Neutrino mass and mixing:

1. Neutrino mass and mixing: Leptons versus Quarks A. Yu. Smirnov International Centre for Theoretical Physics, Trieste, Italy Institute for Nuclear Research, RAS, Moscow, Russia NO-VE 2006: ``Ultimate Goals’’

2. Leptons vs Quarks Unification of Understanding particles and forces Fermion Masses GUT's, Strings... Two fundamental issues

3. Comparing results Mixing Quarks Leptons 1-2, q12 13o 34o 2-3, q23 2.3o 45o 1-3, q13 ~ 0.5o <10o Hierarchy of masses: Neutrinos |m2/m3| ~ 0.2 2-3 Charged leptons |mm/mt| = 0.06 1-2 Down quarks |ms/mb| ~ 0.02 - 0.03 1s 1-3 |mc/mt| ~ 0.005 Up-quarks 0 0.2 0.4 0.6 0.8 |sin q|

4. Mass Ratios up down charged neutrinos quarks quarks leptons Regularities? 1 10-1 mu mt = mc2 10-2 Vus Vcb ~ Vub 10-3 Koide relation 10-4 Mass-mixing 10-5 relation? at mZ

5. Neutrino symmetry? Can both features be accidental? Zero Maximal 1-3 mixing 2-3 mixing nm - nt permutation symmetry Often related to equality of neutrino masses Neutrino mass matrix in the flavor basis: Discrete symmetries S3, D4 For charged leptons: D = 0 Can this symmetry be extended to quark sector? A B B B C D B D C Are quarks and leptons fundamentally different?

6. Universal 2-3 symmetry? A. Joshipura, hep-ph/0512252 2-3 symmetry 2-3 symmetry Does not contradict mass hierarchy Maximal (large) 2-3 leptonic mixing Smallness of Vcb X A A A B C A C B Universal mass matrices + dm - Hierarchical mass spectrum - Small quark mixing Quarks, charged leptons: B ~ C, X << A << B - Degenerate neutrino mass spectrum; - Large lepton mixing Neutrinos: B >> C, X ~ B additional symmetries are needed to explain hierarchies/equalities of parameters Still

7. Remark: nm - nt permutation symmetry Matrix for the best fit values of parameters (in meV) A B B B C D B D C 3.2 6.0 0.6 24.8 21.4 30.7 sin2q13 = 0.01 sin2q23 = 0.43 Bari group Substantial deviation from symmetric structure Structure of mass matrix is sensitive to small deviations Of 1-3 mixing from zero and 2-3 mixing from maximal

8. Additional structure? Very different mass and mixing patterns Similar gauge structure, correspondence Particular symmetries in leptonic (neutrino) sector? Q-L complementarity? Lepton sector Quark sector Symmetry correspondence Additional structure exists which produces the difference. Is this seesaw? Something beyond seesaw?

9. The hope is Neutrality Majorana masses Basis of seesaw mechanism Qg = 0 Qc = 0 Is this enough to explain all salient properties of neutrinos? mix with singlets of the SM Dynamical effects

10. Window to hidden world? A S Standard Model A nl nR S l ... s L lR ... H M S s Planck scale physics

11. Plan Symmetry & Unification Quark-lepton Universality Complementarity Diversity Screening of the Dirac structure Induced effects of new neutrino states

12. Quark-Lepton symmetry ur , ub , uj <-> n dr , db , dj <-> e Correspondence: color Pati-Salam Symmetry: Leptons as 4th color form multiplet of the extended gauge group, in particular, 16-plet of SO(10) Unification: Can it be accidental? More complicated connection between quarks and leptons? Complementarity?

13. GUT's generically Give relations between masses of leptons and quarks Provide with all the ingredients necessary for seesaw mechanism mb = mt In general: ``sum rules’’ RH neutrino components large 2-3 leptonic mixing Large mass scale b - t unification Lepton number violation But - no explanation of the flavor structure

14. 2. Quark-Lepton universality

15. Universality approximate I. Dorsner, A.S. NPB 698 386 (2004) is realized in terms of the mass matrices (matrices of the Yukawa couplings) and not in terms of observables – mass ratios and mixing angles. Eigenvalues = masses Mass matrices M = Y V diagonalization Eigenstates = mixing Universal structure for mass matrices of all quarks and leptons in the lowest approximation: YU = YD = YnD = YL = Y0 Small perturbations: Yf = Y0 + DYf ( Y0)ij >> (DYf)ij f = u, d, L, D, M

16. Singular mass matrices Important example: Det M = 0 l4 l3 l2 Y0 = l3 l2 l l2 l 1 l~ 0.2 - 0.3 Unstable with respect to small perturbations Yfij = Y0ij (1 + efij) f = u, d, e, n Perturbations e ~ 0.2 – 0.3 Universal singular Small perturbations allow to explain large difference in mass hierarchies and mixings of quarks and leptons Form of perturbations is crucial

17. Seesaw plays crucial role Seesaw: m ~ 1/M Nearly singular matrix of RH neutrinos leads to - enhancement of lepton mixing - flip of the sign of mixing angle, so that the angles from the charged leptons and neutrinos sum up

18. Universality of mixing A Joshipura, A.S. hep-ph/0512024 In some (universality) basis in the first approximation all the mass matrices but Ml (for the charged leptons) are diagonalized by the same matrix V: V+ Mf V = Df For the charged leptons, the mass VT Ml V* = Dl is diagonalized by V* V for u, d, n V* for l Ml = MdT Diagonalization: SU(5) type relation In the first approximation Another version is when neutrinos have distinguished rotation: Quark mixing: VCKM = V+ V = I Lepton mixing: VPMNS = VT V V for u, d, l V* for n

19. In general In general, up and down fermions can be diagonalized by different matrices V’ and V respectively VPMNS = VT V’ VCKM = V’+ V VPMNS = VTV VCKM+ = V0PMNS VCKM + Quark and lepton rotations are complementary to VVT VPMNS VCKM = VTV - symmetric, characterized by 2 angles; - close to the observed mixing for q/2 ~ f ~ 20 – 25o - 1-3 mixing near the upper bound V0PMNS = VTV • gives very good description of data • predicts sin q13 > 0.08 VPMNS (with CKM corr.)

20. Origin of universal mixing Universal mixing and universal matrices Ml ~ m D A D* Mu, n ~ m D* A D* Md ~ m D*A D D = diag(1, i, 1) A is the universal matrix: e12 e22 e12 e2 e1 e2 . . . e1 e2 e1 1 ei ~ 0.2 – 0.3 A ~ Can be embedded in to SU(5) and SO(10) with additional assumptions

21. 3. Quark-Lepton complementarity

22. Quark-Lepton Complementarity A.S. M. Raidal H. Minakata ql12 + qq12 ~ p/4 qsol + qC = 46.7o +/- 2.4o qatm + Vcb = 45o +/- 3o ql23 + qq23 ~ p/4 1s H. Minakata, A.S. Phys. Rev. D70: 073009 (2004) [hep-ph/0405088] Difficult to expects exact equalities but qualitatively 2-3 leptonic mixing is close to maximal because 2-3 quark mixing is small may not be accidental 1-2 leptonic mixing deviates from maximal substantially because 1-2 quark mixing is relatively large

23. Possible implications ``Lepton mixing = bi-maximal mixing – quark mixing’’ Quark-lepton symmetry sin qC = 0.22 as ``quantum’’ of flavor physics or Existence of structure which produces bi-maximal mixing sinqC = mm /mt Mixing matrix weakly depends on mass eigenvalues sinqC ~ sin q13 Appears in different places of theory Vquarks = I, Vleptons =Vbm m1 = m2 = 0 In the lowest approximation:

24. Bi-maximal mixing F. Vissani V. Barger et al Ubm = U23mU12m ½ ½ -½ ½ ½ ½ -½ ½ 0 Two maximal rotations Ubm = As dominant structure? Zero order? UPMNS = Ubm • - maximal 2-3 mixing • - zero 1-3 mixing • maximal 1-2 mixing • - no CP-violation Contradicts data at (5-6)s level Deviation of 1-2 mixing from maximal Generates simultaneously In the lowest order? Corrections? UPMNS = U’ Ubm Non-zero 1-3 mixing U’ = U12(a)

25. H. Minakata, A.S. R. Mohapatra, P. Frampton, C. W.Kim et al., S. Pakvasa … Possible scenarios QLC-1 QLC-2 CKM mixing Charged leptons Maximal mixing ml ~ md q-l symmetry CKM mixing Maximal mixing Neutrinos q-l symmetry mDT M-1 mD mD ~ mu sinq12 = sin(p/4 - qC) + 0.5sin qC( 2 - 1) sin(p/4 - qC) tan2q12 = 0.495 ~ Vub sinq13 = sin qC/ 2

26. 1-2 mixing Utbm = Utm Um13 UQLC1 = UC Ubm Give the almost same 12 mixing coincidence tbm QLC2 QLC1 3s SNO (2n) 2s 1s Strumia-Vissani 99% 90% Fogli et al 29 31 33 35 37 39 q12 3n - analysis does change bft but error bars become smaller q12+ qC ~p/4

27. Tri/bimaximal mixing L. Wolfenstein P. F. Harrison D. H. Perkins W. G. Scott 2/3 1/3 0 - 1/6 1/3 1/2 1/6 - 1/3 1/2 Utbm = U23(p/4)U12 Utbm = n3 is bi-maximally mixed n2is tri-maximally mixed - maximal 2-3 mixing - zero 1-3 mixing - no CP-violation sin2q12= 1/3 in agreement with 0.315 In flavor basis… relation to masses? No analogy in the Quark sector? Implies non-abelian symmetry Mixing parameters - some simple numbers 0, 1/3, 1/2 Relation to group matrices? S3 group matrix

28. 1-3 mixing In agreement with 0 value T2K Double CHOOZ Dm212/Dm322 qC QLC1 Strumia-Vissani 99% 90% 3s Fogli et al 2s 1s 0 0.01 0.02 0.03 0.04 0.05 sin2q13 Non-zero central value (Fogli, et al): Atmospheric neutrinos, SK spectrum of multi-GeV e-like events Lower theoretical bounds: Planck scale effects RGE- effects V.S. Berezinsky F. Vissani M. Lindner et al

29. 4. Effects of new neutrino states 1). Superheavy MS >> vEW - decouple 2). Heavy: vEW >> mS >> mn 3). Light: mS ~ mn play role in dynamics of oscillations two applications

30. Screening of Dirac structure M. Lindner M. Schmidt A.S. JHEP0507, 048 (2005) Double (cascade) seesaw 0 mD 0 m = mDT 0 MDT 0 MD MS n N S Additional fermions mD << MD << MS R. Mohapatra PRL 56, 561, (1986) MR = - MDTMS-1 MD R. Mohapatra. J. Valle MS – Majorana mass matrix of new fermions S mn = mD MD-1MS MD-1mD A.S. PRD 48, 3264 (1993) A ~ vEW/MGU If MD = A-1mD mn= A2 MS mD similar (equal) to quark mass matrix - cancels Structure of the neutrino mass matrix is determined by MS -> physics at highest (Planck?) scale immediately

31. Reconciling Q-L symmetry and different mixings of quarks and leptons Seesaw provides scale and not the flavor structure of neutrino mass matrix Structure of the neutrino mass matrix is determined by MS ~ MPl ? MS leads to quasi-degenerate spectrum if e.g. MS ~ I, origin of ``neutrino’’ symmetry origin of maximal (or bi-maximal) mixing Q-l complementarity

32. Induced mass matrix Mixing with sterile states change structure of the mass matrix of active neutrinos Active neutrinos acquire (e.g. via seesaw) the Majorana mass matrix ma Consider one state S which has - Majorana mass M and - mixing masses with active neutrinos, miS (i = e, m, t) After decoupling of S the active neutrino mass matrix becomes (mn)ij = (ma )ij - miSmjS/M induced mass matrix sinqS = mS/M mind = sinqS2 M

33. Effects and benchmarks Induced matrix can reproduce the following structures of the active neutrino mass mind = sinqS2 M Dominant structures for normal and inverted hierarchy sinqS2 M > 0.02 – 0.03 eV Sub-leading structures for normal hierarchy sinqS2 M ~ 0.003 eV Effect is negligible sinqS2 M < 0.001 eV

34. Tri-bimaximal mixing In the case of normal mass hierarchy 0 0 0 0 1 -1 0 -1 1 1 1 1 1 1 1 1 1 1 m2 = Dmsol2 mtbm ~ m2/3 + m3/2 Assume the coupling of S with active neutrinos is flavor blind (universal): miS = mS = m2 /3 Then mind can reproduce the first matrix mtbm = ma +mind ma is the second matrix Two sterile neutrinos can reproduce whole tbm-matrix

35. Bounds on active-sterile mixing Two regions are allowed: R. Zukanovic-Funcal, A.S. in preparation MS ~ 0.1 – 1 eV MS > (0.1 – 1) GeV and

36. Summary • Q & L: • - strong difference of mass and mixing pattern; • possible presence of the special leptonic (neutrino) symmetries; • quark-lepton complementarity This may indicate that q & l are fundamentally different or some new structure of theory exists (beyond seesaw) Still approximate quarks and leptons universality can be realized. • Mixing with new neutrino states can play the • role of this additional structure: • screening of the Dirac structure • - induced matrix with certain symmetries.

37. 2-3 mixing SK (3n) - no shift from maximal mixing sin22q23 > 0.93, 90% C.L. T2K maximal mixing QLC1 QLC2 SK (3n) 90% 3s Gonzalez-Garcia, Maltoni, A.S. 2s 1s Fogli et al 0.2 0.3 0.4 0.5 0.6 0.7 sin2q23 1). in agreement with maximal 2). shift of the bfp from maximal is small 3). still large deviation is allowed: 2s (0.5 - sin2q23)/sin q23 ~ 40%

38. Bounds on active-sterile mixing R. Zukanovic-Funcal, A.S. in preparation

40. Are Neutrino Particles just like the other Fundamental Fermions? Possibility that their properties are related to very high scale physics Why not? Violate fundamental symmetries, Lorentz inv. CPT, Pauli principle? Smallness of mass Large mixing Can propagate in extra dimensions Manifestations of non- QFT features?