of neutrino mass

1. The A. Yu. Smirnov R i Max-Planck Institute for Nuclear Physics, Heidelberg, Germany d NOW 2014 September 8– 13, 2014 d l e of neutrino mass

2. The riddle of neutrino mass: There is something hidden and beyond the standards which strongly suppresses badly confuses and mixes violates the law or maybe, does not violate the law which is difficult to prove and probably the first and the second are because of the third What is this?

3. New physics? Version adapted to physicist: what is behind of Smallness of neutrino mass in comparison to masses of the charged leptons and quarks 2. “Unusual” lepton mixing pattern with two large mixing angles (one is close to maximal) and one small which differs from the quark mixing 3. Weaker (or no) mass hierarchy than the hierarchy of charged leptons and quarks In general, what is the type of mass spectrum and mass ordering?

4. and connected questions: Nature of neutrino mass are they of Dirac or Majorana type? are they “hard” or “soft” (medium dependent)? Recall that in oscillation experiments we probe dispersion relations and not masses immediately Effective neutrino masses in oscillation experiments in beta decay in cosmology and bb-decay can be different Does the nature of neutrino mass differ from the nature of the quarks and charged lepton masses? Usual neutrino masses can be strongly suppressed, e.g. by the seesaw, so that ”unusual contributions” dominate Are sterile neutrinos (if exist) relevant for the solution ?

5. Content: 1. Challenging the riddle 2. Scales of new physics 3. Mixing and CP-violation 4. Steriles – the key? 5. Some guesses

6. Challenging the riddle are we asking right questions? do we interpret the data correctly?

7. The riddle and the solution It is not excluded that the correct solution (or the key to the solution) already exists among hundreds of approaches, models, mechanisms, schemes, etc. Still something fundamental can be missed The problem is then to identify the correct solution

8. Smallness of mass? comparing within generation: Special m3 mt Similar for other generations if spectrum is hierarchical ~ 3 10-11 Neutrinos: no clear generation structure as well as the correspondence light flavor – light mass, especially if the mass hierarchy is inverted or spectrum is quasi-degenerate Normal? me mt m3 me ~ 3 10-6 ~ 3 10-6 due to neutrality of neutrinos? ? gap 103 100 1012 106 10-3 109 mass, eV

9. Leptons & quarks The riddle is formulated as comparison with masses (and mixing) of quarks There is no solution of the riddle of quark masses Can we solve the neutrino mass riddle? Do efforts make sense? Yes, if we still hope (as it was before) that neutrinos will uncover something simple and insightful which will allow to solve the quark mass riddle neutrino mass generation and generation of the charged lepton and quark masses are independent Higgs triplet Radiative mechanisms Seesaw type III, etc. we will try to explain the difference of masses and mixing of neutrinos and quarks, and not masses and mixing completely

10. Masses and mixing Should mixing be included in the riddle? Quarks Leptons Relation between masses and mixing Maximal mixing - quasi- degenerate mass states ? md ms Tri-Bi-Maximal mixing (TBM) sinqC~  no connection between masses and mixing (at least in the lowest order) In 3 generations: Fritzschansatz Realized in the residual symmetry approach Form invariance of the mass matrices

11. Mixing: quarks and leptons Completely related Largely unrelated Partially related with the only difference that originates from Majorana nature of neutrinos, symmetries Higgs triplet Seesaw type I, Quark-lepton unification Radiative mechanisms GUT, seesaw type II Seesaw type II and III

12. The riddle and Dark Universe Neutrino mass riddle Dark Matter Riddle Dark radiation Dark Energy Riddle Solution may come from unexpected side Baryon asymmetry in the Universe Inflation

13. The riddle and scales of New Physics The riddle of new physics

14. A guess Two types of new physics Neutrino new physics CKM type additional structures in lepton sector such as the see – saw common for quarks and leptons responsible for small quark mixing and hierarchical structure of the Dirac masses responsible for smallness of neutrino mass and large lepton mixing These two types are different but probably should somehow “know” about each other Counter example, seesaw with degenerate RH neutrinos does not work in this framework

15. 28 orders of magnitude Scales GUT - Planck High scale seesaw Quark- lepton symmetry /analogy GUT of new mass VEW2 mn physics Low scale seesaw, radiative mechanisms, RPV, high dimensional operators Electroweak – Unification LHC Looking under the lamp Scale of neutrino masses themselves Relation to dark energy, MAVAN? eV- m n sub-eV Neutrino mass itself is the fundamental scale of new physics Spurious scale?

16. High scale seesaw, unification 1 MR mn = - mDTmD q – l similarity: mD~ mq ~ ml MGUT ~ 1016GeV for the heaviest in the presence of mixing MGUT2 MPl MR ~ 108 - 1014GeV double seesaw 1016 - 1017GeV many heavy singlets (RH neutrinos) …string theory N ~ 102 In favor Gauge coupling unification BICEP-II ? Leptogenesis

17. High scale seesaw, unification Natural, minimalistic, in principles Neutrality, zero charges Realizes relations: Majorana Nature Smallness of mass – high mass scale Large mixing Partial relation of the quark and neutrino properties T. Higaki et al, arViv:1405.0013 “Neutrinoful Universe” Seesaw sector is responsible for inflation (scalar which breaks B-L and gives masses of RH neutrinos), dark matter, leptogenesis Fine tuning - Proton decay - Majorana masses Testable?

18. High scale line: the problem Simplest seesaw implies new physical scale << MPl MR ~ mD2/mn ~ 1014GeV (Another indication: unification of gauge couplings) nR F. Vissani hep-phl9709409 nL H H J Elias-Miro et al, 1112.3022 [hep-ph] nR y2 (2p )2 dmH2 ~ MR2 log (q /MR) M. Fabbrichesi MR3mn (2p v)2 Cancellation? ~ log (q /MR) AYS New physics below Planck scale Small Yukawas, Leptogenesis ? “Partial” SUSY? MR < 107GeV

19. EW – LHC scale - No hierarchy problem (even without SUSY) - testable at LHC, new particles at 0.1 – few TeV scale - LNV decays Small VEV Low scale seesaw Radiative Higgs Triplet 0ne loop nMSM New Higgs doublets Two loops L-R Low scale Three loops Rp-SUSY Neutralino as RH neutrino Inverse seesaw High dimensional operators Connection to Dark Matter Radiative seesaw

20. nMSM M. Shaposhnikov et al Everything below EW scale  small Yukawa couplings L R • - generate light • mass of neutrinos • generate via oscillations • lepton asymmetry • in the Universe • can be produced in • B-decays (BR ~ 10-10 ) Few 100 MeV – GeV very small split BAU split ~ eV very small mixing WDM 3 - 10 kev - warm dark matter - radiative decays  3.5 kev line RH neutrino? Normal Mass hierarchy Higgs inflation EW seesaw Nothing new below Planck scale

21. eV - sub eV scale physics - new scalar bosons, majorons, axions, - new fermions (sterile neutrinos, baryonic nu) , - new gauge bosons (e.g. Dark photons) Very light sector which may include M. Pospelov Maybe related to Dark energy, MAVAN Generate finite neutrino masses, usual Dirac masses can be suppressed by seesaw with MR = MPlor multi singlet mechanism eV scale Seesaw with RH neutrinos for sterile anomalies LSND/ MiniBooNE .... A. De Gouvea 5th force searches experiments Tests: Modification of dynamics of neutrino oscillations Checks of standard oscillation formulas, searches for deviations

22. Mixing and CP-violation

23. In a spirit two types of new physics and partial relations PMNS & CKM C. Giunti, M. Tanimoto UPMNS= VCKM+ UX H. Minakata, A Y S From charged leptons or Dirac matrices of charged leptons and neutrinos Related to mechanism of neutrino mass generation New neutrino structure CKM type new physics Related to (any) mechanism that explains smallness of neutrino mass In general, has similar hierarchical structure determined (as in Wolfensteinparametrization) by powers of Should be fixed to reproduce correct Lepton mixing angles l = sinqC UX ~ UTBM VCKM ~ I

24. Prediction: q13 ~ ½ qc Pheno. level C. Giunti, M. Tanimoto H. Minakata, A Y S ………………………………. can be obtained in the context of UPMNS= VCKM+ UX if UX =U23(p/2) U12 Realized in QLC (Quark-Lepton Complementarity) e.g. UX= UBM, UTBM TBM-Cabibbo scheme S. F. King et al U12(qc) U23(p/2) permutation - to reduce the lepton mixing matrix to the standard form leads to q13~ ½ qc sin2q13~ ½sin2qC

25. The same value with completely different implications 1-3 mixing implications relation Quark-Lepton Complementarity GUT, family symmetry, … ~ ½sin2qC Dm212 Dm322 ``Naturalness’’, absence of fine tuning of mass matrix O(1) sin2q13 Analogy with quark mixing relation ¼ sin2q12sin2q23 ? ~ ½cos2 2q23 universal nm- nt– symmetry violation q13 = 21/2(p/4- q23) Eby,Frampton, Matsuzaki > 0.025 Mixing anarchy

26. CP-phase prediction UPMNS~ VCKM+ UX No CPV If the only source of CP violation B. Dasgupta, A.S. sinq13 sin dCP = (-cosq23) sinq13qsindq l3 dq = 1.2 +/- 0.08 rad l sin dCP ~ l3/s13 ~ l2 ~ 0.046 where d = (s13q /s13) c23sin dq dCP ~ - d or p + d If the phase dCP deviates substantially from 0 or p, new sources of CPV beyond CKM should exists (e.g. from the RH sector) or another framework New sources may have specific symmetries or structures which lead to particular values of dCP e.g. -p /2, and q - l unification will give just small corrections

27. In general neglecting terms of the order ~ l3 sin dCP = s13-1 [sin(am+ dX)Vud|Xe3| – sin ae |Vcd|Xm3 ] here am, dX and ae are parameters of the RH neutrinos Some special values ofdCP can be obtained under certain assumptions if Xe3 = 0 we have sin dCP ~ – sin ae dCP ~ 3p/2 ifae = p /2 One can find structure of the RH sector which lead to these conditions

28. In the Seesaw type I B Dasgupta A.S mDn ~ mDq Ux is the matrix diagonalizes MX= - mDdiagUR+ (MR)-1 UR*mDdiag Here mD= UL(mDdiag) UR+ In contrast to quarks for Majorana neutrinos the RH rotation that diagonalizesmD becomes relevant and contributes to PMNS UX= UR US CPV from U In the LR symmetric basis R From seesaw Minimal extension is the L- R symmetry: UR = UL ~ VCKM* and no CPV in MR Seesaw can enhance this small CPV effect so that resulting phase in PMNS is large

29. A guess Quark-lepton universality Vub = ½ VusVcb sinq13 ~ ½ sinq12 sinq23 The same relations between coupling strength between generations Similar structure of mass matrices but with different expansion parameter ll= 1 -lq Realization: FritzschAnzatzsimilar to quark sector, RH neutrinos with equal masses Normal mass hierarhy, relation between masses and mixing Expectations: Flavor alignment in mass matrix

30. Steriles is the key?

31. ns New neutrino states mixing dm ~ qaS2mS qaS2 1 MeV • Warm Dark • matter • Pulsar kick (1 – 2) 10-8eV 2 10-11 5 - 10 keV 1 keV • - LSND, MB • Reactor • Ga anomalies • - Extra radiation 0.02 eV 1 eV 0.02 0.5 - 2 eV 10-6eV 10-3 (2 – 4) 10-3eV - Solar neutrinos - Extra radiation in the Universe 10-3eV Compare with large elements of the mass matrix 0.02 eV

32. Effect of sterile neutrinos on the 3n structure mn = ma + dm Original active mass matrix e.g. from see-saw Induced mass matrix due to mixing with nu sterile ma =0.025 eV Decouples from generation of the light neutrino masses argument that this is not RH neutrino but has some other origin dm << ma For keV Not a small perturbation dm ~ ma For eV dm can change structure (symmetries) of the original mass matrix completely be origin of difference of and VCKM UPMNS can be be considered as very small perturbation of the 3n system For meV dm << ma

33. New physics: neutrino portal New structure (but physics is the same) Through this portal neutrino gets mass 1 Ln(F)- 3/2 L H F where F is the fermionic operator s nR S nR is the key to the solution of the riddle? nL S H s S s S Neutrino new physics S Scale symmetries S S s

34. Some guesses

35. Two different types of new physics are involved in explanation of data: the CKM type common to quarks and leptons and physics responsible for smallness of neutrino mass and large lepton mixing. The latter may have certain symmetries It makes sense to identify the second one which explains the difference between the quarks and leptons Still generation of quark and neutrino masses can be essentially independent High (GUT) scale new physics: still appealing EW scale: see LHC14 results Sub eV –eV scale: interesting, worth to explore New neutrino physics may have certain symmetries which leads to specific values of mixing angles and CP phase. Phase from CKM part is strongly suppressed Sterile neutrinos may be the key to solution to a riddle

36. and your solution to the riddle?