A Yu Smirnov International Centre for Theoretical Physics

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

Smallness is related to existence of new physics at high energy scales 2 (V ) EW Mnew ~ mn ~ 1010 - 1016 Ge. V e GUT scal Leptoge nesis Studying neutrino mass and mixing physics w e n f o probe scales at these Te. V scale mechanisms of neutrino mass generation ? Neutrinos and LHC Atmospheric neutrinos in Ice Cube E = 4 102 Te. V Cosmic neutrinos ( ? ) with E ~ 103 Te. V s = (1 Te. V )2

All well established/ confirmed results are described by Discovery of the 1 -3 mixing of y r e v o c s i D inos r t u e n c i cosm gies ? r e n e h g i of h y - Mass hierarch - CP violation -absolute scale ana? ) - nature (Major Theory beyond Weinber g operat or? Reactor, Con nect ed ? Galllium LSND, Mini. Boo. NE ional t i d d A n in o i t a i rad rse e v i n the U New sol ar neutrin o anomaly 1 e. V sterile neutrino: not a small perturbation of the 3 n picture

M. G Aarsten, et al. ar. Xiv: 1304. 5356 [astro-ph. HE] January 2012 Centers of two cascades E = 1. 04 +/- 0. 16 Pe. V Atmospheric neutrino background: 0. 082 +/- 0. 004 (stat) +0. 041/– 0. 057(syst. ) August 2012 p-value 2. 9 10 -2 (2. 8 s) ``Hint’’ of cosmic neutrinos or New physics with atmospheric neutrinos Excess at lower energies 0. 02 – 0. 3 Pe. V 28 events (7 with muons) are observed ~ ~ 11 expected E = 1. 14 +/- 0. 17 Pe. V

ect ff MSW-e Oscillati ons Can be resonantly enhanced in matter Parametric efects

15 years after discovery: routinely detect oscillation effects Daya Bay MINOS KAMLAND In wide energy range: from 0. 3 Me. V to 30 Ge. V confirming standard oscillation picture with standard dispersion relations

ne nm nt g 1 -3 mixin MASS ? Dm 232 n 1 MASS n 3 Dm 221 Symmetry: TBM? Dm 232 = 2. 4 x 10 -3 e. V 2 Dm 221 = 7. 5 x 10 -5 e. V 2 Dm 221 Dm 223 n 3 Normal mass hierarchy Two large mixings n 2 n 1 Inverted mass hierarchy (cyclic permutation) ra are t c e p s s utrino e n i f the n m t o n a n o r i t Fo u ue to (distrib d t ) n n e r d e 2 n diff n n 1 a i s r o v a l f and n t lation o i v P C possible

QLC m-t breaking Gonzalez-Garcia et al, 1 s Fogli et al, 1 s mass ratio Daya Bay, 1 s RENO, 1 s Double Chooz, 1 s T 2 K 90% 0. 010 0. 020 sin 2 q 13 0. 030 0. 040

Gonzalez-Garcia et al, 1 s QLC Fogli et al, 1 s MINOS, 1 s SK (NH), 90% SK (IH), 90% 0. 30 0. 35 0. 40 0. 45 0. 50 sin 2 q 23 0. 55 0. 60 0. 65 0. 70

symmetry

The same 1 -3 mixing with completely different implications ``Naturalness’’ Absence of Fine tunning of 2 ix r Dm t a m s s a m 21 O(1) q 13 = 21/2(p/4 - ~ ½cos 2 2 q 23 Dm 322 sin 2 q 13 ~ ½sin 2 q. C Quark. Lep Complem ton entarity GUT, fa mily symmetr y > 0. 025 Mixing anarchy q 23) nm - nt – symmetry violation ~ ¼ sin 2 q 12 sin 2 q 23 th Analogy wi g quark mixin relation q 13 + q 12 = q 23 Self-complemen tarity 1/3 – |Ue 2|2 ~ sin 2 q 13

ture c u r t cale s e g Lar vers i n U e of th Oscillations m > Dm 312 > 0. 045 e. V m 2 > NH m 3 IH Dm 212 ~ 0. 18 Dm 322 Dm 212 ~ = 1. 6 10 -2 2 m 1 2 Dm 32 Cosmology (Planck BAO) S m < 0. 23 e. V (68 % CL) Direct kinematic measurements (future) meeff < 2. 2 0. 2 e. V (90% CL) The weakest hierarchy SDSS Strong degeneracy symmetry KATRIN

mee = Ue 12 m 1 + Ue 22 m 2 eia + Ue 32 m 3 eib 76 Ge 76 Se + e Qee = 2039 ke. V p n Heidelberg-Moscow W 5 detectors, 71. 7 kg yr e n x mee = (0. 29 – 0. 35) e. V n e W p mee = Sk Uek 2 mk eif(k) EXO-200 Xe- Observatory mee < (0. 14 – 0. 38) e. V 136 Xe

S M Bilenky C Giunti ar. Xiv: 1203. 5250 [hep-ph] NEMO Cuoricino Heidelberg. Moscow EXO-200 Upper bounds, boxes – uncertainties of NME GERDA I Kam. LAND-Zen GERDA II CUORE H-M: mee = (0. 29 – 0. 35) e. V EXO-200: mee < (0. 14 – 0. 38) e. V m 1 EXO and Kamland-Zen Almost exclude H-M (interpretation in terms of light Majorana neutrinos

GERmanium Detector Array Phase I in absense of signal for 20 kg year: T 1/2 > 1. 9 1025 yr (90% CL) Heidelberg- Moscow: T 1/2 = 1. 19 1025 yr 3 s range: (0. 69 – 4. 19) 1025 yr Blind analysis, the box should be opened now Can confirm but not exclude completely Phase II: 37. 5 kg y: 0. 09 – 0. 29 e. V Phase III: 1 ton 0. 01 e. V

Phenomenology: to a large extend elaborated In spite of 1 -3 mixing determination… Still at the cross-roads from e. V to Planck ~ 10 -9 – 1019 Ge. V etry m m y s m rchy fro a n a y arch to and hier far from real understanding this new physics? Some interesting developments along different lines From minimalistic scenario of nu. MSM to sophisticated structures at several new scales Discovery of new physics BSM in some other sectors would have …. .

L. Wolfenstein In the first approximation Utbm = 2/3 - 1/6 1/3 1/3 0. 15 0 - 1/2 0. 62 1/2 0. 78 P. F. Harrison D. H. Perkins W. G. Scott n 3 is bi-maximally mixed n 2 is tri-maximally mixed - maximal 2 -3 mixing - zero 1 -3 mixing - no CP-violation - sin 2 q 12 = 1/3 Symmetry from mixing matrix Utbm = U 23(p/4) U 12 Uncertainty related to sign of 2 -3 mixing: q 23 = p/4 - p/4

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 A 4 Gf S 4 T 7 T’ Sn Zm Symmetry transformatios in mass bases Gl Gn Ml Mn T Sn Z 2 x Z 2 ? 1 Residual symmetries of the mass matrices Generic symetries which do not depend n on values of masses to get TBM Sn M n S n T = M n In this framework bounds on mixing can be obtained without explicit model-building In flavor basis Si. U

Transformations should be taken in the basis where CC are diagonal (Si. U T) p = (Wi. U) p = I (Si. U T) p = I In flavor basis Explicitly ( UPMNS Si UPMNS+ T ) p D. Hernandez, A. S. 1204. 0445 =I The main relation: connects the mixing matrix and generating elements of the group in the mass basis Equivalent to Tr ( UPMNS Si UPMNS + T ) = a a = Sj lj lj p = 1 j = 1, 2, 3 Tr (Wi. U) = a lj - three eigenvalues of Wi. U

D. Hernandez, A. S. ka = 0 a =0 For column of the mixing matrix: |Ubi|2 = |Ugi|2 |Uai|2 = S 4 1–a 4 sin 2 (pk/m) k, m, p integers which determine symmetry group d = 1030 Also S. F. Ge, D. A. Dicus, W. W. Repko, PRL 108 (2012) 041801 D. Hernandez, A Y S. 1304. 7738 [hep-ph] If symmetry transformations Sn depend on specific mass spectrum, Relations include also masses and Majorana CP phases sin 2 2 q 23 = sin d = cos k = m 2 /m 1 = 1

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

Tests of the low (Te. V) -scale mechanisms of neutrino mass generation esaw Low scale Se types t n e r e f f i d Of Radiative at LHC mechanisms Search for mediators of seesaw, accompanying particles No good motivations Tests of BSM framework which can lead to the neutrino mass generation Tests of the physics framework SUSY, extra. D … R-parity violatio n RH neutrinos at LHC

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

P. S Bhupal Dev, et al, 1305. 0056 [hep-ph] nn

ns ts n e n o p RH-com os rin t u e n f o Light No weak interactions: - singlets of the SM symmetry group Mix with ac tive neutrin os 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 …

Dm 412 = 1 - 2 e. V 2 SAGE LSND G. Mention et al, ar. Xiv: 1101. 2755 P Huber Mini. Boo. NE Gallex, GNO

ns mass nm nt LSND/Mini. Boo. NE: vacuum oscillations n 4 P ~ 4|Ue 4 |2|Um 4 |2 Dm 241 n 3 n 2 n 1 ne Dm 2 restricted by short baseline exp. BUGEY, CHOOZ, CDHS, NOMAD For reactor and source experiments 31 Dm 221 P ~ 4|Ue 4|2 (1 - |Ue 4|2) With new reactor data: - additional radiation in the universe - bound from LSS? Dm 412 = 1. 78 e. V 2 Ue 4 = 0. 15 ( 0. 89 e. V 2) Um 4 = 0. 23

Controversial situation J. Kopp , P. A. N. Machado, M. Maltoni, T. Schwetz, 1303. 3011 [hep-ph] Tension between disappearance data and νμ → νe LSND-Mini. Boo. NE signals All positive evidences vs null results 0 PERA cosmology OPERA, Collaboration 1303. 3953 [hep-ex]

Effective number of neutrino species + 0. 54 Neff = 3. 30 - 0. 51 (95 % CL) After Planck +WP+high. L+BAO Neff = 3. 30 +/- 0. 27 (68% CL) + 0. 50 Neff = 3. 62 - 0. 48 (95 % CL) Planck +WP+high. L + H 0 BBN Neff = 3. 68 + 0. 80 - 0. 70 Y. I. Izotov and T X Thuan Astrophys J 710 (2010) L 67 (68 % CL) Inconclusive

Very short baseline reactor experiment NUCIFER SCRAAM Source experiments Accelerator SBL experiments Micro. Boo. NE (LAr. TPC), G Bellini et al 1304. 7721 SOX Tens kilocurie source 50 k. Ci 144 Ce - 144 Pr (3 Me. V) or 106 Ru - 106 Rh (3. 54 Me. V) Osc. SNS Boo. NE NESSi. E 51 Cr Mini. Boo. NE + Sci. Boo. NE BOREXINO, Kam. LAND, SNO+ M. Cribier et al, 1107. 2335 [hep-ex]] ar. Xiv: 1304. 7127 [physics. ins-det] 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.

Ice. Cube H Nunokawa O L G Peres R Zukanovich-Funchal Phys. Lett B 562 (2003) 279 nm - ns oscillations with Dm 2 ~ 1 e. V 2 are enhanced in matter of the Earth in energy range 0. 5 – few Te. V This distorts the energy spectrum and zenith angle distribution of the atmospheric muon neutrinos S Choubey JHEP 0712 (2007) 014 S Razzaque and AYS , 1104. 1390, [hep-ph]

CC interactions, muon tracks Possible distortion of the zenith angle distribution due to sterile neutrinos < 3% stat. error A. Gross, 1301. 4339 [hep-ex] IC 79 no sterile Varying |Ut 0|2 Less than 5% puls

A Esmaili, AYS

With 5% uncorrelated systematics

ns nm m 0 ~ 0. 003 e. V mass Dm 2 n 0 n 1 sin 2 2 a ~ 10 -3 sin 2 2 b ~ 10 -1 nt Very light sterile neutrino n 3 n 2 ne 31 Dm 221 Dm 2 dip M 2 MPlanck DE scale? M ~ 2 - 3 Te. V Motivated by - solar neutrino data - additional radiation in the Universe if mixed in n 3 no problem with LSS (bound on neutrino mass) can be tested in atmospheric neutrinos with DC Ice. Cube

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

P. de Holanda, AYS m 0 ~ 0. 003 e. V m 0 = M 2 MPlanck M ~ 2 - 3 Te. V

n L M. Shaposhnikov et al Everything below EW scale small Yukawa couplings R BAU Few 100 Me. V split ~ few kev WDM 3 - 10 kev Normal Mass hierarchy EW seesaw - generate light mass of neutrinos - generate via oscillations lepton asymmetry in the Universe - can beproduced in B-decays (BR ~ 10 -10 ) - warm dark matter - radiative decays X-rays gy of o l o n e m o Phen utrinos e n e l i r e st

Astrophysics Reconstruction of the mass and mixing spectrum Detection of high ener gy cosmic ne utrinos Detection of Galactic SN neutrinos relic SN os neutrin Neutrino mass Checks of hierarchy existence n o i t la of sterile CP-vio neutrinos deviation of 2 Solar neutrinos: -3 mixing DN - asymmetry, from maximal Study of geo. CNO, spectral Absolute neutrinos upturn m a s s scale Majorana gy: o l o m s o c nature Searches for d n eutrinos a N os n i r t u e n bb 0 n- decay f so a Majoran connection verse i n U k r a s d phase to the

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

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

M. Blennow and A Y Smirnov Advances in High Energy Physics Volume 2013 (2013), Article ID 972485 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.

Segmented scimtillator detector 14 k. T Nu. MI beamoff-axis (14 mrad) baseline 810 km CP/MH/osc. parameters MH: 2 - 3 s in half d space WC, V = 0. 99 Mt Fid. V = 0. 56 Mt   99, 000, 20 inch PMTs 20% photocoverage JPARC beam, off-axis Baseline 295 km  CP/MH/astro ICAL Iron calorimeter scintillator MH/astro

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

Oscillation physics with Huge atmospheric neutrino detectors ANTARES Deep. Core Ice Cube Oscillations 2. 7 s Oscillations at high energies 10 – 100 Ge. V in agreement with low energy data no oscillation effect at E > 100 Ge. V

M G Aarten et al [Ice. Cube Collaboration] ar. Xiv: 1305. 3909

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

Denser array PINGU v 6 DC: h = 350 m d =250 20 new strings (~60 DOMs each) in 30 MTon Deep. Core volume 6 m vertical Few Ge. V threshold in inner 10 Mton volume Energy resolution ~ 3 Ge. V Existing Ice. Cube strings Existing Deep. Core strings New PINGU strings 75 m 125 m 26 m

E. Akhmedov, S. Razzaque, A. Y. S. ar. Xiv: 1205. 7071 nm + n m + h Em q m E h cascade 105 events/year muon track En = E m + E h Eh E m q m q n Stot ~ s n 1/2

Smearing with Gaussian reconstruction functions characterized by (half) widths sq ~ 1/E 0. 5 s. E = 0. 2 E s. E = A E n sq = B (mp / E n)1/2 sq ~ 0. 5/E 0. 5

S tot = [S ij Sij 2 ]1/2 Improvements of reconstruction of the neutrino angle leads to substantial increase of significance without degeneracy of parameters E , Ge. V 10 – 20 20 – 50 s. E , Ge. V 2. 3 sq 8. 3 o Tyce De Young, March 2013 7. 8 4. 3 o 3, 14 o

with experimental smearing s. E = (0. 7 En)1/2 y 0 = 20 o bad nu – nubar separation Mathieu Ribordy, A. Y. S. , 1303. 0758 [hep-ph] Incr ease s sig by 3 nific 0– 7 ance 0% bad angular resolution y-integrated

sin 2 q 32, fit = 0. 50 sin 2 q 32, true = 0. 42

Difficult with PINGU but can be done with next update With E ~ 0. 1 Ge. V Shape does not change the amplitude changes Large significance at low energies

The last mixing a ngle the 1 -3 mix ing is measured. on phenomenolog Strong impact y , theory and fu ture experiment al programs. Race for thre neutrino mass hierarchy and CP has started Critical check of the 0 nbb - decay observation claim Theory: still at the cross-roads. The same 1 -3 mixing from different relations with different implications. TBM, Flavor symmetries…? for everything. e ng le al ch s: no ri ut ne le Steri Ice Cube can help Ice. Cube: hint for detection of cosmic neutrinos of high energies or new physics in neutrino interactions? e field can be th in e) as ph ew (n ts en m New important develop e, underwater ic er d un e al sc s as m on related to Multi-megat ORCA) , U G IN (P d ol sh re th gy e. V) ener detectors with low (~1 G 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?

indirect connection HDM Light active neutrinos Direct connection New neutrino states Warm DM of the Universe Mechanism of neutrino mass generation Z 2 new particles Mixing pattern Flavor symmetries ensure stability of DM particles Dark Energy right handed neutrinos play the role of DM Neutrinos and gravitino as DM W. Buchmueller Everything from one

L. Wolfenstein Dominant approach Utbm = 2/3 - 1/6 - maximal 2 -3 mixing - zero 1 -3 mixing - no CP-violation 1/3 1/3 0. 15 0 - 1/2 0. 62 1/2 0. 78 P. F. Harrison D. H. Perkins W. G. Scott n 3 is bi-maximally mixed n 2 is tri-maximally mixed Utbm = U 23(p/4) U 12 - sin 2 q 12 = 1/3 Form invariance Symmetry from mixing matrix

Tr (Wi. U) = Tr ( UPMNS Si UPMNS + T ) Sa (2|Uaj|2 – 1) e ifa D. Hernandez, A. S. to be submitted =a - 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 |Uej|2 = |Umj|2 = a. R cos (fe /2) + cos (3 fe /2) – a. I sin (fe /2) 4 sin (fem /2) sin (fte /2) a. R cos (fm /2) + cos (3 fm /2) – a. I sin ( fm /2) 4 sin (fem /2) sin (fmt /2) fab = fa - fb

Interesting possibilities 2/3 1/6 1/3 1/3 For i =1 Trimaximal 1 1/4 1/2 1/4 For i = 2 Trimaximal 2 Another class of possibilities: with (m – p) permutation T (Si. U T) = Wi. U

Values of elements gradually decrease from m tt to mee corrections wash out sharp difference of elements of the dominant mt-block and the subdominant e-line This can originate from power dependence of elements on large expansion parameter l ~ 0. 7 – 0. 8. Another complementarity: l = 1 - q. C Froggatt-Nielsen?

Also excess of events at lower energies: 27 events are observed 12 are expected Number of photo-electons Atm. Neutrino Background: 0. 082 +/- 0. 004 (stat) + 0. 041 / – 0. 057(syst. )

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

ns 40 - 70 Me. V - LSND, Mini. Boo. NE 1 Me. V 1 - 10 ke. V 10 -3 e. V 0. 5 - 2 e. V - Warm Dark matter - Pulsar kick - LSND, Mini. Boo. NE - Reactor anomaly - Ga-calibration experiments - Extra radiation (2 – 4) 10 -3 e. V - Solar neutrinos - Extra radiation in the Universe

M. Smy No distortion of the energy spectrum at low energies : the upturn is disfavored at (1. 1 – 1. 9) s level Increasing tension between Dm 221 measured by Kam. LAND and in solar neutrinos 1. 3 s level This is how new physics may show up

ne Normal hierarchy ogy Cosmol bb-decay MASS n 3 wij = Dm 2 ij /2 E w 32 n 1 w 31 Mass states can be marked by ne - admixtures w 31 > w 32 Oscillations D 31 ~ 2 D 32 Matter effect Inverted hierarchy nm nt w 32 n 1 w 31 n 3 w 31 < w 32 Fourier analysis makes the e-flavor heavier changes two spectra differently w S. Petcov M. Piai

J. Kopp , P. A. N. Machado, M. Maltoni, T. Schwetz, 1303. 3011 [hep-ph]