Neutrinos, GUTs, and the Early Universe

Transcription

1 Neutrinos, GUTs, and the Early Universe Department of Physics Max-Planck-Institut für Physik (Werner-Heisenberg-Institut) What is nu...?, Invisibles 12, Smirnov Fest GGI, Florence June 26, 2012

2 Three challenges GUTs & Flavour Neutrino masses Early Universe Inflation 2

3 Overview: Two topics Part 1: Neutrinos and inflation Part 2: Is there a footprint of GUTs in U PMNS? 3

4 First part of my talk: Neutrinos and inflation 4

5 Inflation = Era of accelerated expansion in the very early universe Why inflation? - Solves flatness problem - Solves horizon problem - Provides seed of structure A. Guth ('81), A. D. Linde, A. Albrecht and P. J. Steinhard, V.F. Mukhanov, G.V. Chibisov, A.H. Guth and S.Y. Pi, A.A. Starobinsky, S.W. Hawking picture from WMAP website 5

6 How can inflation be realised? Simple and attractive possibility: Slowly rolling scalar field ϕ (minimally coupled to gravity) 1 T µν = µ φ ν φ g µν 2 ρφ ρ φ + V (φ) If the vacuum energy V(ϕ) dominates: and the universe inflates! Important: The field ϕ is dynamical inflation can end! 6

7 Dynamics during and after inflation Inflation while vacuum energy dominates over kinetic energy } V 0 Vacuum energy during inflation: (V 0 ) 1/4 ~ GeV ~ M GUT 7

8 Dynamics during and after inflation Inflation while vacuum energy dominates over kinetic energy } V 0 Decays of the inflaton: matter & antimatter, and possibly their asymmetry get produced! 8 Vacuum energy during inflation: (V 0 ) 1/4 ~ GeV ~ M GUT

9 Dynamics during and after inflation Requirements: more than ~ 60 e- foldings of inflation consistency with CMB observables viable reheating beyond the SM (or change gravity) Inflation while vacuum energy dominates over kinetic energy } V 0 Decays of the inflaton: matter & antimatter, and possibly their asymmetry get produced! 9 Vacuum energy during inflation: (V 0 ) 1/4 ~ GeV ~ M GUT

10 Two major questions: Which particle physics scenario can give rise to successful inflation? And finally: Who is the inflaton particle? 10

11 Bottom-up considerations Various considerations & viewpoints: generically: r = O(0.1) 'Large field' (chaotic) inflation Basic classes of inflation models Often: One just adds a singlet scalar field plus potential without connection to the rest of the theory Small field' (new) inflation Take SM particle (e.g. Higgs) and modify gravity (e.g. introduce nonminimal coupling to gravity ) generically: r < 0.01 'Hybrid-type' inflation models Look for candiates in extensions of the SM 11

12 Top-down viewpoints... Various top-down possibilities: Grand Unified Theories (GUTs)? Family symmetries? } V 0 ~ M GUT Supersymmetry/Supergravity vs. Seesaw mechanism for ν-masses String theory, extra dimensions 12

13 How does inflation fit into a more fundamental theory? Various top-down possibilities: Grand Unified Theories (GUTs)? Various considerations & viewpoints: Basic classes of inflation models Family symmetries? Supersymmetry/Supergravity Seesaw mechanism for ν-masses String theory, extra dimensions Often: One just adds a singlet scalar field plus potential without connection to the rest of the theory Take SM particle (e.g. Higgs) and modify gravity (e.g. introduce nonminimal coupling to gravity ) Look for candiates in extensions of the SM 13

14 Seesaw + SUSY The RH sneutrino as the inflaton m ν m ν y2 νv 2 EW M R The right-handed neutrino superfield: M R ν R = N R + 2θN R + θθf NR P. Minkowski ('77), Mohapatra, Senjanovic, Yanagida, Gell-Mann, Ramond, Slansky, Schechter, Valle,... The right-handed sneutrinos, i.e. the scalar superpartners of the RH neutrinos excellent candidates for acting as the h 0 h 0 inflaton field! N R Framework: local supersymmetry = supergravity 14

15 Two possibilities for the origin of the large RH neutrino masses two options for realising inflation with RH sneutrinos 15

16 Origin of right-handed neutrino masses I) Direct mass terms: II) Mass terms from spontaneous symmetry breaking W MR = M R ν R ν R W MR = λ M Pl ν R ν R HH 16

17 Origin of right-handed neutrino masses I) Direct mass terms: II) Mass terms from spontaneous symmetry breaking W MR = M R ν R ν R W MR = λ M Pl ν R ν R HH For example: In SO(10) GUTs: 1 Λ 16 i16 j H 16H 16 In some A 4 flavour models (with θ (i) flavons in 3 of A 4 ): 1 Λ ν Riν Rj θ (i) θ (j) 17

18 Chaotic Sneutrino Inflation I) Direct mass terms: Murayama, Suziki, Yanagida, Yokoyama ( 93) W MR = M R ν R ν R Inflaton potential from: F νr 2 = W ν R = M R Ñ R 2 θ=0 Predictions for CMB observables: n s 0.96, r 0.16 Predictions for neutrino physics: M R GeV Note: ν R has to be a total singlet! 18 'Large field' (chaotic) sneutrino inflation In supergravity: W+ suitable Kähler potential K

19 Sneutrino Hybrid Inflation II) Mass term from spontaneous symmetry breaking (SSB) W = κs(h 2 M 2 )+ Additional term in W is just a SUSY version of a SSB potential F S 2 V(H, Ñ R =0) λ M Pl ν R ν R HH S.A., Bastero-Gil, King, Shafi ( 04) i) <Ñ R > 0 can stabilise H at <H> = 0 and leads to large vacuum energy V 0 ~ M ii) Large masses for the RH (s)neutrinos when H gets a vev after inflation } V 0 'Hybrid-type' sneutrino inflation 19

20 Chaotic Hybrid models can be distinguished by the results of the Planck satellite Prediction of Chaotic Sneutrino Inflation Murayama, Suziki, Yanagida, Yokoyama ( 93) (WMAP 10, WMAP '08) Prediction of Sneutrino Hybrid Inflation S.A., Bastero-Gil, King, Shafi ( 04) (WMAP 10, WMAP '08) 20

21 Sneutrino Hybrid Inflation W = κs(h 2 M 2 )+ λ M Pl ν R ν R HH Driving superfield (its F-term generates the potential for H and provides the vacuum energy V 0 ; During and after inflation: <S> = 0.) F S 2 Waterfall superfield (contains the waterfall field (e.g. GUT- or Flavour-Higgs field) that ends inflation by a 2 nd order phase transition) V(H,Ñ R =0) } V 0 In supergravity: W + suitable Kähler potential K 21

22 Sneutrino Hybrid Inflation F S 2 W = κs(h 2 M 2 )+ λ M Pl ν R ν R HH V(H, Ñ R =0) } V 0 During inflation: Inflaton superfield (ν R contains the inflaton field Ñ R as scalar component; For <Ñ R > > Ñ R,crit it stabilises H at <H> = 0) 22 <Ñ R > > Ñ R,crit Ñ R 22

23 Sneutrino Hybrid Inflation W = κs(h 2 M 2 )+ λ M Pl ν R ν R HH During inflation: with V = V tree + L loop Inflaton superfield (ν R contains the inflaton field Ñ R as scalar component; For <Ñ R > > Ñ R,crit it stabilises H at <H> = 0) Ñ R 23

24 Sneutrino Hybrid Inflation W = κs(h 2 M 2 )+ λ M Pl ν R ν R HH End of inflation: Inflaton superfield (ν R contains the inflaton field Ñ R as scalar component; For <Ñ R > > Ñ R,crit it stabilises H at <H> = 0) Ñ R 24

25 Sneutrino Hybrid Inflation W = κs(h 2 M 2 )+ λ M Pl ν Ri ν Ri HH +(y ν ) ij ν Ri hl j Neutrino Yukawa couplings After inflation: Reheating... 1 Ñ R 25

26 Sneutrino Hybrid Inflation W = κs(h 2 M 2 )+ λ M Pl ν Ri ν Ri HH +(y ν ) ij ν Ri hl j Neutrino Yukawa couplings After inflation: 1 Non-thermal leptogenesis after sneutrino inflation: very efficient way of generating the observed baryon asymmetry! Ñ R In Sneutrino Hybrid Inflation: S.A., Baumann, Domcke, Kostka ( 10) 26

27 CMB observables running of the spectral index (α S ) spectral index n s r = A T /A S M: scale of the phase transition very small (as typical for Hybridtype models) ~ M GUT Example: Predictions in a toy model... S.A., K. Dutta, P. M. Kostka ('09) 27

28 Sneutrino hybrid inflation and non-thermal leptogenesis Ñ R1 inflaton decay asymmetry ε depends on seesaw flavour structure! S.A., Baumann, Domcke, Kostka ( 10) 28

29 Sneutrino hybrid inflation and non-thermal leptogenesis Requirements for neutrino ( seesaw ) parameters: m N1 = O( ) GeV m ν ev y ν1 = O( ) Ñ R1 inflaton in a simple example model of Sneutrino Hybrid Inflation... S.A., Baumann, Domcke, Kostka ( 10) 29

30 Sneutrino Hybrid Inflation belongs to a more general class of models: Matter Inflation W = κs(f(h) M 2 )+g(φ,h) Driving superfield Waterfall superfield Inflaton superfield (resides in the matter sector) Also referred to as Tribrid Inflation, because three fields play some role in the superpotential of the models S.A., M. Bastero-Gil, K. Dutta, S. F. King, P. M. Kostka ( 08) 30

31 Further developments & possibilities in Matter Inflation Inflaton does not have to be a gauge singlet. It can also be a gauge nonsinglet (e.g. a D-flat direction of GUT representations) S.A., Bastero-Gil, Baumann, Dutta, King, Kostka ( 10) The (2 nd order) phase transition at the end of inflation can be... a GUT phase transition... the breaking of a family symmetry (e.g. A 4, ) Dvali, Shafi, Schaefer ( 94) S. A., King, Malinsky, Velasco-Sevilla, Zavala ( 07) Possibilites for realising Matter Inflation in Heterotic String Theory... S. A., Halter, Erdmenger ( 11) 31

32 Further developments & possibilities in Matter Inflation No monopoles are generated at the end of inflation if the inflaton is a gauge non-singlet ( group broken during inflation)... if a family symmetry is broken at the end of inflation (as in flavon inflation )... in pseudosmooth versions of tribrid inflation S.A., Bastero-Gil, Baumann, Dutta, King, Kostka ( 10) S. A., King, Malinsky, Velasco-Sevilla, Zavala ( 07) S.A., Nolde, Ur Rehman ( 12) The η-problem ( flatness problem of the inflaton potential) can be solved in SUGRA by symmetry (e.g. by a Heisenberg or shift symmetry in the Kähler potential) S.A., M. Bastero-Gil, K. Dutta, S. F. King, P. M. Kostka ( 08) S.A., K. Dutta, P. M. Kostka ('09) 32

33 Second part of my talk: Are there GUT-footprints in fermion masses and mixings? 33

34 One motivation: Why are the observed masses of down-type quarks and charged leptons similar (but not equal)? m b m τ? m s m µ? (running masses at the top-mass scale; errors are 3 times the 1σ errors...) 34

35 GUTs: Unification of forces and of matter particles i) Unification of forces at M GUT ~ GeV... with SUSY ii) Unification of matter particles in joint representations of the GUT group E.g. in SU(5) GUTs: In SO(10) GUTs: 5 i + 10 i + ν Ri in 16 i 35 _

36 GUTs: Unification of forces and of matter particles i) Unification of forces at M GUT ~ GeV... with SUSY ii) Unification of matter particles in joint representations of the GUT group E.g. in SU(5) GUTs: One consequence: Elements of the matrices M d and M e can be generated by one single operator they differ only by group theoretical Clebsch factors In SO(10) GUTs: 5 i + 10 i + ν Ri in 16 i _ 36

37 This leads to GUT relations between the masses of down-type quarks and charged leptons (e.g. in SU(5) GUTs): Relations from fundamental operators: bottom-tau unification Georgi, Jarlskog ( 79) SM Higgs particle in GUT representation H 45 37

38 Remark: In models aiming at explaining the fermion mass hierarchies, the masses << m t are typically generated by effective operators! Froggatt, Nielsen ( 79) With effective operators new interesting GUT predictions for m τ /m b and m µ /m s can arise! S. A., Spinrath ( 09) 38

39 This leads to GUT relations between the masses of down-type quarks and charged leptons (e.g. in SU(5) GUTs): Relations from effective operators, e.g.: S. A., Spinrath ( 09) Their viablity depends on RG running and threshold corrections (in SUSY)! i) The GUT Higgs H 24 breaks the GUT symmetry to the SM ii) The effective operators can explain the hierarchy of masses 39

40 M u U CKM = U u U d M d GUT relations Mass M GUT, e.g.: m τ m b = c 33 = 1, 3 2 m µ m s = c 22 = 3, 9 2, 6 m ν M e (c ij : group theory Clebsch factors) U PMNS = U e U ν Clebsch factors {1,3} in GUTs: Georgi, Jarlskog ( 79) New possible Clebsch factors {3/2,3,9/2,6,...}: S.A., Spinrath ( 09) 40

41 In addition to GUT relations for the mass eigenvalues, there are also relations for the mixing angles... 41

42 M u M d Mixing angle M GUT, e.g.: U CKM = U u U d GUT relations m ν M e θ e 12 = c 12 c 22 θ d 12 = c 12 c 22 θ C U PMNS = U e U ν Such GUT relations for the mixings can leave footprints in the observable leptonic (PMNS) mixing parameters... Possible new combinations of Clebsches leading to large θ 13 PMNS : S.A., Maurer ( 11) Mazocca, Petcov, Romanino, Spinrath ( 11) 42

43 M u M d U CKM = U u U d Let us consider... Specific mixing pattern in m ν, e.g.: m ν U PMNS = U e U ν M e Tri-bimaximal mixing: U ν = U TB Bimaximal mixing: U ν = U Bimax } with θ 13 ν 0 43

44 More hierarchical masses in M u than in M d θ ij u << θ ij d typically θ 12 d θ C and θ 13d, θ 23 d << θ C M u M d U CKM = U u U d Let us consider U ν with: θ 13 ν 0 m ν U PMNS = U e U ν M e 44

45 θ 12 d θ C M u M d U CKM = U u U d GUT relations Let us consider U ν with: θ 13 ν 0 m ν U PMNS = U e U ν M e θ e 12 = c 12 c 22 θ d 12 = c 12 c 22 θ C and θ 13e, θ 23 e << θ C 45

46 θ 12 d θ C M u M d U CKM = U u U d GUT relations Let us consider U ν with: θ 13 ν 0 m ν U PMNS = U e U ν M e θ e 12 = c 12 c 22 θ d 12 = c 12 c 22 θ C and θ 13e, θ 23 e << θ C The PMNS mixing parameters result from U ν and charged lepton mixing effects (U e ) Two main effects 46

47 Charged lepton mixing effects: works by many authors... θ 12 d θ C M u M d Let us consider U ν with: θ 13 ν 0 m ν U CKM = U u U d M e GUT relations θ e 12 = c 12 c 22 θ d 12 = c 12 c 22 θ C and θ 13e, θ 23 e << θ C 1) Prediction for θ 13 PMNS : θ PMNS 13 = θe 12 2 = θ C 2 c 12 c 22 U PMNS = U e U ν under simple conditions in GUTs e.g.: θ PMNS 13 = θ C 2 S.A., Maurer ( 11); Mazocca, Petcov, Romanino, Spinrath ( 11); King ( 12); S.A., Gross, Maurer, Sluka ( 12) Remark: θ 13 PMNS = θ C / 2 also appears, e.g., in a variant of Quark-Lepton- Complementarity: Minakata, Smirnov ( 04) 47

48 θ 12 d θ C M u M d Let us consider U ν with: θ 13 ν 0 m ν U CKM = U u U d M e GUT relations θ e 12 = c 12 c 22 θ d 12 = c 12 c 22 θ C and θ 13e, θ 23 e << θ C 2) Lepton Mixing Sum Rule : U PMNS = U e U ν θ PMNS 12 = θ ν 12 + θ PMNS 13 cos(δ PMNS ) King ( 05); Masina ( 05); S.A., King ( 05) 48

49 Reconstructing θ 12 ν using the lepton mixing sum rule θ 12 PMNS = θ 12 ν + θ 13 PMNS cos(δ PMNS ) δ PMNS = ± 90 Bimaximal ν-mixing Tri-Bimaximal ν-mixing δ PMNS = 180 using present data, θ 13 PMNS = 8.8 ± 1.0 figure from S.A., Gross, Maurer, Sluka ( 12) 49

50 Note: Predictions emerge at high energies RG running required RGEs for the leptonic mixing angles (in LO in θ 13 ; in the MSSM): (RGEs in the SM: above equations times -3/2) S.A., Kersten, Lindner, Ratz ( 03) Including RG effects from Y ν (analytical formulae + software REAP): S.A., Kersten, Lindner, Ratz, Schmidt ( 05) 50

51 Summary and conclusions The RH sneutrino is an attractive candidate for the Inflation: Chaotic vs Hybrid-like (= Tribrid ) GUTs & Flavour Neutrino masses In Sneutrino Tribrid Inflation: The end of inflation can be associated with GUT or family symmetry breaking Early Universe Inflation θ 13 PMNS θ C / 2 can emerge under simple conditions from GUTs high energies (M GUT ): careful model analysis including RG running required...! 51