Neutrinos and the Flavour Problem

Transcription

1 Neutrinos and the Flavour Problem Part I. The Flavour Problem Part II. Neutrino Phenomenology Part III. Flavour in the Standard Model Part IV. Origin of Neutrino Mass Part V. Flavour Models Part VI. Discrete Family Symmetry Part VII. GUT Models

2 Part I. The Flavour Problem

3 The Flavour Problem 1. Why are there three families of quarks and leptons? Quarks Leptons Horizontal u up d down ν e e-neutrino e electron c charm s strange ν μ μ-neutrino μ muon t top b bottom ν τ τ-neutrino τ tau I II III Generations of matter Vertical 04/02/2010 Steve King, University of Warwick, Coventry

4 The Flavour Problem 2. What is the origin of quark and lepton masses? t ν 1 < Horizontal direction e 10 4 ν d 10 3 μ 10 2 ν 3 u s 10 2 τ 10 1 c b Vertical direction 1

5 quark and lepton masses Normal Inverted Absolute neutrino mass scale?

6 The Flavour Problem 3. Why is quark mixing so small? Cabibbo Kobayashi Maskawa V CKM i δcp c13 0 s13e c12 s12 0 = 0 c23 s s12 c12 0 i δcp 0 s23 c23 s13e 0 c θ θ θ = 13 ± 0.1 = 2.4 ± 0.1 = 0.20 ± 0.05 All these angles are pretty small why? While the CP phase is quite large δcp 70 o ± 5 o

7 The Flavour Problem 4. What is origin of quark CP violation? Wolfenstein λ A 0.81 ρ 0.13 η 0.35 V V + V V + V V = * * * ud ub cd cb td tb 0 α 90 o ± 4 o δcp γ 70 o ± 5 o

8 The Flavour Problem 5. Why is lepton mixing so large? ν e μ e μ L L ν ν τ τ L Standard Model states Neutrino mass states Pontecorvo Maki Nakagawa Sakata m 3 m m 2 1 iδ iα1 / c s13e c12 s12 0 e 0 0 iα2 /2 UPMNS = 0 c23 s s12 c e 0.. iδ.. 0. s23 c 23. s13e 0 c sij = sinθij Atmospheric Reactor Solar Majorana c = cosθ ij ij Oscillation phase δ Majorana phases α, α masses + 3 angles + 1(3) phase(s) = 7(9) new parameters for SM

9 Part II. Neutrino Phenomenology

10 Global Fit to Atmospheric and Solar Data Atmospheric Solar

11 There is a 2σ hint for θ 13 being non-zero Fogli et al 08 Fogli et al 09 The 2009 estimate includes the MINOS results which show a 1.5σ excess of events in the electron appearance channel

12 Neutrino mass squared splittings and angles Normal Inverted Absolute neutrino mass scale? Why are neutrino masses so small? θ θ θ = 34.5 ± 1.4 = 43 ± 4 10 Two of these angles are pretty large why?

13 Tri-bimaximal mixing matrix U TB Harrison, Perkins, Scott TB angles θ = 35, θ = 45, θ = 0. c.f. data θ = 34.5 ± 1.4, θ = 43.1 ± 4, θ = 8 ± o o Current data is consistent with TB mixing (ignoring the 2σ hint for θ 13 )

14 Useful to parametrize the PMNS mixing matrix in terms of deviations from TBM SFK 07 r = reactor s = solar a = atmospheric e.g. r 0, s=0, a=0 gives Tri-bimaximal-reactor (TBR) mixing SFK 09 TBR not as simple as TB but is required if θ 13 0

15 Leptonic CP violation is unknown r δ Scaled triangle 1 Neither r nor δ is measured UT could be a straight line!

16 Neutrinos can have Dirac and/or Majorana Mass Majorana masses CP conjugate mll M ν L ν c L ν ν c RR R R Violates L Violates L,, e Lμ Lτ Neutrino=antineutrino Dirac mass m ν ν LR L R Conserves L Violates L,, e Lμ Lτ Neutrino antineutrino

17 In general a mass term can be thought of as an interaction between left and right-handed chiral fields e e L R e L R me e Left-handed neutrinos ν L can form masses with either righthanded neutrinos ν R or with their own CP conjugates ν c L ν L Majorana Dirac m ν ν ν LR L R m ν ν ν c LL L L ν R c ν L

18 Right-handed neutrinos ν R can also form masses with their own CP conjugates ν R c ν R M ν ν c RR R R Majorana c ν R In principle there is nothing to prevent the right-handed Majorana mass M RR from being arbitrarily large since ν R is a gauge singlet e.g. M RR =M GUT On the other hand it is possible that M RR =0 which could be enforced by lepton number L conservation

19 Absolute ν mass scale and the nature of ν mass Neutrinoless double beta decay Tritium beta decay Present Mainz < 2.2 ev KATRIN ~0.35eV m = U m 2 ee ei i i mν =Σ U m 2 e i ei i 1/2 2/2 U = c c e, U = s c e, U = s e i α i α i δ e e e3 13 Majorana (no signal if Dirac) Klapdor- 76 Ge ~0.4 ev (signal) Majorana 76 Ge ~0.05 ev GERDA 76 Ge Non- 76 Ge: CUORE, NEMO3 SuperNEMO ~0.1 ev (phase II) ~0.01 ev (phase III ) 50meV=0.05 ev COBRA Cd116?? EXO Xe136 1 ton 5y 50-70meV= eV SNO+ Nd150 start 2011? 50meV=0.05 ev The Future I meV SNemo CUORE GERDA EXO SNO+ II 15-50meV 1 ton 10y? III 2-5meV 100 tons 20y??

20 Cosmology vs Neutrinoless DBD Inverted hierarchy is TESTABLE 0ν DBD Approx. degeneracy is TESTABLE Normal hierarchy is NOT TESTABLE future cosmo from: F. Feruglio, A. Strumia, F. Vissani ('02)

21 Part III. Flavour in the Standard Model

22 Yukawa matrices H ψ i Yψ j L ij R U D E N ij ij ij ij ij Y Y, Y, Y, Y + E i H eg.. Y ( ν e) e L 0 H j ij e R ψ ψ

23 Quark mixing matrix V CKM mu 0 0 UL U UR V Y = LRV v 0 mc mt md 0 0 DL D DR V YV = LR v 0 ms mb Defined as V CKM = V U V L D L 5 phases removed Lepton mixing matrix U PMNS m e = 0 μ 0 EL E ER V YLRV v m m τ Light neutrino Majorana mass matrix m 0 0 = m3 1 ν ν ν L LT V mv LL m2 Defined as U PMNS EL = V V ν L 3 phases removed

24 Recall the origin of the electron mass in + H the SM are the Yukawa couplings: 0 H + e y ( ν e e) e L 0 R H 0 e y ( ν e e) e L v R < > 0 = < H > v = e y veler m e Yukawa coupling y e must be small since <H 0 >=v=175 GeV m = y H 0.5 MeV y e e e Unsatisfactory Introduce right-handed neutrino ν er with zero Majorana mass c 0 ylh ν ν er = yν H νelνer then Yukawa coupling generates a Dirac neutrino mass ν m = y H 0.2 ev y 10 LR ν 0 12 ν Even more unsatisfactory

25 Part IV. The Origin of Neutrino Mass

26 Three important features of the SM 1. There are no right-handed neutrinos ν R 2. There are only Higgs doublets of SU(2) L 3. There are only renormalizable terms In the Standard Model neutrinos are massless, with ν e, ν μ, ν τ distinguished by separate lepton numbers L e, L μ, L τ Neutrinos and anti-neutrinos are distinguished by the total conserved lepton number L=L e +L μ +L τ To generate neutrino mass we must relax 1 and/or 2 and/or 3

27 Neutrino Mass Models Road Map Dirac or Majorana? Majorana Dirac Extra dims? See-saw mechanisms, Higgs Triplets, Loops, RPV, Very precise TB? Degenerate? Yes Family symmetry? Yes No Type I see-saw? No Yes No Anarchy, see-saw, etc Alternatives? Type II see-saw? GUTs and/or Strings? 04/02/2010 Steve King, University of Warwick, Coventry

28 Origin of Majorana Neutrino Mass Renormalisable ΔL =2 operator λ Non-renormalisable ΔL =2 operator LLΔ ν λν M LLHH where Δ is light Higgs triplet with VEV < 8GeV from ρ parameter = λν M H 0 2 c ν elν el Weinberg This is nice because it gives naturally small Majorana neutrino masses m LL <H 0 > 2 /M where M is some high energy scale The high mass scale can be associated with some heavy particle of mass M being exchanged (can be singlet or triplet) H L M H L H L M H L e.g. see-saw mechanism

29 The See-Saw Mechanism Light neutrinos Heavy particles 04/02/2010 Steve King, University of Warwick, Coventry

30 The see-saw mechanism Type I see-saw mechanism P. Minkowski (1977), Gell-Mann, Glashow, Mohapatra, Ramond, Senjanovic, Slanski, Yanagida (1979/1980) Type II see-saw mechanism (SUSY) Lazarides, Magg, Mohapatra, Senjanovic, Shafi, Wetterich (1981) λ Δ ν L ν R c M RRν Rν R ν L m m M m I 1 T LL LR RR LR Type I m ν L II LL Y Δ ν L 2 vu λ Δ Y Δ M Δ Type II Heavy triplet

31 The See-Saw Matrix Type II contribution Dirac matrix II c c LL LR L L R T mlr MRR ν R ( ν ν ) m m ν Heavy Majorana matrix Diagonalise to give effective mass c mllν Lν L Light Majorana matrix m m m M m ν II 1 T LL LL LR RR LR m m / M ν 2 LL LR RR suggests new high energy mass scale(s) radiative corrections

32 Part V. Flavour Models

33 Hierarchical Symmetric Textures Consider the following ansatz for the upper 2x2 block of a hierarchical Y d 0 y d 12 Yij = 1 2 y12 y 22 md Vus λ m s Gatto et al successful prediction This motivates having a symmetric down quark Yukawa matrix with a 1-1 texture zero and a hierarchical form λ λ λ λ λ λ λ 1 d Y y b 3 2 λ 0.2 is the Wolfenstein Parameter D ( mlr ) 23 2 Vcb λ m b D ( mlr ) 13 3 Vub λ m successful predictions b

34 Up quarks are more hierarchical than down quarks G.Ross et al This suggests different expansion parameters for up and down Y 0 ε ε 3 3 d d D LR εd εd εd yb εd 3 2 εd εd 1 m m m ε ε 4 2 d : s : b = d : d : Y 0 ε ε 3 3 u u U LR εu εu εu yt εu 3 2 εu εu 1 m m m ε ε 4 2 u : c : t = u : u : Charged leptons are well described by similar matrix to the downs but with a numerical factor of about 3 in the 2-2 entry (Georgi-Jarlskog) Y 0 ε ε d d E LR εd εd εd yb εd 3 2 εd εd 1 md me : m : m = : 3ms : m at M μ τ b U 3 md mb RGE me, mμ ms, mτ at m b 9 3 N.B. Electron mass is governed by an expansion parameter ε d 0.15 which is not unnaturally small providing we can generate these textures from a theory

35 Textures from U(1) Family Symmetry Consider a U(1) family symmetry spontaneously broken by a flavon vev For D-flatness we use a pair of flavons with opposite U(1) charges φ 0 Q( φ) = Q( φ ) Example: U(1) charges as Q (ψ 3 )=0, Q (ψ 2 )=1, Q (ψ 1 )=3, Q(H)=0, Q(φ )=-1,Q(φ)= Then at tree level the only allowed Yukawa coupling is H ψ 3 ψ 3 Y = The other Yukawa couplings are generated from higher order operators which respect U(1) family symmetry due to flavon φ insertions: = φ φ φ φ φ Hψ 2ψ3+ Hψ2ψ2 + Hψψ 1 3+ Hψψ Hψψ 1 1 M M M M M When the flavon gets its VEV it generates small effective Yukawa couplings in terms of the expansion parameter ε = φ M ε ε ε 4 2 Y = ε ε ε 3 ε ε 1 Not quite of desired form non-abelian

36 Froggatt-Nielsen Mechanism What is the origin of the higher order operators? Froggat and Nielsen took their inspiration from the see-saw mechanism H H ν L ν R M ν R ν R ν L 2 H ν ν Mν R L L φ H ψ 2 χ M χ M χ ψ 3 φ M χ Hψ ψ 2 3 Where χ are heavy fermion messengers c.f. heavy RH neutrinos

37 There may be Higgs messengers or fermion messengers H 0 φ 1 φ 1 H 0 H 1 1 H M H ψ 2 0 χ M χ 0 χ ψ 3 ψ 2 ψ 3 Fermion messengers may be SU(2) L doublets or singlets φ 1 H 0 H 0 φ 1 M χ Q M χu c Q 2 0 χ Q Q 0 c χ Q U χ c U 1 χ U c U c 3 04/02/2010 Steve King, University of Warwick, Coventry

38 SFK, Ross,Varzielas Textures from SU(3) Family Symmetry In SU(3) with ψ i =3 and H=1 all tree-level Yukawa couplings Hψ i ψ j are forbidden SU (3) Ytree level = In SU(3) with flavons i φ = 3 the lowest order Yukawa operators allowed are: 1 i j 2 M φ φ H ψψ For example suppose we consider a flavon generates a (3,3) Yukawa coupling 1 M 2 i j 3 φφ Hψψ i j φ i 3 i j i with VEV φ = (0,0,1) u then this u M Note that we label the flavon with a subscript 3 which denotes the direction of its VEV in the i=3 direction. i φ3

39 i Next suppose we consider a flavon with VEV φ then this 23 = (0,1,1) u2 generates (2,3) block Yukawa couplings 1 M φ i u M i φ 2 i j 2 φ 2 23 φ23 Hψψ i j i To complete the model we use a flavon with VEV φ 123 = (1,1,1) u then this generates Yukawa couplings in the first row and column 1 M φ φ Hψψ uu 1 M 1 i j i j u3 2 u Taking uu ε ε we generate desired structures 2 2 M M M φ φ ε ε 2 0 ε φ ε ε ε ε ε 3 2 ε ε 1

40 Froggatt-Nielsen diagrams Right-handed fermion messengers dominate with M u 3 M d H 0 M φ φ ψψ ε ε i j i j ud, ud, ud, εud, εud, ε d = <φ 23 >/M d 0.15 and ε u = <φ 23 >/M u 0.05 Unsatisfactory features: 1. Suggests y b >y t! 2. First row/column is only quadratic in the messenger mass. To improve model we introduce sextet and singlet flavons

41 Flavon sextets for the third family SFK,Luhn 09 Idea is to use flavon sextets χ = 6 and Higgs messengers to generate the third family Yukawa couplings 1 H i ij H M ψ χψ Third family Yukawas j 33 χ = V y y V / M t b H V M H 04/02/2010 Steve King, University of Warwick, Coventry

42 Flavon singlet for first row/column SFK,Luhn 09 Flavon singlet ξ = 1 leads to first row and column Yukawa couplings involving a cubic messenger mass 1 M 0 ε ε ξφ φ Hψ ψ ε i j i j u, d ud, 3 εud, 3 3 ud, ud, So finally we arrive at desired quark textures (with y t y b ) Y 0 ε ε 3 3 d d D LR εd εd εd yb εd 3 2 εd εd Y 0 ε ε 3 3 u u U LR εu εu εu yt εu 3 2 εu εu /02/2010 Steve King, University of Warwick, Coventry

43 Part VI. Discrete Family Symmetry

44 Discrete neutrino flavour symmetry Consider the TB Neutrino Mass Matrix m 0 0 M U m U 0 0 m 3 1 ν T TB = TB TB M ν TB = TB Neutrino Mass Matrix is invariant under a discrete Z 2 Z 2 group generated by S,U M = SM S ν TB ν TB T M = UM U ν TB ν TB T

45 S 4 family symmetry Lam In this basis the charged lepton matrix is invariant under a diagonal phase symmetry T me 0 0 E = E M 0 mμ 0 = TM T 0 0 mτ S,T,U generate the discrete group S T = 0 ω 0 ω = e ω πi /3 Suggests using a discrete family symmetry S 4 broken by three types of flavons φ S, φ T, φ U which each preserve a particular generator Charged leptons preserve T Neutrinos preserve S,U

46 Indirect models SFK, Luhn Alternatively it is possible to realise the neutrino flavour symmetry indirectly as an accidental symmetry Introduce three triplet flavons φ 1, φ 2, φ 3 with VEVs along columns of U TB These flavons break S,U The following Majorana Lagrangian preserves S,U accidentally

47 G Family SU(3) PSL 2 (7) Δ 96 SO(3) Δ 27 Z 2 Z 7 S 4 Discrete family symmetry preferred by: - Vacuum alignment - String theory A 4

48 Part VII. GUT Models Strong Weak Electromagnetic

49 GUTs and Family Symmetry Gauge coupling unification suggests GUTs TB mixing suggests a discrete family symmetry t ν 1 < Family symmetry e 10 4 ν d 10 3 μ 10 2 ν 3 u s 10 2 τ 10 1 c b GUT symmetry 1

50 G GUT E 6 SO(10) SU (5) U (1) SU (3) SU (3) SU (3) C L R SU (4) SU (2) SU (2) PS L R SU (5) SU (3) SU (2) SU (2) U (1) C L R B L SU (3) SU (2) U (1) C L Y

51 GUT relations and sum rule.. TB + charged lepton corrections + GUTs leads to predictions:.... θ 13 θ C 3 2 3, Bjorken; Ferrandis, Pakvasa; SFK e o Georgi-Jarlskog θ d. 12 θ C θ θ θ cosδ Sum Rule SFK, Antusch, Masina, Malinsky, Boudjemaa

52 θ θ cosδ Testing the sum rule o.. Antusch, Huber, SFK, Schwetz Bands show 3σ error for optimized neutrino factory determination of θ 13 cos δ θ 12 =34.5 o ± 1.4 o (current value)

53 Conclusions Neutrino mass and mixing is first new physics BSM and adds impetus to solving the flavour problem Many possible origins of neutrino mass, but focus on ideas which may lead to a theory of flavour: see-saw mechanism and family symmetry broken by flavons If TB mixing is accurately realised this may imply discrete family symmetry GUTs discrete family symmetry with see-saw is very attractive framework for TB mixing

54 SFK,Luhn 09 PSL 2 (7) x SO(10) Model Attractive features of PSL 2 (7): - The smallest simple finite group containing complex triplets and sextets - Contains S 4 as subgroup (i.e. contains the generators S,T,U) - Contains sextet reps allows flavon sextets χ = 6 used both for third family Yukawas and for TB mixing where <χ TB > preserve S,U - Flavon triplets φ 23, φ 123 and flavon singlet ξ as before

55 Yukawa Sector (as before)

56 Majorana Sector (new) c Δ126 M GUT M RR Type II see-saw is dominant Very heavy type I see-saw is subdominant

57 Type II neutrino phenomenology mee mee m min m min m i mi m min m min

58 Indirect type I see-saw models SFK Consider Example of Form dominance TB mixing independently of masses Constrained sequential dominance corresponds to m 1 0