1 / 95

Neutrino Mass, Mixing, and Discrete Symmetries

This paper discusses the current status and implications of neutrino masses and mixing, as well as the race for determining the mass hierarchy and CP violation. It also explores the role of discrete symmetries in patterns of lepton mixing and the challenge posed by sterile neutrinos. The content includes global fits, relations and implications of mixing angles, flavor symmetries, and the matter effect on neutrino oscillations.

dchilds
Download Presentation

Neutrino Mass, Mixing, and Discrete Symmetries

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Neutrino mass, mixing and discrete symmetries A. Yu. Smirnov International Centre for Theoretical Physics, Trieste, Italy Discrete 2012 , IST , Lisboa , Portugal December 3– 7, 2012

  2. Content: 1. Masses, mixing, status & implications 2. Race for the mass hierarchy and CP 3. Discrete symmetries and patterns of lepton mixing 4. Sterile challenge

  3. 1. Masses and mixing: status & implications

  4. Global fit 1 G. L. Fogli et al, 1205.5354 Non-zero, relatively large 1-3 mixing Substantial deviation of the 2-3 mixing from maximal dCP ~ p Weak dependence on hierarch, mainly in 2-3 mixing quadrant

  5. Global fit 2 M. Gonzalez-Garcia, M Maltoni, J. Salvado, T. Schwetz Red – NH Blue - IH

  6. Global fit 3 D. V. Forero, M.Tortola, J. W. F. Valle , 1205.4018 v 4 solid- NH dashed - IH

  7. Gonzalez-Garcia et al, 1s m-t breaking QLC mass ratio Fogli et al, 1s Daya Bay, 1s RENO, 1s Double Chooz, 1s T2K 90% 0.0 0.010 0.020 0.030 0.040 sin2 q13 Measurements of 1-3 mixing

  8. Gonzalez-Garcia et al, 1s QLC Fogli et al, 1s MINOS, 1s SK (NH), 90% SK (IH), 90% 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 sin2 q23 Measurements of 2-3 mixing

  9. Relations & Implications sin2q13 ~ 0.025 The same 1-3 mixing with completely different implications Dm212 Dm322 ``Naturalness’’ of mass matrix O(1) Quark Lepton Complementarity GUT, family symmetry ~ ½ sin2qC sin2q13 = nm - nt - symmetry violation ~ ½cos2 2q23 Mixing anarchy > 0.025 q13 + q12 = q23 Self-complementarity

  10. q13~ ½qc First obtained in the context of Quark-Lepton Complementarity sin2q13~ ½sin2qC H. Minakata, A Y S Follows from permutation of matrices U12(qc) U23(p/2) From charged leptons Maximal from neutrinos Permutation - to reduce the lepton mixing matrix to the standard form Related to smallness of mass See-saw, symmetry of RH neutrino sector QLC Realizations:

  11. Quark-lepton universality? Vub= ½ VusVcb sinq13 ~ ½ sinq12 sinq23 The same coupling strength between generations Similar Ansatzfor structure of mass matrices FritzschAnzatzsimilar to quark sector RH neutrinos with equal masses Normal mass hierarhy, Right value of 13 mixing Relations between masses and mixing Flavor ordering in mass matrix

  12. Flavor alignment Values of elements gradually decrease from mtt to mee corrections wash out sharp difference of elements of the dominant mt-block and the subdominant e-line This can originate from power dependence of elements on large expansion parameter l ~ 0.7 – 0.8 . Another complementarity: l = 1 - qC Froggatt-Nielsen?

  13. Glimpses of CP and hierarchy Third way Neutrino-antineutrino asymmery Dependence of probabilities on energy in wide range Reconstruction of unitarity triangle Key measurement: amplitudes of the nm - nm oscillations due to solar and atmospheric mass splittings dCP ~ p for both hierarchies Atmospheric neutrino data, excess of the e-like events G. L. Fogli et al Do we have predictions for the phase in quark sector?

  14. M. Gonzalez-Garcia, M Maltoni, J. Salvado, T. Schwetz dCP ~ 3000 for bothhierarchies

  15. dCP ~ 0.8 pfor NH D. V. Forero, M.Tortola, J. W. F. Valle , 1205.4018 v 4 dCP ~ 0for IH NH IH

  16. 2. Race for hierarchy and CP Dm231  - Dm231 Discrete symmetry?

  17. ne Mass hierarchy (ordering) nm nt Normal hierarchy Inverted hierarchy Cosmology w32 n3 n2 bb-decay n1 wij= Dm2ij /2E w32 MASS w31 Mass states can be marked by ne - admixtures n2 n1 n3 w31 w31 > w32 w31 < w32 Fourier analysis Oscillations S. Petcov M. Piai D31 ~ 2D32 w Matter effect makes the e-flavor heavier changes two spectra differently

  18. Race for hierarchy Cosmology Matter effect Precise on 1-3 mixing measurements Sm of Dm2 at reactors Double beta mee Atmospheric decay Supernova neutrinos LBL neutrinos experiments Earth matter effect Energy spectrs PINGU INO NOvA Sterile neutrinos may help? NH  IH Neutrino beam Fermilab-PINGU(W. Winter) nu  antinu

  19. Supernova neutrinos and mass hierarchy Level crossing scheme Inverted hierarchy Normal hierarchy Dm2 (effective) the Earth matter effect – in the neutrino channel only the Earth matter effect in the antineutrino channel only Independently of possible collective effects

  20. Atmospheric neutrinos Oscillation physics with Huge atmospheric neutrino detectors Oscillations 2.7s ANTARES Oscillations at high energies 10 – 100 GeV in agreement with low energy data DeepCore Ice Cube no oscillation effect at E > 100 GeV

  21. Oscillograms contours of constant oscillation probability in energy- nadir (or zenith) angle plane 100 IceCube ne nm , nt NuFac 2800 0.005 CNGS 0.03 IC Deep Core Pyhasalmi 0.10 10 LENF E, GeV MINOS NOvA PINGU-1 HyperK T2K 1 T2KK 0.1

  22. Oscillogramsof the Earth E. Kh. Akhmedov, Razzaque, A.S. Oscillations test dispersion relation for neutrinos

  23. Precision IceCube Next Generation Upgrade PINGU ORCA

  24. IC, DeepCore and PINGU Digital Optical Module IceCube : 86 strings (x 60 DOM) 100 GeV threshold Gton volume Deep Core IC : - 8 more strings (480 DOMs) - 10 GeV threshold - 30 Mton volume PINGU: 18, 20, 25 ? new strings (~1000 DOMs) in DeepCore volume Existing IceCube strings Existing DeepCore strings New PINGU strings D. Cowen

  25. PINGU Geometry Precision IceCube Next Generation Upgrade PINGU v2 Denser array 20 new strings (~60 DOMs each) in 30 MTon DeepCore volume Few GeV threshold in inner 10 Mton volume Energy resolution ~ 3 GeV Existing IceCube strings Existing DeepCore strings New PINGU-I strings 125 m

  26. Nu-mu - events E. Akhmedov, S. Razzaque, A. Y. S. arXiv: 1205.7071 nm + n  m + h cascade muon track measurements EhEmqm  Em qm Eh reconstruction En = Em + Eh EhEmqm qn 105 events/year

  27. Hierarchy asymmetry Oscillations test dispersion relation for neutrinos Quick estimation of significance Stot ~ s n1/2

  28. Smearing the distributions E. Akhmedov, S. Razzaque, A. Y. S. arXiv: 1205.7071 Reconstruction of neutrino energy and angle Smearing with Gaussian reconstruction functions characterized by (half) widths ( sE , sq ) sE = A E n sq = B (mp / E n)1/2 Significance S tot = [Sij Sij2 ]1/2 Sij2 = [ NijIH - NijNH]2 / sij2 S = [ Sij Sij2 ] sij2 = NijNH + (f NijNH) 2 Systematics reduces significance by factor 2 Uncorrelated systematic error

  29. Smeared asymmetries sE= 0.2E sq ~ 1/E0.5 sq ~ 0.5/E0.5

  30. Smeared asymmetries sE= 2 GeV sq ~ 1/E0.5 sq ~ 0.5/E0.5

  31. Total significance S tot = [Sij Sij2 ]1/2

  32. Nu-tau contribution nt  t  m Background 5 – 7 %

  33. CP-violation Due to specific form of matter potential matrix (only Vee = 0) P(nenm) = |cos q23Ae2e id + sin q23Ae3|2 ``solar’’ amplitude ``atmospheric’’ amplitude dependence on d and q23is explicit For maximal 2-3 mixing f = arg (Ae2* Ae3) P(ne nm)d = |Ae2 Ae3| cos (f - d ) P(nm nm)d = - |Ae2 Ae3| cosf cos d P(nm nt)d = - |Ae2 Ae3| sinf sind S = 0

  34. Sensitivity to CP phase d - true (experimental) value of phase df - fit value Interference term: D P = P(d) - P(df) = Pint(d) - Pint(df) For ne nm channel: DP = 2 s23 c23 |AS| |AA| [ cos(f + d) - cos (f + df)] (along the magic lines) AS = 0 AA = 0 D P = 0 (f+d ) = - (f + df) + 2p k int. phase condition f(E, L) = - ( d + df)/2 + p k depends on d

  35. ``Magic lines'' V. Barger, D. Marfatia, K Whisnant P. Huber, W. Winter, A.S. For nmnm channel Pint ~ 2s23c23|AS||AA|cosf cosd • - The survival probabilities is CP-even functions of d • no CP-violation • dependences on phases factorize Dependence on d disappears form magic grid AS = 0 AA = 0 Pint = 0 f= p/2 + p k interference phase does not depends on d Form the phase line grid

  36. CP asymmetry Shape does not change the amplitude changes Large significance at low energies

  37. 3. Discrete symmetries and pattern of lepton mixing

  38. Tri-bimaximal mixing L. Wolfenstein P. F. Harrison D. H. Perkins W. G. Scott Dominant approach 0.15 2/3 1/3 0 - 1/6 1/3 - 1/2 - 1/6 1/3 1/2 Utbm = 0.62 0.78 n3 is bi-maximally mixed - maximal 2-3 mixing - zero 1-3 mixing - no CP-violation n2is tri-maximally mixed Utbm = U23(p/4) U12 - sin2q12= 1/3 Form invariance Symmetry from mixing matrix

  39. Framework Mixing appears as a result of different ways of the flavor symmetry breaking in neutrino and charged lepton sectors Gf A4 T7 S4 Residual symmetries Gl Gn T’ ? Mn TBM-type Ml diagonal 1n Flavons the difference originates from different flavor assignments of the RH components of Nc and lc and different higgsmultiplets

  40. Symmetry building Bottom-up - Majorananeutrinos - symmetry can be embedded in SU(3) Assumptions D. Hernandez, A.S. in the mass basis Gl Gn the symmetry transformation of the charged lepton mass matrix : (the simplest discrete symmetry which lefts the matrix diagonal) the symmetry transformation of the neutrino mass matrix for generic values of masses S1 = diag (1, -1, -1) ifm ift ife T = diag (e , e , e ) S2 = diag (- 1, 1, -1) fa= 2pka/m Si2 = I Tm = I Z2x Z2 Zm Klein symmetry Bigger symmetry if masses take specific values, e.g. equal or one is zero S fa= 0

  41. Reconstructing the symmetry D. Hernandez, A.S. 1204.0445 In the flavor basis T is the same SiU = UPMNSSi UPMNS+ Take one Si so that Gn = Z2 (SiU T ) belongs toGf If SiU and T generate Gf If the group is finite, p exist such that (SiU T) p = I Si2 = Tm = (SiU T)p= I Presentation of the von Dyck group D(2, m, p) D(2,3,4) = S4 D(2,3,3) = A4 D(2,3,5) = A5 The group is finite if 1/n + 1/m + 1/p > 1

  42. Relations between matrix elements D. Hernandez, A.S. 1204.0445 (SiU T) p = I (SiU T) p = (WiU) p = I Explicitly ( UPMNSSi UPMNS+ T ) p = I The main relation: connects the mixing matrix and generating elements of the group in the mass basis Equivalent to Tr (WiU) = a Tr ( UPMNSSi UPMNS+ T ) = a a = Sjlj lj- three eigenvalues of WiU j = 1,2,3 ljp= 1

  43. Relations between matrix elements D. Hernandez, A.S. to be submitted Tr (WiU) = Tr ( UPMNSSi UPMNS+ T ) ifa Sa (2|Uaj|2 – 1) e = a • bounds on moduli of matrix elements • elements of a given column j determined by index of S • two relations corresponding to real and imaginary of a • the column j is completely determined aRcos (fe /2) + cos (3fe /2) – aI sin (fe /2) fab= fa- fb |Uej|2= 4 sin (fem /2) sin (fte /2) aRcos (fm/2) + cos (3fm /2) – aI sin ( fm/2) |Umj|2= 4 sin (fem /2) sin (fmt /2)

  44. Special case aI = 0 ka = 0 D. Hernandez, A.S. For column of the mixing matrix: A4 |Ubi|2 = |Ugi|2 S4 1 – a 4 sin2 (pk/m) |Uai|2 = k, m, p integers which determine symmetry group d = 1030 S4 Also S. F. Ge, D. A. Dicus, W. W. Repko, PRL 108 (2012) 041801

  45. For finite groups Interesting possibilities 2/3 1/6 1/6 1/3 1/3 1/3 1/4 1/2 1/4 For i =1 Trimaximal 1 For i = 2 Trimaximal 2 Another class of possibilities: with (m – p) permutation T (SiU T) = WiU

  46. Finite subgroups of infinite von Dyck Large m and n 1/n + 1/m + 1/p < 1 D. Hernandez, A.S to be submitted. 1) (WiU) p = (SiU T) p = I 2) Add another relation Consider elements generated by SiU and T X = SiU T-1 SiUT Xq= I Tr X = x (SiU T-1 SiUT) q = I x = Sjlj ljq= 1 - Make the group finite - Constrain the same elements of mixing matrix which are already determined by the relation 1) Consistency condition fa= 2pka/m bound onfa or ka

  47. Examples Modular groups PSL(2, Z7 ) R A Toorop, F. Feruglio, C Hagedorn Symmetry assignment {p, a, m, ke , km } = {3, 0, 7, 5 , 3} |Uti|2 = ¼ [1 + cos (p /7)]-1 |Umi|2 = ¼ [1 + sin (p /14)]-1 For i = 2 – very good fit d = 600 - 900 D (384) Symmetry assignment {p, a’, m, ke‘, km‘} = {16, (1 + i) /\sqrt{2} , 3, - 1 , 1 } Fits well for i =3 i.e. fixes 2-3 and 1-3 mixings

  48. Klein group for neutrinos D. Hernandez, A.S. as the residual symmetry in the neutrino sector Gn = Z2x Z2 Two sets of presentations Sj2 = Tm = (SjU T) p(j)= I j = 1, 2 [S1U , S2U] = 0 Two sets of relations ifa Sa (2|Uaj|2 – 1) e = a(j) Two columns and therefore whole the matrix is fixed Compatibility For {p(1) , p(2), m} = {4, 3, 3} TBM ce ct cm cmce ct ct cmce Permutation of elements |Ua2|2= |U f(a) 1|2 f – permutation operation

  49. Framework Gf Gl Gn 1n Mixing originates from - different nature of the mass terms of the charged leptons (Dirac) and neutrinos (Majorana) - Mixing from new degrees of freedom (e.g. singlets of SM )

  50. Summary Determination of 1-3 mixing , indications of the deviation of2-3 mixing from maximal strong impact on phenomenology , theory and future experimental programs First glimpses of CP and mass hierarchy  important implications for theory The same 1-3 mixing from different relations with different implications Race for mass hierarchy and CP: studies of atmospheric neutrinos with huge (multi-megaton scale detectors) : fast, cheap, reliable? Eath matter effect on Supernova neutrinos Discrete symmetries - model independent approach, relations between the mixing matrix elements misleading?

More Related