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

Transcription

1 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

2 E, GeV contours of constant oscillation probability in energy- nadir (or zenith) angle plane n e n m, n t 100 IceCube NuFac 2800 ICAL, INO 10 1 IC Deep Core PINGU LENF T2KK CNGS MINOS NOvA T2K HyperK LAr OK for CP 0.1

3 Phased IceCube Next Generation Upgrade Pingu-I: physics with ~ 1 GeV energy threshold 18 new strings (~1000 DOMs) in 30 MTon DeepCore volume Few GeV threshold in inner 10 Mton volume Existing IceCube strings Existing DeepCore strings New PINGU-I strings D. Cowen

4 Collective flavor trasformation Shock wave effect on conversion MSW flavor conversion inside the star Propagation in vacuum Oscillations inside the Earth

5 Flavor evolution of neutrino states is highly adiabatic Strong suppression of the neutronization peak: Permutation of the electron and non-electron neutrino spectra NH n e n 3 Shock wave effect Earth matter effects 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!

6 F e = (1 p) F e 0 + p F x 0 p = 1 - P ee Permutation parameter F n e p = 1 F n m n m n e E E Partial permutation composite (mixed) spectra H hard spectrum MS mixed-soft spectrum: 2/3 of the original spectrum MH mixed-hard spectrum: with 1/3 part of original spectrum

7 Neutrinos (resonance channels): P ee = U e3 2 p = 1 - U e3 2 Antineutrinos (no resonances): P ee = P E 1e = U 1e 2 without Earth matter effect: p = 1 - U e1 2 ~1/3 ~ complete permutation of spectra Partial permutation of spectra: mixed soft spectrum Disppearance of neutronization peak No earth matter effect the Earth matter effect in the antineutrino channel only

8 Neutrinos (L resonance ): P ee = P E 2e = U 2e 2 without Earth matter effect p = 1 - U e2 2 ~ 2/3 Partial permutation: mixed hard spectra Antineutrinos (H - resonance): P ee = U e3 2 p = 1 - U e3 2 ~ Complete permutation of spectra Partial suppression of neutronization peak the Earth matter effect in the neutrino channel only No Earth matter effect

9 neutrinosphere R = km usual matter potential: l = V = 2 G F n e neutrino potential: x n n r m = 2 G F (1 cos x) n n n n ~ 1/r 2 x ~ 1/r for large r m ~ 1/r 4 in neutrinosphere in all neutrino species: n n ~ cm -3 electron density: n e ~ cm -3 l >> m

10 nn n e Z 0 n e n e Z 0 n b Refraction in neutrino gases n b n b n b t-channel n e (p) n e n e A = 2 G F (1 v e v b ) velocities n b n b (q) elastic forward scattering n e n e u-channel (q) n b n e (p) n b J. Pantaleone can lead to the coherent effect Momentum exchange flavor exchange flavor mixing Collective flavor transformations

11 sin 2 q 13 ~ 0.02 O(1) Dm 21 2 Dm 32 2 ``Naturalness of mass matrix sin 2 q 13 = ~ ½ sin 2 q C Quark Lepton Complementarity ~ ½ cos 2 2q 23 n m - n t - symmetry violation q 13 + q 12 ~ p/4 Mixing anarchy The same 1-3 mixing with completely different implications TBM?

12 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 - relation between masses and mixing

13 Mass matrix in the flavor basis l l l l 1 1 l 1 1 l << 1 (matrix elements are defined up to coefficients ~ O(1)) If there is no fine tuning of 12 and 13 elements tan2 q 12 Dm 2 sin q = 2 tan q 23 Dm 2 cos 2q ~ 0.2 E. Akhmedov, G. Branco et al 2002 sin q 13 = ½ sin2q 12 cotq 23 Dm 21 2 Dm 31 2 m em = 0 W. Rodejohann et al, arxiv sin q 13 = ½ sin2q 12 tanq 23 Dm 21 2 Dm 31 2 m et = 0

14 sin 2 q 13 ~ ½ cos 2 2q n m - n t symmetry of m n - maximal 2-3 mixing - zero 1-3 mixing 2. breaking of n m - n t symmetry by corrections to matrix elements: m em - m et ~ m mm - m tt = dm 3. Normal mass hierarchy sinq 13 ~ dm 2m 3 D = ½ - sin 2 q 23 ~ dm 2m 3 D - deviation from maximal 23 mixing dm ~ m 2 also: the n m - n t symmetry is broken by charged leptons

15 Behind neutrino mass?

16 mn / mt < 10-10

17 n Forbid the usual Dirac mass terms Overlap mechanism different localization Radiative generation High dimension operators small VEV ``Chiral mismatch

18 If no new particles at the EW scale, after decoupling of heavy degrees of freedom set of non-renormalizable operators H 1 L L L H H H x S. Weinberg n n

19 D=5 operator can be suppressed by symmetry H i H H 1 H 2 H n-1... H n 1 L n-1 L L H n allows to reduce the scale of new physics responsible for neutrino mass generation m n = <H> n L n-1 n n 1 m n = P i = 1 n <H i > L n-1

20 Type 1 P. Minkowski T. Yanagida M. Gell-Mann, P. Ramond, R. Slansky S. L. Glashow R.N. Mohapatra, G. Senjanovic x H H x m n n Y M R > x < S S T T Y n m D = Y<H> m D Type 3 ( SU(2) triplet intermediate state) R Foot, H Lew, X G He, G C Joshi Mass matrix: M R n N n N m n = - m T D M -1 if M 0 m R >> m D R m D D m T D M R

21 H f H M. Magg and C. Wetterich G. Lazarides, Q Shafi and C Wetterich R. Mohapatra, G. Senjanovic, D Seesaw for VEV s: n h D n <D> = <H> 2 f/m D 2 m n = h D <D > = h f <H> 2 /M D 2 Natural smallness of VEV Light triplet?

22 Three additional singlets S which couple with RH neutrinos 0 m D T 0 m D 0 M D T 0 M D m n n c S R.N. Mohapatra J. Valle Beyond SM: many heavy singlets string theory m n = m DT M D -1T m M D -1 m D m = 0 m << M D m >> M D m - scale of B-L violation massless neutrinos Inverse seesaw Cascade seesaw m ~ M Pl, M ~ M GU violation of universality, unitarity lower the scales of neutrino mass generation explains intermediate scale for the RH neutrinos M ~ M GU2 /M Pl ~ GeV

23 Quark-lepton symmetry m D ~ m q - small mixing, - strong mass hierarchy Screening: if m D ~ M D m n = A 2 m A ~ v EW /M GU m ~ M Pl Structure of the neutrino mass matrix is determined by m origin of ``neutrino symmetry origin of maximal (or bi-maximal) mixing leads to quasi-degenerate spectrum, if e.g. M S ~ I, Q-l complementarity

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

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26 U tbm = 2/3 1/3 0-1/6 1/3-1/2-1/6 1/3 1/2 L. Wolfenstein 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 U tbm = U 23 (p/4) U 12 Uncertainty related to sign of 2-3 mixing: q 23 = p/4 - p/4

27 G.L Fogli et al., [hep-ph] Correlations of parameters 1-2 mixing deviates fom 1/3 Deviation of 2-3 mixing from maximal Non-zero 1-3 mixing TBM QLC New reactor fluxes - shift by arrows

28 Mixing from diagonalization of mass matrix m TBM = U TBM m diag U TBM T m diag = diag ( m 1, m 2 e i2f 2, m 3 e i2f 3 ) m TBM = a b b ½(a + b + c) ½(a + b - c) ½(a + b + c) a = (2m 1 + m 2 )/3 b = (m 2 m 1 )/3 c = m 3 The matrix has S 2 permutation symmetry n m <-> n t

29 Invariance: V i T m TBM V i = m TBM V i T U TBM = U TBM S = U = The mass matrix of the charged leptons is diagonal due to symmetry T = w 2 0 w w = exp(-2ip/3) T + (m e+ m e)t = m e+ m e C.S Lam S, T, U elements of S 4

30 In flavor basis: search for S which satisfy for all V: S V i = l i V i V i are columns of U TBM l i are eigenvalues = elements of diagonalized matrix S

31 No exact flavor symmetry 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 13-mixing T M l diagonal M n TBM-type 1 n the split originates from different flavor assignments of the RH components of N c and l c and different higgs multiplets

32 Singlet of gauge symmetry group Separation of the EW symmetry and flavor symmetry breakings 1 L n-1 L e c H f n L - above GUT scale? Many Higgs doublets - tests at LHC Strongly restricted: - FCNC - anomalous magnetic moment of muon difficult to test

33 with irreducible representations 3 Group Order Representations A , S T T * D(27)

34 E. Ma G Branco, H P Nilles A 4 Symmetry group of even permutations of 4 elements Symmetry of tetrahedron Generators: S, T Presentation of the group: S 2 = 1 T 3 = 1 (ST) 3 = 1 no U = A mt Irreducible representations: 3, 1, 1, 1 Products and invariants 3x3 = x 1 ~ 1

35 T M l diagonal A 4 S M n TBM-type ``accidental symmetry due to particular selection of flavon representations and configuration of VEV s In turn, this split originates from different flavor assignments of the RH components of N c and l c and different higgs multiplets

36 G. Altarelli D. Meloni Yukawa sectors Charged lepton i L l c i 1, i, -1 f T f S n f T i x x x k < f T > = v S (0, 1, 0) h d n = 1, k = 0, Flavon sector U(1) R 1 0 Neutrinos 1-1 f S i 1 L N c x h i u M A 4 < f S > = v S (1, 1, 1) Particular selection of representations Z 4 1 i -1 -i at multiplets f T f 0 S x Driving fields Vacuum alignment GUT-scale or higher?

37 Mechanism of mass generation - different contributions - high order corrections Yukawa couplings VEV s VEV alignment follow from independent sectors Yukawa sector Scalar potential All these components should be correlated ``Natural consequence of symmetry? tune by additional symmetries one step constructions do not work

38 sin 2 q 12 TBM = sin 2 q 12 fit = D sin 2 q 12 ~ 0.02 Normal mass hierarchy Generation of 1-3 mixing leads to correction to the 1-2 mixing: 27 m sinq 13 ~ 2 D(sin 2 q 12 ) 8 m 3 sinq 13 ~ 0.6 D(sin 2 q 12 ) ~ Observed: sinq 13 ~ 0.15 Additional tuning is needed

39 1. Experiment: deviations from TBM mixing Symmetry mass relations can be broken maximally 2. No simple and convincing model for TBM 3. Often: no connection between masses and mixing additional symmetries are introduced 4. Inclusion of quarks: further complication. GUT additional requirements

40 As zero order structure U bm = U 23 m U 12 m Two maximal rotations F. Vissani V. Barger et al U bm = ½ ½ 0 -½ ½ ½ ½ -½ ½ - maximal 2-3 mixing - zero 1-3 mixing - maximal 1-2 mixing - no CP-violation Scenario: In the lowest approximation: V quarks = I, U leptons = V bm m 1 = m 2 = 0 Corrections generate: - mass splitting - CKM and - deviation from bi-maximal

41 based on relations: q l 12 + q q 12 ~ p/4 q l 23 + q q 23 ~ p/4 A.S. M. Raidal H. Minakata ``Lepton mixing = bi-maximal mixing quark mixing Quark-lepton symmetry Existence of structure which produces bi-maximal mixing Grand Unification or family symmetry See-saw? Properties of the RH neutrinos

42 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.

43 BM mass relations m em = m et m mm = m tt m ee = m mm + m mt Invariance: V i T m BM V i = m BM S BM = 0 - ½ - ½ - ½ ½ -½ - ½ -½ ½ U = The mass matrix of the charged leptons is diagonal due to symmetry with respect to transformations: T = diag (- 1, -i, i ) T, S BM generators of S 4

44 Order 24, permutation of 4 elements Generators: S, T Presentation: Irreducible representations: S 4 = T 3 = (ST 2 ) 2 = 1 1, 1, 2, 3, 3 3 x 3 = 3 x 3 = x 3 = Products 1 x 1 = 1 and invariants 2 x 3 = 2 x 3 = New flavor structure 2 x 2 = x 2 = 2

45 Charged lepton e c -1, -i, -i L Flavon sector f l 1 m c t c f l n c l < f l > = v l (0, 1, 0) < c l > = v l (0, 0, 1) No doublet representations i i c l c 0 l f 0 y 0 l n i f n i * x k x 0 1 q m h d U(1) R 0 2 Driving fields Neutrinos 1 f n 1 i 1 L N c x h u M < f n > = v n (0, 1, -1) i U(1) FN x G. Altarelli F. Feruglio, L. Merlo * e c, m c, t c S Froggatt-Nielsen sector * q 2, 1, 0-1 Z 4 1 i -1 -i at multiplets

46 Based on relation Bi-maximal mixing q 13 + q 12 ~ p/4 Octahedral group H. J. He, X. J. Xu [hep-ph] Geometric violation of residual symmetry in the charged lepton sector (additional rotation from charged leptons) q 13 ~ e q 12 ~ p/4 - e

47 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: