbm = 2/3 1/3 0 - 1/6 1/3 - 1/2 - 1/6 1/3 1/2 2 is tri-maximally mixed 3 is bi-maximally mixed - sin 2 12 = 1/3 L. Wolfenstein Symmetry from mixing matrix 0.15 0.62 0.78 Dominant approach Form invariance

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D. Hernandez, A.S. to be submitted - bounds on moduli of matrix elements - elements of a given column j determined by index of S - two relations corresponding to real and imaginary of a - the column j is completely determined Tr (W iU ) = Tr ( U PMNS S i U PMNS + T ) (2|U j | 2 – 1) e = a ii |U ej | 2 = a R cos ( e /2) + cos (3 e /2) – a I sin ( e /2) 4 sin ( e /2) sin ( e /2) = - a R cos ( /2) + cos (3 /2) – a I sin ( /2) 4 sin ( e /2) sin ( /2) |U j | 2 =

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Interesting possibilities 2/3 1/6 For i =1 Trimaximal 1 1/3 For i = 2 Trimaximal 2 1/4 1/2 1/4 T (S iU T) = W iU Another class of possibilities: with (m – p) permutation

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corrections wash out sharp difference of elements of the dominant -block and the subdominant e-line Values of elements gradually decrease from m to m ee This can originate from power dependence of elements on large expansion parameter ~ 0.7 – 0.8. Another complementarity: = 1 - C Froggatt-Nielsen?

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Number of photo-electons Also excess of events at lower energies: 27 events are observed 12 are expected Atm. Neutrino Background: 0.082 +/- 0.004 (stat) + 0.041 / – 0.057(syst.)

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0 m D T 0 m D 0 M D T 0 M D m n = m D T M D -1T M D -1 m D Beyond SM: many heavy singlets …string theory R.N. Mohapatra J. Valle Three additional singlets S which couple with RH neutrinos c S allows to lower the scales of the neutrino mass generation << M D explains intermediate scale for the RH neutrinos ~ M Pl, M ~ M GU - scale of B-L violation = 0 massless neutrinos M ~ M GU 2 /M Pl ~ 10 -14 GeV violation of universality, unitarity Inverse seesaw Cascade seesaw >> M D

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(2 – 4) 10 -3 eV 0.5 - 2 eV 1 - 10 keV 40 - 70 MeV - LSND, MiniBooNE - Warm Dark matter - Pulsar kick - Solar neutrinos - Extra radiation in the Universe - LSND, MiniBooNE - Reactor anomaly - Ga-calibration experiments - Extra radiation s 1 eV 1 keV 1 MeV 10 -3 eV

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M. Smy No distortion of the energy spectrum at low energies : the upturn is disfavored at (1.1 – 1.9) level Increasing tension between m 2 21 measured by KamLAND and in solar neutrinos 1.3 level This is how new physics may show up

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e 2 1 1 2 3 3 MASS 32 ij = m 2 ij /2E D 31 ~ 2D 32 Inverted hierarchyNormal hierarchy Oscillations Mass states can be marked by e - admixtures 31 Cosmology 31 32 31 > 32 31 < 32 makes the e-flavor heavier changes two spectra differently Fourier analysis S. Petcov M. Piai Matter effect -decay

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J. Kopp, P. A. N. Machado, M. Maltoni, T. Schwetz, 1303.3011 [hep-ph]

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