A. Yu. Smirnov. A. Yu. Smirnov

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1 A. Yu. Smirnov A. Yu. Smirnov

4 before nu2012 G. L. Fogli Serious implications for theory Non-zero, relatively Large 1-3 mixing Substantial deviation of the 2-3 mixing from maximal d CP ~ p DB new Robust?

5 d 23 = ½ - sin 2 q 23 the key to ( probe) understand the underlying physics n m - n t symmetry violation Connection to 1-3 mixing Quark -Lepton Complementarity q 23 ~ p/2 - V cb NH MINOS, 1s Fogli et al, 1s SK, 90% sin 2 q 23

n e - oscillation effects F e F e 0-1 = P e2 (r c 23 2-1) r

deviation of the 2-3 mixing from maximal (first quatrant) P

6 n e - oscillation effects F e F e 0-1 = P e2 (r c ) r = F m0 /F e 0 ~ 2 = P e3 (rs 23 2 r) sub-gev range multi-gev range ``screening factor The e-like event excess ar low energies and deficit at higher energies - signature of deviation of the 2-3 mixing from maximal (first quatrant) P me ~ sin 2 q 13 sin 2 q 23 P mm ~ sin 2 2q 23 - appearance - disappearance

Neutrinoantineutrino asymmery Third way Key measurement: amplitudes of the n m - n m oscillations due to solar and atmospheric mass splittings G. L. Fogli First glimpses? T. Yanagida Do we have predictions for the phase in quark sector?

7 Neutrinoantineutrino asymmery Third way Key measurement: amplitudes of the n m - n m oscillations due to solar and atmospheric mass splittings G. L. Fogli First glimpses? T. Yanagida Do we have predictions for the phase in quark sector? Why do we think that we can predict leptonic mixing? Again because of neutrinos are special? Symmetries? d CP ~ p/2 +/- 0.02

8 sin 2 q 13 ~ The same 1-3 mixing with completely different implications O(1) Dm 21 2 Dm 32 2 ``Naturalness of mass matrix sin 2 q 13 = ~ ½ sin 2 q C Quark Lepton Complementarity ~ ½cos 2 2q 23 n m - n t - symmetry violation > Mixing anarchy A. De Gouvea, H.Murayama q 13 + q 12 = q 23 ~ p/4 Self-complementarity

9 With different implications

Mixing appears as a result of different ways of the flavor symmetry breaking in neutrino and charged lepton sectors G f A 4 T 7 S 4 Residual symmetries G l G

11 Mixing appears as a result of different ways of the flavor symmetry breaking in neutrino and charged lepton sectors G f A 4 T 7 S 4 Residual symmetries G l G n? T M l diagonal M n TBM-type 1 n the splitting originates from different flavor assignments of the RH components of N c and l c and different higgs multiplets

12 If G is von Dyck group D(2, m, p) For column of the mixing matrix: D. Hernandez, A.S. U bi 2 = U gi 2 S 4 A 4 U ai 2 = 1 a 4 sin 2 (pk/m) A is determined from condition l 3 + a l 2 - a* l - 1 = 0 l p i = 1 d = 77 0 S 4 k, m, p integers which determine symmetry group Also S. F. Ge, D. A. Dicus, W. W. Repko, PRL 108 (2012)

13 q 13 ~ ½q c sin 2 q 13 ~ ½sin 2 q C First obtained in the context of Quark-Lepton Complementarity Follows from permutation of matrices U 12 (q c ) U 23 (p/2) H. Minakata, A Y S From charged leptons Permutation - to reduce the lepton mixing matrix to the standard form Maximal from neutrinos Related to smallness of mass

14 sin 2 q 13 ~ sin 2 q 23 sin 2 q C D. Hernandez, A.S. Improves also predictions for 1-2 mixing Bi-maximal mixing? RGE effect sin 2 q 13 ~ sin 2 q 23 sin 2 q C

P. Ramond Deviations from BM due to high order corrections Complementarity: implies quark-lepton symmetry or GUT, or horizontal symmetry Weak complementarity or Cabibbo haze Altarelli et al

15 P. Ramond Deviations from BM due to high order corrections Complementarity: implies quark-lepton symmetry or GUT, or horizontal symmetry Weak complementarity or Cabibbo haze Altarelli et al Corrections from high order flavon interactions generate Cabibbo mixing and deviation from BM, GUT is not necessary sinq C = m m m t sin q C = 0.22 as ``quantum of flavor physics Self-complementarity relations Xinyi Zhang Bo-Qian Ma, arxiv:

16 Similar Ansatz for structure of mass matrices Relations between masses and mixing M Fukugita T. Yanagida Fritsch Anzatz similar to quark sector 3 RH neutrinos with equal masses Normal mass hierarhy, Right value of 13 mixing Flavor ordering

Values of elements gradually decrease from m tt to m ee corrections wash out sharp difference of elements of the dominant mt-block and the subdominant

17 Values of elements gradually decrease from m tt to m ee 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 ~ Another complementarity: l = 1 - q C Froggatt-Nielsen?

sin 2 q 13 ~ Dm 21 2 Dm 32 2 1. Two mass scales in the mass matrix Dm 21 2 Dm 31 2 2. Two large mixing angles 3. Normal mass hierarchy 4.

18 sin 2 q 13 ~ Dm 21 2 Dm Two mass scales in the mass matrix Dm 21 2 Dm Two large mixing angles 3. Normal mass hierarchy 4. No fine tuning - no equalities of matrix elements sinq 13 ~ Dm 21 2 / Dm 31 2 = no particular (for leptons) flavor symmetries, - normal mass hierarchy

19 After many speculations back to good old picture? High scale seesaw Something is still missed The same mechanism which explains smallness of neutrino mass is responsible for large lepton mixing Difference of quark and lepton mixings is related to smallness of neutrino mass

RH-neutrino u r, u b, u y, n d r, d b, d y, e - Enhance mixing - Produce randomness (anarchy) - Seesaw symmetries - Increase seesaw scale - produce bi-maximal mixing B.

20 RH-neutrino u r, u b, u y, n d r, d b, d y, e - Enhance mixing - Produce randomness (anarchy) - Seesaw symmetries - Increase seesaw scale - produce bi-maximal mixing B. Feldstein, W. Klemm arxiv: u rc, u bc, u yc, n c d rc, d bc, d yc, e c S S S S S S S S Statistical distribution S S S S S S S S S S S S S S S S S S S S S Hidden sector

M. Smy No distortion of the energy spectrum at low energies : the upturn is disfavored at (1.1 1.

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

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

24 mass n s n e n m n t n 3 Very light sterile neutrino m 0 ~ ev DE scale? Dm 2 31 M 2 M Planck M ~ 2-3 TeV n 2 n 0 n 1 Dm 2 21 Dm 2 dip - solar neutrino data sin 2 2a ~ 10-3 sin 2 2b ~ 10-1

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

26 Accumulating data at SK SK I - IV Day-Night effect: at 2.3 s level in agreement with the LMA MSW solution New precision level - new possibilities: HyperKamiokande, LENA, MICA

27 Be neutrino line A Ioanissian, AYS Period of oscillations in energy scale ~ width of Beryllium nu line Width of the Be nu line central temperature of the Sun Precise measurements of Dm 21 2 Tomography of the Earth with resolution 20 km

28 Huge Atmospheric Neutrinos Detectors

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

Oscillation physics with Huge atmospheric

agreement with low energy data no oscillation

31 Oscillation physics with Huge atmospheric neutrino detectors ANTARES DeepCore Ice Cube Oscillations 2.7s Oscillations at high energies GeV in agreement with low energy data no oscillation effect at E > 100 GeV P. Coyle G. Sullivan Bounds on non-standard interaction, Lorentz violation etc

32 Precision IceCube Next Generation Upgrade PINGU v2 Denser array 20 new strings (~60 DOMs each) in 30 MTon DeepCore volume Few GeV threshold in inner 10 Mton volume Energy resolution ~ 3 GeV Existing IceCube strings Existing DeepCore strings New PINGU-I strings 125 m

33 High statistics can cure other problems

34 2 GeV, E. Akhmedov, S. Razzaque, A. Y. Smirnov arxiv: Smearing with Gaussian reconstruction functions characterized by (half) widths ( s E, s q ) 3 GeV, GeV,

35 s E = 0.2E s q ~ 1/E 0.5 Degeneracy

BUGEY, CHOOZ, CDHS, NOMAD n 3 n 2 n 1 Dm 2 31 Dm 2 21 For reactor and source experiments P ~

36 mass n s n e n m n t LSND/MiniBooNE: vacuum oscillations n 4 P ~ 4 U e4 2 U m4 2 Dm 2 41 restricted by short baseline exp. BUGEY, CHOOZ, CDHS, NOMAD n 3 n 2 n 1 Dm 2 31 Dm 2 21 For reactor and source experiments P ~ 4 U e4 2 (1 - U e4 2 ) With new reactor data: - additional radiation in the universe - bound from LSS? Dm 41 2 = 1.78 ev 2 ( 0.89 ev 2 ) U e4 = 0.15 U m4 = 0.23

37 In general For different mixing schemes Varying U t0 2 < 3% stat. error Zenith angle distribution depends on admixture of n t in 4 th mass state

sin 2 2a = 10-3 (red), 5 10-3 (blue) SK-I SNO-LETA P.

40 sin 2 2a = 10-3 (red), (blue) SK-I SNO-LETA P. De Holanda, A.S. SK-III R D = 0.2 Borexino SNO-LETA Dm 2 = ev 2

41 De Gouvea, Murayama

42 from global fits with salient probably features smallness of mass Peculiar (?) pattern of mixing related strongly differs from quark mixing - Mass hierarchy (ordering) - Deviation of 2-3 mixing from maximal - CP violation - Majorana nature - Absolute scale Usual ``hard masses Generated at the electroweak and higher mass scales Sterile neutrinos Not a small perturbation of the standard framework

L. Wolfenstein P. F. Harrison D. H. Perkins W. G. Scott U tbm = 2/3 1/3 0-1/6 1/3-1/2-1/6 1/3 1/2 0.6 0.

43 L. Wolfenstein P. F. Harrison D. H. Perkins W. G. Scott U tbm = 2/3 1/3 0-1/6 1/3-1/2-1/6 1/3 1/ maximal 2-3 mixing - zero 1-3 mixing, no CP-violation - sin 2 q 12 = 1/3 n 3 is bi-maximally mixed n 2 is tri-maximally mixed Mass matrix in flavor basis: Mass relations Should be broken m TBM = a b b c d c m em = m et m mm = m tt m ee + m em = m mm + m mt

Level crossing in the H-resonance is highly adiabatic Strong suppression of the neutronization peak: Permutations of flavor spectra which depend on mass hierarchy NH n e n 3 Earth matter effects

44 Level crossing in the H-resonance is highly adiabatic Strong suppression of the neutronization peak: Permutations of flavor spectra which depend on mass hierarchy NH n e n 3 Earth matter effects Shock wave effect Adiabaticity is broken in shock front if the relative width of the front: DR/R < km if larger no shock wave effect: probe of the width of front If the earth matter effect is observed for antineutrinos NH is established!

neutrinosphere R = 20 50 km usual matter potential: l = V = 2 G F n e neutrino potential: r 1 r 2 Multiple spectral splits -swaps Multi-angle effect: r 2 < r 1 x n r n f 2 < f 1 m

45 neutrinosphere R = km usual matter potential: l = V = 2 G F n e neutrino potential: r 1 r 2 Multiple spectral splits -swaps Multi-angle effect: r 2 < r 1 x n r n f 2 < f 1 m = 2 G F (1 cos x) n n n n ~ 1/r 2 x ~ 1/r for large r Different phases from different directions due to usual matter potential n n ~ cm -3 n e ~ cm -3 l >> m decoherence

46 H. Minakata, A.S. Leptons U n = U bm seesaw Quarks V u = I U l = U CKM q-l symmetry V d = V CKM U PMNS = U l+ U n = U CKM+ U bm V quarks = V u+ V d = V CKM 1-3 mixing is generated by permutation of U 12 and U 23 sinq 13 = sinq 23 sinq C ~ 0.16 sinq 12 = sin(p/4 - q C ) + 0.5sinq C ( 2-1- V cb cos d) D 23 = 0.5 sin 2 q C + cos 2 q C V cb cos d = / sin 2 q 12 = RGE -> can reduce M. Schmidt, A.S.

47 If G is von Dyck group D(2, m, p) D(2,3,3) = A 4 D(2,3,4) = S 4 D(2,3,5) = A 5 D. Hernandez, A.S. the mixing matrix should satisfy condition (S i U PMNS+ T U PMNS ) p = I i = 1, 2, 3 S i is the symmetry transformation of the neutrino mass matrix in mass basis S 1 = diag (1, -1, -1) S 2 = diag (- 1, 1, -1) S i 2 = I T is the symmetry transformation of the charged lepton mass matrix in mass basis T = diag (e if 1, e if 2, e if 3 ) f i = 2p k i / m T m = I

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

Lecture 3. A. Yu. Smirnov International Centre for Theoretical Physics, Trieste, Italy

Lecture 3. A. Yu. Smirnov International Centre for Theoretical Physics, Trieste, Italy Lecture 3 A. Yu. Smirnov International Centre for Theoretical Physics, Trieste, Italy 25 Spring School on Particles and Fields, National Taiwan University, Taipei April 5-8, 2012 E, GeV contours of constant