A. Yu. Smirnov

1. Status & interpretation of neutrino mixing A. Yu. Smirnov International Centre for Theoretical Physics, Trieste, Italy Institute for Nuclear Research, RAS, Moscow, Russia Launch Heidelberg, March-07

2. 1. Status

3. 50 years ago... B. Pontecorvo ``Mesonium and antimesonium’’ Zh. Eksp.Teor. Fiz. 33, 549 (1957) [Sov. Phys. JETP 6, 429 (1957)] translation First mentioning of a possibility of neutrino mixing and oscillations Another line: Wu experiment, 1957: Parity violation  V-A theory, two-component massless neutrino

4. The first phase of studies of neutrino mass and mixing is essentially over The main results: Discovery of non-zero neutrino masses Determination of the dominant structure of the lepton mixing: discovery of two large mixing angles Establishing strong difference of the quark and lepton mass spectra and mixing patterns New phase starts in 2008 – 2010 the main objectives - determination of the absolute scale of neutrino mass; - subdominant structures of mixing matrix; - identification of the mass hierarchy, etc.

5. Mixing: summary M.C. Gonzalez-Garcia, M. Maltoni, Moriond, March 2007 (Phys. Rep.) The angles 1s (3 s) very good agreement with other fits + 4.3 - 3.5 q12o = 33.7 +/- 1.3 small shift from maximal mixing + 4.3 - 3.8 + 9.8 - 8.8 q23o = 43.3 b.f. value is zero; stronger upper bound + 11.5 - 0.0 + 5.3 - 0.0 q13o = 0.0 Mixing matrix (moduli of matrix elements) 0.81 – 0.85 0.53 – 0.58 0.00 – 0.12 0.32 – 0.49 0.52 – 0.69 0.60 - 0.76 0.27 – 0.46 0.47 – 0.64 0.65 – 0.80 UPMNS = 90 % C.L.

6. 1-2 mixing Give the almost same 12 mixing Utbm = Utm Um13 UQLC1 = UC Ubm QLCl p/4 -qC QLCn tbm 3s SNO (2n) 2s 1s Strumia-Vissani 99% 90% Fogli et al 3s Gonzalez-Garcia, Maltoni 1s q12 29 31 33 35 37 39 q12+ qC ~p/4

7. 1-3 mixing T2K Double CHOOZ QLCl QLCn Dm212/Dm322 qC 3s Gonzalez-Garcia, Maltoni 1s 99% Strumia-Vissani 90% 3s Fogli et al 2s 1s sin2q13 0 0.01 0.02 0.03 0.04 0.05 * Non-zero central value (Fogli, et al): Atmospheric neutrinos, SK spectrum of multi-GeV e-like events * MINOS lead to stronger the bound on 1-3 mixing (G-G, M.)

8. 2-3 mixing SK: sin22q23 > 0.93, 90% C.L. maximal mixing T2K QLCn QLCl Gonzalez-Garcia, Maltoni, 2007 3s 1s SK (3n, one mass scale) 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 * in agreement with maximal, though all complete 3n - analyses show shift * shift of the bfp from maximal is small * still large deviation is allowed: (0.5 - sin2q23)/sin q23 ~ 40% 2s

9. Masses: summary + 0.44 - 0.26 MINOS: Dm312 = 2.74 x 10-3 eV2 (1 s) 1.27 1020 p.o.t. in future: tension with SK? new physics? Dm312 = 2.6 +/- 0.2 (0.6) x 10-3 eV2 Global fit: + 1.10 - 0.89 + 0.27 - 0.28 M. Gonzalez-Garcia, M. Maltoni, 2007 Dm212 = 7.90 x 10-5 eV2 |m2/m3| > 0.18 the weakest mass hierarchy Cosmology: Si mi < 0.42 eV (95% C.L. ) S. Hannestadt U. Seljak et al Si mi < 0.17 eV (95% C.L. ) < 0.6 eV At least for one neutrino: m ~ 0.05 – 0.10 eV if confirmed, other than light neutrino Mass mechanism? mee = 0.24 – 0.58 eV Heidelberg-Moscow:

10. Forthcoming results MINOS: results 2 years data taking (double statistics) Dm2 = (2.5 - 3.1) x 10-3 eV2 Improvements of the 1-2 mixing determination Ue2 SNO: results of the third phase: He counters Improvement of sensitivity to 1-2 mixing comparable to solar neutrino sensitivity KAMLAND: update + calibration MiniBooNE: oscillation results Tests of LSND, overall picture of mass and mixing BOREXINO CNGS

11. ``Standard'' neutrino model 1. There are only 3 types of light neutrinos 2. Interactions are described by the Standard (electroweak) model 3. Masses and mixing have pure vacuum origin; they are generated at the EW and probably higher mass scales = ``Hard’’ masses Tests of these statements; Search for physics beyond

12. More light neutrinos? LSND: not clear that light neutrinos are relevant Gallium calibration C. Giunti, M. Laveder Cosmology: effective number of light neutrino species in the epoch when structures start to form Warm dark matter: very small mixing, produced in EU by some mechanism which differs from mixing with light neutrinos. M. Shaposhnikov Small perturbations How inclusion of these neutrinos affect standard neutrino model? Strong changes?

13. Bounds on active - sterile mixing R. Zukanovic-Funchal, A.S. Contours of constant induced mass and bounds bb0n thermalization line: above if S are in equilibrium CMB For benchmark parameters S were thermalized X-rays Bounds - in non-equilibrium region LSS reactors atmospheric

14. New interactions Short range Long range interactions interactions Heavy particle exchange Light particles New scalars New scalars exchange Majorons, Accelerons Cosmons… With some cosmological motivations SUSY with R-parity breaking Phenomenology: T. Ota Restrictions: see talk S. Hannestadt

15. ``Soft'' neutrino mass? Are neutrino masses usual? in the context of MaVaN scenario ln Exchange by very light scalar D B Kalplan, E. Nelson, N. Weiner , K. M. Zurek M. Cirelli, M.C. Gonzalez-Garcia, C. Pena-Garay V. Barger, P Huber, D. Marfatia nR nL f mf ~ 10-8 - 10-6 eV f = e, u, d, n lf fL fR chirality flip – true mass: lf ~ f/M Pl msoft = ln lfnf /mf mvac mvac + msoft In the evolution equation: medium and energy dependent mass generated by some short range physics (interactions) EW scale VEV

16. to 2. Interpretation of lepton mixing results

17. High vs. Low mass scales Grand Low scale unification mechanisms Planck M3 ~ MGUT Intermediate EW scale? scale scale kev-scale mechanisms? With many O(100) RH neutrinos R. Mohapatra M. Shaposhnikov W. Buchmuller, M. Ratz et al Problem of unification: difference of mass and mixing patterns Origin of difference: seesaw? FUT + flavor symmetry – even more complicated

18. Analyzing data mass-mixing tri-bimaximal GST-approach mixing Quark-lepton No-symmetry Complementarity Large mixing is related to weak mass hierarchy of neutrinos Have different implications

19. 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 = n3 is bi-maximally mixed n2is tri-maximally mixed - maximal 2-3 mixing - zero 1-3 mixing - no CP-violation Utbm = U23(p/4) U12 sin2q12= 1/3 In flavor basis… relation to masses? No analogy in the Quark sector? Implies non-abelian symmetry Clebsch-Gordan coefficients immediate relation to group matrices?

20. Possible implications Utbm = Umag U13(p/4) 1 1 1 Umag = 1 w w2 1 w2 w w = exp (-2ip/3) tetrahedron Symmetry: symmetry group of even permutations of 4 elements A4 representations: 3, 1, 1’, 1’’ Other possibilities: T’ , D4 , S4 ,D(3n2 ) … C.Hadedorn Extended higgs sector, Auxiliary symmetries, Flavor alignment, Extra dimensions? Relation to masses? No analogy in the quark sector? Unification?

21. Quark-Lepton Complementarity A.S. M. Raidal H. Minakata QLC- relations: ql12 + qq12 ~ p/4 q12 + qC = 46.5o +/- 1.3o ql23 + qq23 ~ p/4 1s q23 + Vcb = 43.9o + 5.1/-3.6o H. Minakata, A.S. Phys. Rev. D70: 073009 (2004) [hep-ph/0405088] Qualitatively correlation: 2-3 leptonic mixing is close to maximal because 2-3 quark mixing is small 1-2 leptonic mixing deviates from maximal substantially because 1-2 quark mixing is relatively large

22. Possible implications ``Lepton mixing = bi-maximal mixing – quark mixing’’ Quark-lepton symmetry Existence of structure which produces bi-maximal mixing Mixing matrix weakly depends on mass eigenvalues Appears in different places of theory Vquarks = I, Vleptons =Vbm m1 = m2 = 0 In the lowest approximation:

23. 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

24. QLC_nu: V_bm from neutrinos In the symmetry basis Quarks Leptons Seesaw? Vu = I Vn = Vbm Vd = VCKM Vl= VCKM q-l symmetry Vquarks = Vu+Vd = VCKM VPMNS = Vl+Vn= VCKM+Vbm (or both rotations from neutrinos) Predictions: sinq12 = sin(p/4 - qC) + 0.5sinqC ( 2 - 1- Vcb) sin2q12 = 0.330 large ! sinq13 = sinq23 sinqC = 0.16 D23 = 0.5 sin2qC + cos2qC Vcbcos a = 0.02 +/- 0.04 H. Minakata, A.S.

25. QLC_l: V_bm from charged leptons M. Raidal Leptons Quarks Vn = VCKM+ q-l symmetry Vu = VCKM+ Vl= Vbm+ Vd = I ``Lopsided’’ Vleptons = VbmVCKM + Vquarks = Vu+Vd = VCKM Predictions: sinqsun ~ sin(p/4 - qC ) sinq13 = - sin qsun Vcb = 0.03 H. Minakata, A.S. D23 = cos qsun Vcb cos d < 0.03

26. tbm vs. QLC Physical parameter Ue2 = cos q13 sin q12 Global fit: 0.53 – 0.58 (90% C.L.) tbm: 0.577 (depending on Majorana CP –phases) QLC: 0.576 – 0.584 QLC RGE tbm RGE for tbm: A. Dighe, S. Goswami, W. Rodejohann hep-ph/0512328 data Ue2 0.53 0.55 0.57 0.59 tbm: RGE q13 < 10-3 for hierarchical nu  0.1 for degenerate nu

27. QLC & RGE effects M. A. Schmidt, A.S. hep-ph/0607232 D q12 D q12 MSSM SM positive f2 - f1 tan b m1/eV m1/eV seesaw-I  bi-maximal mixing, mD ~ mu ml ~ md

28. Real or accidental? Tri-bimaximal mixing Small 1-3 mixing Q-L-complementarity Maximal 2-3 mixing Koide relation

29. Perturbative approach Fermion mass matrices Mf = M0 + dMf f = u, d, l, n Determined by symmetry? corrections due to new interactions Planck scale effects… What is zero order structure? What it should explain? • - third generation masses • 2-3 mixing • - 1-3 mixing The rest: from perturbations?

30. ...but Koide relation Y. Koide, Lett. Nuov. Cim. 34 (1982), 201 me + mm + mt = 2/3 ( me + mm + mt )2 with accuracy 10-5 mm - me all three families are substantially involved! tanqC = 3 2 m t - mm - me Both relations can be reproduced if mi = m0(zi + z0)2 C A Brannen Si zi = 0 Neutrinos, hierarchical spectrum z0 = Si zi2/3

31. From the bottom & from the top Data String theory * Existence of a number O(100) of singlets of SM and GUT symmetry group * GUT no simple relations between masses and mixing  can not be described in terms of a few parameters * Several U(1) gauge factors * Discrete symmetries * Heavy vector-like families * Non-renormalizable interaction * Selection rules for interactions * Explicit violation of symmetry * Incomplete GUT multiplets No simple ``one-step’’ explanations How one can get from this complicated structure simple pattern we observed at low energies?  data look complicated  data look too simple

32. Framework String inspired… Non-abelian flavor (family symmetry) G with irreducible representation 3 SO(10) 3 fermionic families in complete representations 16F, 10H , 16H 16F ~ 3 Singlet sector: several (many ?) singlets (fermionic and bosonic) of SO(10), S, additional symmetries No higher representations no 126H Heavy vector-like families of 10F, 16F their mixing corrects masses of charged fermions C. Hagedorn M. Schmidt A.S. Non-renormalizable interactions

33. Singlet sector Singlet sector C. Hagedorn M. Schmidt, A.S. in progress 16F 16H - several (many ?) singlets (fermionic and bosonic) of SO(10), - additional symmetries (U(1), discrete)  hierarchy of masses and couplings with neutrinos from 16 - some singlets can be light – sterile neutrinos Due to symmetries only certain restricted subset is relevant for neutrino mass and mixing Mixing of singlets with neutrinos (neutral components of 16). responsible for neutrino mass and mixing and strong difference of quark and lepton patterns Easier realizations of symmetries

34. Neutrinos & LHC The EW-scale mechanisms of neutrino mass generation HE scale: seesaw New Higgs bosons at the EW scale ? Zee, Babu-Zee radiative mechanisms R-parity violation Double charged bosons New fermions?

35. Seesaw at LHC W. Buchmuller, D. Wyler Can RH neutrinos be detected at LHC? Type-I: RH neutrinos- singlets of the SM symmetry group RH neutrinos can be produced/decay Via mixing with light neutrinos Additional interactions Negligible unless strong cancellation occurs - RH gauge bosons in LR models - New higgs bosons Type-III seesaw

36. RH neutrinos at LHC Type III seesaw: B. Bajc G. Senjanovic M. Nemevsek P. Filiviez-Perez SU(2) triplet: H H T+ T = T0 T- y ~ 10-6 x y n n T0 MT ~ 100 GeV S In SU(5): 24F T, S Type I + Type III one usual neutrino is mass less y 5F 24F 5H + y’/M5F 24F 24H 5H EW production: W + *  T+ T0, Z * T0T0 LHC: Decay: T0 W l , T0 Z n , t ~ 10-16 - 10-13 sec T0 T+ l -n G ~ (mixing) 2

37. Mixing and cancellation Single RH neutrino generate a contribution to neutrino mass matrix W. Buchmuller C. Greub, G. Ingelman, J. Rathsman A. Pilaftsis 1 Mi (mi)ab = - mai x mbiT Define mixing: sin qai = mai / Mi (mi)ab = - sinqai sin qbi Mi J. Kersten, A.S. Neutrino data: s ~ (qai)2 qai < 10-6 ( 10 GeV /Mi)1/2 (mi)ab < 0.1 eV negligible effect at HE colliders qai ~ 10-1 If M ~ 1 GeV Bound from m  e g Cancellation at the level 10-10

38. Cancellation and symmetry For 2 and 3 RH neutrinos exact cancellation occurs if and only if y1 ay1 by1 mD = m y2 ay2 by2 y3 ay3 by3 1. the Dirac mass matrix is singular J. Kersten, A.S. J. Gluza 2. the Yukawa couplings and RH neutrino masses are related as y12/M1 + y22/M2 + y32/M3 = 0 Imply conservation of the lepton number and one decoupled heavy neutrino 1 1 1 m D = hv w w w w2 w2 w2 An example motivated by A4 M = M0 diag (1, 1, 1)

39. Cancellation and perturbations Perturbations of the symmetric structure J. Kersten, A.S. in progress T. Underwood non-zero usual neutrino mass negligible consequences for HE (LHC) physics Neutrino mass generation and HE physics ``decouple’’ Indirect relation: imprinted Simple perturbations  correlation of light neutrino properties and heavy leptons Pattern of neutrino mass and mixing reflects features that lead to cancellation,  maximal 2-3 mixing and zero 1-3 mixing

40. Summary Status: ``standard’’ model of neutrino mass and mixing – further confirmations/checks. Deviations? ? ti-bimaximal mixing; possible presence of special leptonic (neutrino) symmetries Q-L complementarity: bi-maximal mixing and Q-L symmetry/unification Real or accidental? GUT + flavor (ultimate unification?): string inspired framework with extended singlet sector, non-renormalizable interactions ? Can LHC help?

41. Launch with non-stop flight to great success!