A. Yu. Smirnov International Centre for Theoretical Physics, Trieste, Italy Institute for Nuclear Research, RAS, Moscow, Russia

``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 B. Pontecorvo

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 The main results: 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. of studies of neutrino mass and mixing is essentially over

 12 o = /- 1.3 M.C. Gonzalez-Garcia, M. Maltoni, Moriond, March 2007 (Phys. Rep.)  (3  )  23 o = 43.3 small shift from maximal mixing  13 o = b.f. value is zero; stronger upper bound 0.81 – – – – – – – – 0.80 Mixing matrix (moduli of matrix elements) very good agreement with other fits U PMNS = The angles 90 % C.L.

 12 Fogli et al Strumia-Vissani 33 22 11 SNO (2 ) QLC l tbm QLC  12  +  C ~   /4 90% 99% U tbm = U tm U m 13 U QLC1 = U C U bm Give the almost same 12 mixing 33 11 Gonzalez-Garcia, Maltoni  /4 -   C

sin 2  13 Fogli et al Strumia-Vissani 33 22 11 T2K 90% 99% Double CHOOZ CC  m 21 2 /  m 32 2 * Non-zero central value (Fogli, et al): Atmospheric neutrinos, SK spectrum of multi-GeV e-like events QLC QLC l Gonzalez-Garcia, Maltoni 33 11 * MINOS lead to stronger the bound on 1-3 mixing (G-G, M.)

sin 2  23 Fogli et al 33 22 11 T2K SK (3  one mass scale) 90% QLC * in agreement with maximal, though all complete 3 - analyses show shift * shift of the bfp from maximal is small * still large deviation is allowed: (0.5 - sin 2  23 )/sin  23 ~ 40%22 maximal mixing Gonzalez-Garcia, Maltoni, A.S. SK: sin 2 2  23 > 0.93, 90% C.L. QLC l 11 33 Gonzalez-Garcia, Maltoni, 2007

 m 31 2 = 2.74 x eV 2 MINOS: (1  ) in future: tension with SK? new physics?  m 31 2 = 2.6 +/- 0.2 (0.6) x eV 2 Global fit: p.o.t.  m 21 2 = 7.90 x eV M. Gonzalez-Garcia, M. Maltoni, 2007 |m 2 /m 3 | > 0.18the weakest mass hierarchy Cosmology:  i m i < 0.42 eV (95% C.L. )  i m i < 0.17 eV (95% C.L. ) U. Seljak et al m ~ 0.05 – 0.10 eVAt least for one neutrino: Heidelberg-Moscow: m ee = 0.24 – 0.58 eV if confirmed, other than light neutrino Mass mechanism? S. Hannestadt < 0.6 eV

MINOS: results 2 years data taking (double statistics) SNO: results of the third phase: He counters  m 2 = ( ) x eV 2 Improvements of the 1-2 mixing determination U e2 KAMLAND: update + calibration Improvement of sensitivity to 1-2 mixing comparable to solar neutrino sensitivity MiniBooNE: oscillation results Tests of LSND, overall picture of mass and mixing BOREXINO CNGS

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

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. How inclusion of these neutrinos affect standard neutrino model? Small perturbations Strong changes? M. Shaposhnikov

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

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

Exchange by very light scalar in the context of MaVaN scenario m  ~ eV L R fLfL fRfR  f = e, u, d, m soft =  f  n f /m  generated by some short range physics (interactions) EW scale VEV chirality flip – true mass: m vac  m vac + m soft f 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 medium and energy dependent mass In the evolution equation: f ~  /M Pl Are neutrino masses usual?

M 3 ~ M GUT Problem of unification: difference of mass and mixing patterns Origin of difference: seesaw? FUT + flavor symmetry – even more complicated EW scale? kev-scale mechanisms? M. Shaposhnikov R. Mohapatra With many O(100) RH neutrinos W. Buchmuller, M. Ratz et al

Large mixing is related to weak mass hierarchy of neutrinos No-symmetry Have different implications

P. F. Harrison D. H. Perkins W. G. Scott U tbm = U 23 (  /4) U 12 - maximal 2-3 mixing - zero 1-3 mixing - no CP-violation U tbm = 2/3 1/ /6 1/3 1/2 1/6 - 1/3 1/2 2  is tri-maximally mixed 3 is bi-maximally mixed sin 2  12 = 1/3 immediate relation to group matrices? In flavor basis… relation to masses? No analogy in the Quark sector? Implies non-abelian symmetry L. Wolfenstein Clebsch-Gordan coefficients

U tbm = U mag U 13  4) U mag = 1   1     = exp (-2i  /3) Relation to masses? No analogy in the quark sector? Unification? Symmetry: A4A4 symmetry group of even permutations of 4 elements representations: 3, 1, 1’, 1’’ tetrahedron T’, D 4, S 4,  (3n 2 ) … C.Hadedorn Other possibilities: Extended higgs sector, Auxiliary symmetries, Flavor alignment, Extra dimensions?

11  l   q 12   12  C = 46.5 o +/- 1.3 o A.S. M. Raidal H. Minakata H. Minakata, A.S. Phys. Rev. D70: (2004) [hep-ph/ ]  l   q 23   23  V  cb = 43.9 o + 5.1/-3.6 o 2-3 leptonic mixing is close to maximal because 2-3 quark mixing is small Qualitatively correlation: 1-2 leptonic mixing deviates from maximal substantially because 1-2 quark mixing is relatively large QLC- relations:

Quark-lepton symmetry Existence of structure which produces bi-maximal mixing Appears in different places of theory Mixing matrix weakly depends on mass eigenvalues In the lowest approximation: V quarks = I, V leptons =V bm m 1 = m 2 = 0 ``Lepton mixing = bi-maximal mixing – quark mixing’’

F. Vissani V. Barger et al U PMNS = U bm U bm = U 23 m U 12 m Two maximal rotations ½ ½ -½ ½ ½ ½ -½ ½ - maximal 2-3 mixing - zero 1-3 mixing - maximal 1-2 mixing - no CP-violation Contradicts data at (5-6)  level 0 U bm = As dominant structure? Zero order?

Leptons sin  12 = sin(  C ) + 0.5sin  C ( V cb ) In the symmetry basis V = V bm V l = V CKM V u = I V d = V CKM V PMNS = V l + V = V CKM + V bm V quarks = V u + V d = V CKM Quarks q-l symmetry sin  13 = sin  23 sin  C = 0.16 sin 2  12 = Seesaw? Predictions: D 23 = 0.5 sin 2  C + cos 2  C V cb cos  = / H. Minakata, A.S. large ! (or both rotations from neutrinos)

Leptons sin  sun ~ sin (  C ) V = V CKM + V l = V bm + V d = I V u = V CKM + V leptons = V bm V CKM + V quarks = V u + V d = V CKM Quarks q-l symmetry sin  13 = - sin  sun V cb = 0.03 ``Lopsided’’ H. Minakata, A.S. M. Raidal Predictions: D 23 = cos  sun V cb cos  < 0.03

Global fit: 0.53 – 0.58 (90% C.L.) tbm: Physical parameter QLC: – (depending on Majorana CP –phases) U e2 = cos  13 sin  12 U e2 RGE tbm QLC data RGE for tbm: A. Dighe, S. Goswami, W. Rodejohann hep-ph/ tbm: RGE   < for hierarchical nu  0.1 for degenerate nu

tan  m 1 /eV     m 1 /eV MSSM SM positive   M. A. Schmidt, A.S. hep-ph/ seesaw-I  bi-maximal mixing,m D ~ m u m l ~ m d

Maximal 2-3 mixing Small 1-3 mixing Tri-bimaximal mixing Q-L-complementarity Koide relation

M f = M 0 +  M f Determined by symmetry? f = u, d, l, corrections due to new interactions Planck scale effects… Fermion mass matrices What is zero order structure? What it should explain? - third generation masses mixing mixing The rest: from perturbations?

m e + m  + m  ( m e + m  + m  ) 2 Koide relation = 2/3 m i = m 0 (z i + z 0 ) 2  i z i = 0 z 0 =  i z i 2 /3 with accuracy tan  C = 3 m  - m e 2 m  - m  - m e Both relations can be reproduced if Y. Koide, Lett. Nuov. Cim. 34 (1982), 201 C A Brannen Neutrinos, hierarchical spectrum all three families are substantially involved!

* GUT * Existence of a number O(100) of singlets of SM and GUT symmetry group * Several U(1) gauge factors * Discrete symmetries * Heavy vector-like families * Incomplete GUT multiplets * Explicit violation of symmetry * Selection rules for interactions * Non-renormalizable interaction no simple relations between masses and mixing  can not be described in terms of a few parameters 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

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

- 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 16 F Singlet sector 16 H 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 C. Hagedorn M. Schmidt, A.S. in progress

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

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

Type III seesaw: x T + T = T 0 T - T0T0 S HH y y ~ M T ~ 100 GeV In SU(5): 24 F T, S y 5 F 24 F 5 H + y’/M 5 F 24 F 24 H 5 H EW production: Type I + Type III one usual neutrino is mass less B. Bajc G. Senjanovic M. Nemevsek P. Filiviez-Perez SU(2) triplet: T 0  W l,Decay:T 0  Z  ~ sec T 0  T + l - W + *  T + T 0,Z *  T 0  T 0  ~ (mixing) 2

(m i ) ab = - m  ai x m bi T 1Mi1Mi sin  ai = m  ai / M  i (m i ) ab = - sin  ai sin  bi M  i Single RH neutrino generate a contribution to neutrino mass matrix J. Kersten, A.S. (m i ) ab < 0.1 eV  ai < ( 10 GeV / M  i ) 1/2 negligible effect at HE colliders  ~ (  ai ) 2 If  ai ~ M ~ 1 GeV Cancellation at the level Bound from   e  Define mixing: Neutrino data: W. Buchmuller C. Greub, G. Ingelman, J. Rathsman A. Pilaftsis

For 2 and 3 RH neutrinos exact cancellation occurs if and only if 1. the Dirac mass matrix is singular 2. the Yukawa couplings and RH neutrino masses are related as Imply conservation of the lepton number and one decoupled heavy neutrino An example motivated by A 4 J. Kersten, A.S. y 1 ay 1 by 1 m D = m y 2 ay 2 by 2 y 3 ay 3 by 3 y 1 2 /M 1 + y 2 2 /M 2 + y 3 2 /M 3 = m D = hv        M = M 0 diag (1, 1, 1) J. Gluza

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

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