Origins of Neutrino Masses and Mixing: Exploring the Theory Landscape

1. Part 1 Theory of n - masses and mixing A. Yu. Smirnov Max-Planck Institute fuerKernphysik, Heidelberg, Germany Pontecorvo School 2019, Sinaia, Romania, September 2, 3, 2019

2. Lepton mixing: n1 ne nm n2 What is behind? nt n3 A. Yu. Smirnov Max-Planck Institute for Nuclear Physics, Heidelberg, Germany

3. Dm412 = 1 - 2 eV2 R. Davis in 80ies: “Models of neutrino masses are so numerous that they can compose the Dark Matter in the Universe” LSND This can not be true: with present number of models the Universe would be overclosed many times contradicting observations • Davis’s remark on n models- DM connection has new turn now: • - joint models of neutrino masses and dark matter • understanding neutrino properties can steam from the Dark sector of theory or • neutrino mass can be sourced by DM

4. “Theory” Landscape Multi dimensional Scanning Models Symmetry Schemes Models effective Schemes Models Schemes Schemes Schemes Ideas Classifications Ideas Schemes Operators Operators Schemes Mechanisms Operators Induced Operators Schemes Operators Operators Schemes Mechanisms Models symmetry Mechanisms Mechanisms Mixing Models Models Mechanisms Models Conjectures Models Models Conjectures Models Schemes Schemes Partial Models Schemes Schemes Ideas Models Schemes Models Anarchy Schemes Models Schemes Models effective Models effective Principles effective Anarchy & codes Intermediate GUT Planck PeV LHC sub-eV EW Extra D Mass scales

5. What is the problem? No theory of flavor, in general No theory of quark masses and mixing No physics BSM has been discovered yet at LHC … Especially no SUSY  UV completion issue. What is the hope? Less ambitious: Neutrinos are the key Understand at least the difference of neutrino mass and mixing from quark mixing and masses It is the neutrino that sheds the light on all these problems

6. 3n - paradigm What we really know All well established/confirmed results fit well a framework - three neutrinos - with interactions described by the standard model - with masses and mixing - negligible feedback of neutrino mass generation on the standard model

7. The theory? 1 S. Weinberg LLHH L Violation of universality, Unitarity? Large scale of new physics h LnR H or maybe: With very small coupling h <<< 1 That’s all? Will we learn more?

8. Outline I. Data and interpretation: bottom-up II. Origins of n - mass and mechanisms of generation III. Mixing and flavor symmetries IV. Models of neutrino mass. Connections

9. Dm412 = 1 - 2 eV2 I. Data and LSND interpretation bottom-up Definitions and parameterization

10. Dirac and Majorana masses Dirac mass term - mDnRnL+ h.c. charge conjugate Instead of independent RH component nR nLC nLC = C (nL)T C = ig0 g2 - ½ mLnLTCnL+ h.c.  two component massive neutrino corresponds to Majorana neutrino: nM= nL + e-ianLC nMC= eianM a is the Majorana phase - ½ mMnMnM = - ½ mMeianLTC nL+ h.c. nLeianL No invariance under Lepton number of the mass operator: L = 2 and -2 (for h.c.) mass term violates lepton number by |DL| = 2 Processes with lepton number violation by |DL| = 2 with probabilities bbon G ~ mL2

11. Vacuum mixing nf = UPMNS nm n1 n2 n3 ne nm nt Ue1Ue2 Ue3 Um1 Um2Um3 Ut1Ut2Ut3 = SM definition of flavor states may differ from ‘’physical’’ ones, if e.g. … New heavy neutral leptons mix with neutrinos Physical flavor states produced e.g. in beta, pion, muon decays depend on kinematics of the process

12. Mixing ne Dual role nm nt |Um3|2 |Ut3|2 n3 |Ue3|2 mass |Ue2|2 n2 n1 |Ue1|2 nt nm ne Flavor content of mass states Mass content of flavor states nmass= UPMNS +nf nf = UPMNSnmass

13. Standard parametrization IM Id = diag (1, 1, eid) UPMNS = U23Id U13I-d U12 Dirac phase matrix 1 0 0 0 c23 - s23 0 -s23 c23 c13 0 s13e-id 0 1 0 -s13eid 0 c13 c12 s12 0 -s12 c12 0 0 0 1 IM ia21 /2 ia31 /2 IM = diag (1, e , e ) - matrix of Majorana phases Not unique parametrization Convenient for phenomenology, especially for oscillations in matter Insightful for theory?

14. Mixing angles ne nm nt Mixing parameters |Um3|2 |Ut3|2 n3 tan2q12 =|Ue2|2 / |Ue1|2 |Ue3|2 sin2q13 = |Ue3|2 MASS2 tan2q23 = |Um3|2 / |Ut3|2 Dm231 |Ue2|2 n2 Dm221 n1 Mixing matrix: |Ue1|2 nf = UPMNSnmass FLAVOR Normal mass hierarchy n1 n2 n3 ne nm nt = UPMNS Dm231 = m23 - m21 Dm221 = m22 - m21 Mixing determines the flavor composition of mass states UPMNS = U23Id U13I-d U12

15. ne Mass Ordering nm nt n3 n2 Dm221 n1 MASS2 MASS2 Dm223 Dm232 n2 Dm221 n1 n3 FLAVOR FLAVOR Inverted mass ordering Normal mass ordering

16. Measurements MINOS T2K NOvA MSW-effect Solar neutrinos 2 D KamLAND m Double Chooz q Daya Bay RENO NEOS Atmospheric Oscillations Can be resonantly enhanced in matter neutrinos SK Antares DeepCore

17. Oscillations and masses Oscillations and adiabatic conversion test the dispersion relations and not neutrino masses nR nL nL pi = Ei2 – mi2 x x m m In oscillations: no change of chirality, so e.g. V, A interactions with medium can reproduce effect of mass. Also interactions with scalar fields It is consistency of results of many experiments in wide energy ranges and different environment: vacuum, matter with different density profiles that makes explanation of data without mass almost impossible. Kinematical methods: distortion of the beta decay spectrum near end point - KATRIN proof of non-zero neutrino mass Neutrinoless double beta decay Cosmology, Large scale structure of the Universe

18. Probing Nature of neutrino mass Determination of masses, mass squared differences from processes at different conditions Searches for dependence of mass on external variables: Vacuum – media with different densities, fields Solar – KamLAND: Dm212 2-3 mixing: T2K - NOvA Energies (in medium, or if Lorentz is violated) Epochs (red shifts) MAVAN Momentum transfer Virtuality: On shell – off shell Neutrinoless Double beta decay – unique?

19. Global 3nu analysis Esteban, Ivan et al. arXiv:1811.05487 [hep-ph] NuFIT 4.1 (2019), www.nu-fit.org Δχ2 profiles minimized with respect to all undisplayed parameters. The red (blue) curves correspond to Normal (Inverted) Ordering. Solid (dashed) curves are without (with) adding the tabulated SK-atm Δχ2. Mass-squared splitting: Dm312 for NO and Dm312 for IO

20. Global 3nu analysis Esteban, Ivan et al. 1811.05487 [hep-ph] NuFIT 4.1 (2019), www.nu-fit.org The two-dimensional projection of the allowed six-dimensional region after minimization with respect to the undisplayed parameters. The regions in the four lower panels are obtained from Δχ2 minimized with respect to the mass ordering. Contours correspond to 1σ, 90%, 2σ, 99%, 3σ CL (2 dof). Coloured regions (black contour curves) are without (with) adding the tabulated SK-atm Δχ2.

21. Summarizing results Data are in a very good agreement with 3n framework Data are internally consistent within error bars Over determined: different experiments are sensitive to the same parameters Some tensions: Solar vs. KamLAND OK within experimental uncertainties - CP-phase: best fit value deviates from 3p/2, p and 3p/2 are equally plausible. - Mass ordering: NO is favored by 2 – 3 s, Dc2 = 7.5 - Deviation of 2-3 mixing from maximal at 1.5s , second (high) octant is preferable UNKNOWNS: LSND, MiniBooNE, Reactor, Gallium: Oscillations into steriles, new interactions, new particles – can dramatically affect our considerations ANOMALIES:

22. bb0n – decay results mbb= Ue12 m1 + Ue22 m2 eia + Ue32 m3 eif p n Approaching the IO horizontal band W e n mbb x e W n p 90% CL upper bound on mbb depending on NME KamLAND-Zen (61 – 165) meV A.Gando, et al, 1605.02889 [hep-ex] G. Anton et al. 1906.02723 [hep-ex] EXO-200 (93 − 286) meV CUORE (110 − 520) meV S. Dell'Oro et al. 1905.07667 [nucl-ex] GERDA (110 − 260) meV

23. Bounds on masses Allowed regions at 2σ (2 dof) obtained by projecting the results of the global analysis of oscillation data (w/o SK-atm) over the plane (Σmν, mee). The region for each ordering is defined with respect to its local minimum Cosmology: Si mi < 0.12 - 0.26 eV Loureiro et al, 1811.02578 [astro-ph.C0]

24. Observations and Implications What these results show, hint? Regularities? Relations?

25. 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 and 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 gap 103 100 1012 106 10-3 109 mass, eV

26. Neutrino Mass Ordering Accidental: selection of values of parameters Fundamental: principle, symmetry Quasi-degenerate symmetry Correlation of masses of neutrinos and charged leptons in weak interactions: Light likes light, heavy – likes heavy m2 m3 Dm m Dm212 2 Dm322 Dm212 Dm322 ~ = 0.18 ~ = 1.6 10-2 the weakest hierarchy m2 m3 but 1-2 mixing strongly deviates from maximal q ~ Similar to quark spectrum rescaling Pseudo-Dirac + 1 Majorana See-saw Flavor symmetries Quark-lepton symmetry Broken Le – Lm – Lt symmetry Unification

27. l Mass hierarchies at mZ up down charged neutrinos quarks quarks leptons 1 m2 m3 > Dm212 Dm322 10-1 ~ 0.18 10-2 Neutrinos have the weakest mass hierarchy (if any) among fermions mass ratios 10-3 10-4 Related to large lepton mixing? Koide relation 10-5 mumt = mc2 sinqC ~ md/ms Gatto–Sartori-Tonin relation

28. TBM mixing: zero order approximation? As the reference point L. Wolfenstein 2/3 1/3 0 - 1/6 1/3 - 1/2 - 1/6 1/3 1/2 P. F. Harrison D. H. Perkins W. G. Scott Utbm = n3 is bi-maximally mixed n2is tri-maximally mixed sin2q12= 1/3 Utbm = U23(p/4) U12(q12) - maximal 2-3 mixing - zero 1-3 mixing - no CP-violation Uncertainty related to sign of 2-3 mixing: q23 = p/4  - p/4

29. Mixing and mass matrices Origin of mixing: off-diagonal mass matrices Ml = Mn Mixing matrix Diagonalization: Mass spectrum for Majorana neutrinos Mn = UnLmndiagUnLT Ml = UlLmldiagUlR+ mndiag= (m1, m2, m3) mldiag= (me, mm, mt) l gm(1 - g5) UPMNSnmass CC in terms of mass eigenstates: UPMNS= UlL+ UnL Flavor basis: Ml = mldiag UPMNS = UnL

30. The TBM- mass matrix Mixing from diagonalization of mass matrix in the flavor basis mTBM = UTBMmdiag UTBMT mdiag = diag (| m1|, |m2|ei2a, |m3|e i2b) a b b … ½(a + b + c) ½(a + b - c) … … ½(a + b + c) mTBM = c = m3 a = (2m1 + m2)/3, b = (m2 – m1)/3, The matrix has S2 permutation symmetry nm<->nt Mixing is determined by relations between the matrix elements: m12= m13 m22= m33 m11+ m12 = m22 + m23 Eigenvalues –by absolute values of elements

31. Deviations & observations bf Certain hierarchy of deviations = additional rotations Deviations from TBM d (sinq12 ) = - 0.017 |d (sinq23 )| = 0.035 d (sinq13 ) = sinq13 = 0.15 Problematic for a number of models, require further assumptions/ complications Deviation from maximal 1-2 mixing: d (sinq12 ) = 0.15 d (sinq12 ) = d (sinq13) = sinq13 1-3 mixing is in agreement with prediction qCCabibbo angle q13~ ½qC sin2q13~ ½sin2qC

32. Leptons versus quarks Quarks Leptons n3 t mass mass n2 c n1 u nf = UPMNSnmass Ud = VCKM+ U U = (u, c, t) Mixings of quarks and leptons are strongly different but still related q12l + q12q ~ p/4 Sum up to maximal mixing angle kind of complementarity Observation: q23l + q23q ~ p/4

33. Quark-lepton complementarity based on relations: A.S. M. Raidal H. Minakata ql12 + qq12 ~ p/4 ql23 + qq23 ~ p/4 ``Lepton mixing = bi-maximal mixing – quark mixing’’ Implications Grand Unification or family symmetry Quark-lepton symmetry Existence of structure which produces bi-maximal mixing See-saw? Properties of the RH neutrinos

34. Bi-maximal mixing Another zero order reference structure F. Vissani V. Barger et al ½ ½ -½ ½ ½ ½ -½ ½ 0 Ubm = Two maximal rotations • - maximal 2-3 mixing • - zero 1-3 mixing • maximal 1-2 mixing • - no CP-violation Ubm = U23m U12m

35. In general: lepton mixing The data are in very good agreement with the ansatz UPMNS= UCKM+ UX UX= UTBM or UBM UCKM+ = VCKM This reproduces QLC approximately can be realized in the seesaw type I gives prediction for 1-3 mixing

36. 13-mixing sinq13~ ½ sinqC Phenomenological level C. Giunti, M. Tanimoto From QLC (Quark-Lepton Complementarity) H. Minakata, A Y S S. F. King et al From TBM-Cabibbo scheme Now accuracy of measurements permits detailed comparison

37. Experimental status F. Capozzi, et al. Prog.Part.Nucl.Phys. 102 (2018) 48, arXiv:1804.09678 [hep-ph] From global fit for sin2 qC 0.04 0.03 0.02 0.01 ~ 20% deviation in sin2q13 can be due to deviation of q12l fromqC sin2q13 Renormalization (RGE) effects from GUT scales to low energies 0.03 0.04 0.05 0.06 0.07 sin2q23 sin2q13 = sin2q23 sin2qC (1 + O(l2)) lines: predictions from QLC

38. Implications Quarks and leptons know about each other, Q L unification, GUT or/and Common flavor symmetries Some additional physics is involved in the lepton sector which explains smallness of neutrino mass and difference of the quark and lepton mixing patterns

39. But may be … 1-3 mixing of different origin ``Naturalness’’: absence of fine tuning of mass matrix Connecting solar and atmospheric neutrino sectors E. K. Akhmedov, G.C. Branco, M.N. RebeloPhys.Rev.Lett. 84 (2000) 3535, [hep-ph/9912205] Dm212 Dm322 sin2q13 = O(1) 0.75 Very small 1-3 mixing would be something special (symmetry) Yet another “normal” relation: almost the same relation in the quark and lepton sectors sin2q13 = C sin2q12sin2q23 K. Patel, A. Y. S. Cq = 0.380 +/- 0.020 Cl = 0.407 +/- 0.033 Similar structure of the mass matrices Abelian symmetry

40. Dm412 = 1 - 2 eV2 II. Mechanisms LSND of neutrino mass generation Nature of is the neutrino mass of the same origins as masses of other particles? neutrino mass

41. Two aspects Similar to cosmological constant Smallness: Finite value Suppression wrt. the EW scale Mechanisms unrelated to suppression of usual Dirac masses Why there is no usual scale Dirac masses? Seesaw type II No RH component  Dirac mass can not be formed Radiative mechanisms symmetry • See-saw or multi-singlet mechanisms • - suppression only • finite contribution • negligible see-saws type-I does both things simultaneously: incomplete suppression

42. D5 operator S. Weinberg If no new particles at the EW scale, after decoupling of heavy degrees of freedom  set of non-renormalizable operators 1 L L L H H H H x n n

43. Neutrino mass and EW Symmetry breaking x Higgs doublet H Dirac mD = h <H> > > nL nR x D Higgs triplet mL = f <D > Majorana > < Elementary or composite operator with IW = 1 nL nL x x H H mL = f <H> <H> > < nL nL

44. Origins of (finite) mass x x Hard mass related to the EW scale H H Gauge invariance small effective coupling n n small induced VEV formed by large VEV’s (seesaw II) x … VEV created at small scales Soft mass x x x D melting at T ~ VEV Environment dependent masses; relic neutrinos MAVAN n n x … Gravitationally induced mass x x Melting couplings Similarly for Dirac neutrinos

45. P. Minkowski T. Yanagida M. Gell-Mann, P. Ramond, R. Slansky S. L. Glashow R.N. Mohapatra, G. Senjanovic See-saw Type 1 x H H x mn n MR > x < Y Y mD = Y<H> mD S T S T n n N MR Type 3 ( SU(2) triplet intermediate state) R Foot, H Lew, X G He, G C Joshi Mass matrix: n N mn = - mDTMR-1mD if MR >> mD 0 mD mDT MR n N MR ~ 1014GeV

46. 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 ~ log (q /MR) Cancellation? New physics below Planck scale Small Yukawas, Leptogenesis ? “Partial” SUSY? MR < 107GeV

47. Planck-scale lepton number violation A Ibarra,et al 1802.09997 [hep-ph] M2 ~ MPl H L N2 x N1 N2 N1 H L 4 Y12 Y22 (16 p2)2 M1 ~ M2 ~ 1014GeV Log M2 / MPl

48. See-saw type-II H M. Magg and C. Wetterich G. Lazarides, Q Shafi and C Wetterich R. Mohapatra, G. Senjanovic, H f D Seesaw for VEV’s: hD <D> = <H>2 f/MD2 n n mn = hD <D > = h f <H>2 /MD2 Natural smallness of VEV Light triplet?

49. Double Seesaw Three additional singlets S which couple with RH neutrinos Beyond SM: many heavy singlets …string theory n nc S 0 mDT0 mD0 MDT 0 MDm R.N. Mohapatra J. Valle m= MS m- scale of B-L violation mn = mDTMD-1T mMD-1mD violation of universality, unitarity massless neutrinos m= 0 lower the scales of neutrino mass generation m<< MD Inverse seesaw explains intermediate scale for the RH neutrinos Cascade seesaw m>> MD M ~ MGU2/MPl ~ 10-14 GeV m ~ MPl, M ~ MGU

50. Screening of Dirac structures A.Y.S M. Lindner, M.A. Schmidt A.Y.S mn= dTMS d d = MD-1mD screening factor 1. Complete screening of the Dirac structure A = vEW/VGUT mD= A MD as a consequence of symmetry Light neutrino mass matrix is determined by the heaviest one MS d = A I mn = A2MS 2. Partial screening of the Dirac structure e.g. d = diag (a, 1, 1) d = diagonal mD, MD = diag Affect mixing d=U23max or Uw S belong to Hidden sector