Theoretical Implications of Neutrino Masses

Transcription

1 Theoretical Implications of Neutrino Masses Thomas Hambye Université Libre de Bruxelles LAUNCH 09 Heidelberg 09/11/09

2 Neutrino masses new physics in the particle physics Standard Model are massless are neutral 2 different possible types of neutrino masses Dirac mass: Majorana mass: L > +> m N R L L > m + > L m NR L L 1 2 m c L L not in SM: no N R in SM not in SM: breaks the L symmetry masses require new physics beyond the SM

3 Neutrino masses: Dirac or Majorana? very important for mass origin model building both are possible but theoretically clear preference for Majorana masses: if we add masses but: - why m observed so small then? to the SM we can have Dirac - a is singlet of SM we expect a Majorana mass N R for gives a Majorana mass for too N R N R L N R > + M N > N R

4 Unique status of neutrino masses If we write down the possible low energy interactions between SM fermions which could be induced by any kind of new physics at a heavy scale : Λ NewP hys - all interactions are suppressed by 1/Λ 2 NewP hys, 1/Λ 3 NewP hys,... - except one in 1/Λ NewP hys : L eff v+ + v λ αβ Λ NewP hys L α L β HH λ αβ Λ NewP hys λ αβ Λ NewP hys Lα > + m αβ > Lβ α β masses: first BSM effect expected and first seen! argument for Majorana masses m αβ λ αβ Λ NewP hys v 2

5 masses can probe new physics up to GeV m αβ λ αβ Λ NewP hys v 2 if λ αβ 1, m 0.1 ev requires Λ NewP hys GeV unique way to probe high scale new physics and GUT in particular provides a natural explanation for the tinyness of if Λ NewP hys is large, m is small: seesaw mechanism masses: yet another argument for Majorana masses

6 Seesaw Models

7 The 3 basic seesaw models i.e. tree level ways to generate the dim 5 λ M LLHH operator Right-handed singlet: (type-i seesaw) Scalar triplet: (type-ii seesaw) Fermion triplet: (type-iii seesaw) + + m = Y T N 1 M N Y N v 2 µ m = Y M 2 v 2 m = Y T Σ 1 M Σ Y Σ v 2 m small if M N large m small if M large m small if M Σ large (or if Y small) (or if Y,µ small) (or if small) Y Σ

8 Can we fit flavour structure in all seesaw models? yes: easily in particular the main features of data m 2 atm m 2 sol 32 2 large mixing angles 2 = squared mass differences larger than for quarks and one small θ 13 θ 23, θ 12 leading to a milder hierarchy between 2 the seesaw models can fit the data even too easily: can give any mass matrix which could be observed than for quarks m 3 m 2 < 6

9 Access to the seesaw parameters from mass matrix data Type II seesaw: µ m ij = Y ij M 2 v 2 mass matrix data gives full access to type II flavour structure Type I or III seesaw model: + m ij = Y T Nik 1 M Nk Y Nkj v 2 mass matrix data: gives access to 9 parameter combinations of Y N and M N 3 masses of the N 15 parameters in Yukawa matrix 9 real parameters 6 phases 18 parameters

10 How could we distinguish experimentally the 3 seesaw models? several possibilities: µ!e"!!e"!!µ" µ!eee!!eee!!µee!!µµe!!µµµ Z!µe Z!!e Z!!µ... combining the mass matrix data with other data rare lepton processes colliders: LHC,... cosmology: baryogenesis,... and/or embedding the seesaw models in broader frameworks supersymmetry U(1) B L L-R model model Grand Unified Theories...

11 Seesaw at colliders if seesaw states are around TeV q ++, 0, +,... > Z 0, γ,w ± Type-II and type-iii are the most promissing because have gauge interactions can be Drell-Yan pair produced q q q > > > Z 0, γ,w ±, 0,,... Σ +, Σ 0,... Σ, Σ,... at LHC up to M 1.5 TeV M Σ 1.5 TeV Chun et al. 03 ; Akeroyd, Aoki 05 ; Hektor et al. 07 ; Chun, Lee, Park 07 ; Garayoa, Schwetz 08 ;Fileviez Perez et al.08, 09 ;del Aguila et al 09 ;... Bajc, Senjanovic 06 ; Bajc, Nemvesek, Senjanovic 07 ; Franceschini, TH, Strumia 08 ; Arhrib et al. 09 ; del Aguila et al 09,... Τ N allow to reconstruct the Yukawa coupling structure from decay branching ratios given the tiny neutrino masses one e.g. expect couplings sufficiently small to lead to observable displaced vertices Franceschini, TH, Strumia 08 m 1 in ev mm mm cm dm m M in GeV

12 Seesaw at colliders Type-I seesaw model: the N R have no SM gauge interactions can be produced only through Yukawas e.g. small if M NR TeV 2 possibilities: - inverse seesaw models allow larger Yukawas production cross section limited by upper bounds on Yukawas from µ eγ,... see e.g. del Aguila et al 06, 09, Kersten, Smirnov 07 - extra production interactions pair production through a Z see e.g. Abbas et al. 08 ; Fileviez-Perez, Han, Li 09 q > > Z N R q N R

13 U(1) B L seesaw models the SM accidentally conserved B-L global U(1) B L it is tempting to gauge U(1) B L require to introduce the N R M NR not anymore an ad hoc scale: M NR v B L can justify TeV scale linking e.g. v to N B L R susy breaking scale Barger, Fileviez-Perez, Spinner 09 ; Fileviez-Perez, Spinner 08, 09 If U(1) B L is ungauged but spontaneously broken: Majoron models other example of consequence at LHC: invisible Higgs decay to Majorons

14 Seesaw models with approximately conserved lepton number rare lepton processes such as µ eγ are e.g. expected very suppressed Y 4 N/Λ 4 NewP hys come from dim-6 operator in 1/Λ 2 NewP hys if Λ NewP hys is as low as 1 TeV they remain e.g. very suppressed but not necessarily: Type II model with a TeV scale scalar triplet: µ m = Y µ v 2 /M 2 Γ(µ eγ) Y 4 /M 4 Y e Y e e 2 step mechanism: Γ(µ eee) Y 4 /M we start from a L conserved situation: Y large µ eγ µ e e e µ =0 m = we introduce a small L breaking: µ 0 m 0

15 Bounds on Type-II seesaw Yukawa couplings Barger e tal 82 ; Pal 83; Bernabeu et al 84, 86; Bilenky, Petcov 87; Gunion et al 89, 06; Swartz 89; Mohapatra 92 Abada, Biggio, Bonnet, Gavela, T.H. 07 rare processes could be seen for M up to 1000 TeV µ eee

16 Inverse seesaw models (type-i or type-iii models) Type-I model with TeV scale N R : same 2 steps mechanism is possible - we start from a L conserved situation: y: 1 light!!l! L N 1 N 2 m =0 Gonzalez-Garcia, Valle Kersten, Smirnov 07 Abada, Biggio, Bonnet, Gavela, T.H. 07 N 1 N 2 Y N large µ eγ - we introduce a small L breaking: y: 1 light!! L N 1 N 2 see S. Antusch talk!l N 1 m 0 N 2 together with mass matrix data we could in principle reconstruct the full seesaw model some of these models are of Minimal Flavour type: all flavour structure is in mass matrix Gavela, T.H., Hernandez, Hernandez, 09

17 Bounds on Type-I and Type-III seesaw Yukawa couplings Type-I seesaw: Antusch, Biggio, Fernandez- Martinez, Lopez-Pavon, Gavela 06 Abada, Biggio, Bonnet, Gavela, T.H. 07 Type-III seesaw: Abada, Biggio, Bonnet, Gavela, T.H. 07

18 Flavour symmetries seesaw models have no flavour symmetries in se we can assume flavour symmetries at level of Yukawa coupling matrices continuous or discrete abelian or non-abelian see L. Everett talk SO(3)f Z U(1) 2 Z 3 Z 4 f... SU(3) f Z 2 Z Froggatt, Nielsen 79, Altarelli, Feruglio 04, Leontaris et al 04,... King, Ross 01, King, Malinski 06, de Medeiros Varzielas, King, Ross 05, Antusch, King 07,... Low, Volkas 03, Mohapatra, Rodejohann A 4 S 4 S 3 D 3 D 4 D 5 D 5 D 6 (48) (75)... T Pakvasa,Sugarawa 78, Harari, Haut, Weyers 78, Wyler 79, Ma 91, 00, 06,Lee, Mohapatra 94, Chou, Wu 97, Ma, Rajasekaran 01,Grimus, Lavoura 03, Babu, Ma, Valle 03, Altarelli, Feruglio 05, Zee 05, Keum, Volkas 06, Chen, Frigerio, Ma 04, Dermisek, Raby 05, Caravaglios, Morisi 05 Kubo, Mandragon et al 03, 05, Kobayashi et al 03, Haba, Yoshioka 05, Hagerdorn, Lindner, Mohapatra 06, Hagedorn, Lindner, Plentiger 06,...

19 Flavour symmetries some of these symmetries lead to the interesting tri-bimaximal mixing pattern A 4,S 4, SO(3), SU(3),... U = θ 13 =0, θ 23 = π 4, sin2 θ 12 = 1 3 Altarelli, Feruglio 05, Babu, He 05, de Medeiros Varzielas, Ross 06, Ma 05, 09, Carr, Frampton 06, Koide 07, Bazzochi et al 08, Adhikary, Ghosal, Roy 09, Ciafolini et al 09 Plentinger, Rodejohann 05 Pakvasa, Rodejohann, Weiler 08,...

20 Flavour symmetries the striking observables for flavour models are: the absolute scale: 02β, Katrin,... the mass hierarchy: expts sensitive to matter effects,... θ 13 θ 23 δ CP : how close to 0? : how close to maximal? : how large is it?

21 Supersymmetric seesaw models to supersymmetrize the seesaw model: - doesn t alterate the successful features of seesaw models - brings new possibilities of seesaw tests even for very high seesaw scale Yukawa couplings can induce large µ eγ,... rates through their effects on the running of slepton masses GUT scale no flavour breaking in slepton masses see e.g. Ellis et al 03 laboratory scale N R ẽ µ Y N large flavour breaking in slepton masses H Y N Br(µ eγ) up to reachable experimentally combined with Davidson, Ibarra 03 data in principle we could reconstruct the full seesaw lagrangian

22 Grand-Unified-Theories L eff λ αβ Λ NewP hys L α L β HH Majorana masses requires a new physics scale Λ NewP hys which could be as large as GeV and give masses with right order of magnitude for couplings of order unity if Λ NewP hys GeV cannot be the Planck scale but is just around the GUT scale 1/! i /! 1 1/! 2 MSSM /! log Q

23 masses and seesaw fit very well in GUT most GUT models predicted masses prior their discovery in particular SO(10) GUT L,l L,l R, u L1,2,3,u R1,2,3, all 15 fermions of a SM generation can be put in a single SO(10) representation,, 16 F d L1,2,3,d R1,2,3 and the 16th fermion is the N R explains the particle content of the SM and its charge quantization leads to masses

24 Close relation between tiny between left and right in SM masses and distinction why parity is broken in SM and why maximally? Pati, Salam 75, Mohapatra, Senjanovic 75 in SO(10) or its left-right subgroup SU(3) c SU(2) R SU(2) L U(1) B L parity is restored at high energies and one finds a one to one relation between the fact that parity is maximally broken in SM and the fact that masses are tiny Mohapatra, Senjanovic 80

25 What data teach us on GUT data point towards particular GUT groups: SO(10),E 6, (SU(5)) data has ruled out various pre-1998 GUT models predicted large mixing angles as for quarks

26 What data teach us on GUT Minimal SO(10) model: renormalizable model with only 2 Yukawa flavour structures m u = Y 10 v u 10 + Y 126 v u 126 m d = Y 10 v d 10 + Y 126 v d 126 m l = Y 10 v d 10 3Y 126 v d 126 m D = Y 10 v u 10 3Y 126 v u 126 M N = Y 126 v R m = Y 126 v L + m T DM 1 N m D from 10 H : Y 10 from 126 H : Y 126 Babu, Mohapatra 93 Lee, Mohapatra 95, Lavoura 93,... Bajc, Senjanovic, Vissani 03, Goh, Mohapatra, Ng 03, Bertolini, Malinski 05, Bertolini, Schwetz, Malinski 06 type-ii contribution type-i contribution type-i and type-ii contributions can be disentangled in general SO(10) models Akhmedov, Frigerio 06, 07 close link between the fact that θ 23 is measured close to maximal and b τ unification,... But: a detailed fit of fermion masses with RGE equations shows that this model cannot fit all masses and give unification at the same time Bertolini, Schwetz, Malinski 06 need for a more complicated Higgs structure and/or more sources of Yukawa flavour Babu, Barr 02 ; Dutta, Mimura, Mohapatra 04 ; Bertolini, Schwetz, Malinski 06 ; Dermisek, Haraba, Raby 06 ; Aulakh, Garg 06 ; Calibbi, Frigerio et al. 09,...

27 Renormalization group equations for neutrinos GUT scale full RGE S have been determined for seesaw models RGE important for GUT and flavour models: laboratory scale especially if especially for are quasi-degenerate θ 12 because associated to small induce deviation from maximal for θ 23 interesting phenomenons for model building Babu, Leung, Pantaleone 93 ; Chankowski, Plucieniek 93 ; Antusch, Drees, Kersten, Lindner, Ratz 01 ; Casas, Espinosa, Ibarra, Navaro 00 Chankowski, Pokorski 02 ; Lindner 05 ; Antusch, Kersten, Lindner, Ratz, Schmidt 05 ; Hagedorn, Kersten, Lindner 04 ; Ellis, Lola 99 ; Chankowski et al. 01 ; Balaji et al 00 ; Mohapatra et al.04 ; Chun 01 ; Bhattacharyya et al 03 ; Joshipura et al03 ; Antusch, Kersten, Lindner, Ratz 03 ; Antusch, Huber, Kersten, Schwetz, Winter 04; Antusch, Kersten, Ratz 02 ; Antusch, Ratz 02 m 2 sol mixing angle magnification through running will become mandatory at the level of precision of new data

28 Strumia)) H Matter-antimatter asymmetry of the universe from the seesaw interactions responsible for neutrino masses one can also explain baryogenesis via leptogenesis type-i: N R N R + N R L Fukugita, Yanagida 86, Buchmüller, Plumacher 97,... type-ii: L " " " + + H L Ma, Sarkar 98,... type-i+ type II: N k H l l (Ma, Sarkar, Hambye) H L L l i H H N k l i l l O Donnell, Sarkar 94, TH, Senjanovic 04 ; Antusch, King 04,... type-iii: T " R " R " R + " R L TH, Lin, Notari, Papucci, Strumia 04 ;...

29 Non seesaw neutrino mass origins

30 masses from R-parity breaking masses can be induced in the MSSM without any new field at the price of breaking R-parity W ɛ i ˆLi Ĥ u + λ ijk ˆLi ˆLj ê Rk + λ ijk ˆL i ˆQj ˆdRk V soft B S i L i H u see e.g. Romao et al 08 gives one gives 2 m m at tree level from neutrino Higgsino mixing at one loop tends to give a hierarchy larger than data doesn t explain the tinyness of masses in se

31 masses from supersymmetry breaking in the MSSM with extra right-handed sneutrinos LÑ =(m 2 Ñ ) ijñ i N R Ñ R Ñj + B ij Ñ i Ñ j + A U ij L i H U Ñ j lead to masses at one loop naturally suppressed the soft susy breaking terms involving bring new sources of L violation: masses Using the Giudice-Masiero mechanism one can: - forbid the seesaw and Y N M NR φ α j N I B A A j χ 0 Grossman, Haber 96 Boubekeur 02 φ β - induce them subsequently from F and D terms giving Y N induce L violating soft A and B terms giving rise to 1-loop mass: k k Arkani-Hamed et al;. 01. Borzumati, Nomura,01 Borzumati, Hamagushi, Yanagida 01 March-Russell, West 03 TH, March-Russell, West 04 M NR MÑR TeV testable TeV scale model m loop µ α w 96π m 9 I v2 M 5 m 5 susy 10 2 ev 10 1 ev

32 masses from extra dimensions: large extra dimension Hierarchy problem: why gravity so weak % electroweak force? M P lanck >> v EW if gravity propagates in 3+1+d dimensions whereas we live in 3 +1 dimensions Arkani-Hamed,Dimopoulos, Dvali 98 gravitons SM fields bulk R gravity is weak in 3+1 dim.: volume suppression M 2 P lanck = M 2+d G V d V d = (2πR) d but is similar to weak force in 3+1+d dim. fundamental gravity scale: M G T ev v EW if the N R propagates in the 3+1+d dim. as graviton: suppression of m lead to tiny Dirac m e.g too small % data in minimal version but OK in non minimal versions interesting phenomenology at TeV scale, effects of Kaluza-Klein (supernovae,...), large µ eγ,... N R Dienes, Dudas, Gerghetta 99 Arkani-Hamed, Dimopoulos, Dvali, March-Russell 00 Dvali, Smirnov 99

33 masses from extra dimensions: Randall-Sundrum scenario suppression of gravity on weak brane if there is an extra curved (warped) dimension with graviton wave function peaked on a distant UV Planck brane gravity brane weak brane m naturally suppressed if the wave function of the is peaked on the UV brane far from the weak brane where sits the Higgs boson L u L,d L t R Higgs

34 mass varying with their environment Fardon, Nelson, Weiner 03, Peccei 04 73% of universe energy content is due to dark energy 2 coincidences between and dark energy: - dark energy scale V 1/ ev of order masses ρ ρ Λ - universe energy densities, and, are within 3 orders of magnitudes today idea: the scalar field φ responsible for masses is the dark energy field φ contributes in 2 ways to universe energy density V (φ) =V 0 (φ) +n m usual scalar potential φ contribution to it induces m early universe (high density): n m large φ small m small today universe (high density): n m small φ large m larger m ρ ρ Λ varying : - keeps track of - because today m V 1/4 T m (ρ T 3 m and ρ Λ V )

35 Short conclusion for long talk data: - provides a unique tool to probe beyond standard model physics up to very high scales - has and will open the door to a large variety of theoretical works related to very fundamental questions