Nucleon Decay. Stuart Raby. DUSEL 2010 Rapid City, SD October 2, 2010

Transcription

1 Nucleon Decay Stuart Raby DUSEL 2010 Rapid City, SD October 2, 2010

2 Nucleon Decay Standard Model Baryon & Lepton number - anomalous global symmetries Weinberg - effective operators consistent with SM 1 M eg. ( * ) ( * µ ) b d 2 a µ uc 0 σ e σ u ε p e + π New physics at scale M breaks B & L eg. Grand unification M = M GUT eg. Universal large extra dims. abc p e π π νν + + M ~ TeV e e ( ) µ π ν + + +

3 Outline Evolution of SUSY GUTs 4 dimensional SUSY GUTs 5 dimensional orbifold GUTs String orbifolds orbifold GUTs Conclusions

4 Outline 4 dimensional SUSY GUTs 5 dimensional orbifold GUTs String orbifolds orbifold GUTs Conclusions

5 The Goal of Beyond SM physics Reduce # fundamental parameters 18 parameters in Standard Model 13 charged fermion masses & mixing + 3 gauge couplings + 2 W & Higgs mass 27 including neutrino masses & mixing 28 including QCD θ parameter 29 including G N

6 Supersymmetric Grand Unified Theories M Z << M G natural Explains charge quantization & Families Unification of gauge couplings Yukawa coupling unification + family symmetry fermion mass hierarchy Neutrino masses via See-Saw LSP - dark matter candidate Baryogenesis via leptogenesis SUSY desert LHC probes physics at M Pl SUSY GUTs natural extension of SM Title of talk 6

7 u ν q=, u, d, l =, e, ν d e Y :,,, 1, + 2, H u + 0 h h, H 0 d = = h h + 1, 1 Q EM = T + 3 Y 2 Title of talk 7

8 All interactions of fermions & Higgs with gauge bosons fixed by their charges Y Dµ = ( µ + igst AGµ A + igtaw µ a + ig Bµ ) 2 Lgauge fermion = [ l i D l + ] + [ Tr( G G ) + ] 2 * µ 1 µν σ µ µν L = DH + DH + V 2 2 gauge Higgs µ u µ d Higgs L = λ le H + λ qd H ij ij Yukawa e i j d d i j d ij ij 1 + λu qu i j Hu + λν liν j Hu Mijνν i j 2 Title of talk 8

9 The MSSM is obtained by defining chiral superfields Ey (, θ) = ey ( ) + 2( θey ( )) + ( θθ) F( y) y µ = x µ iθσ µ θ, ( θey ( )) θ α ey ( ) 4 Y Lgauge matter = d θ [ Li exp( 2 [ gsvg + gvw + g VB ]) Li + ] θ [ ( ) + ] α d Tr W 2 g Wgα h c 8gs L = dθ [ λ LE H + λ QD H 2 ij ij Yukawa e i j d d i j d + λ QU H + λ U V Q =, U, D,L =, EV, D E LV H ij ij u i j u ν i j u 1 Mij Vi V j µ Hu Hd ] + h. c. 2 Title of talk 9 e α

10 Grand Unification & Charge Quantization u u u q= u = d = d d d l ν = e e ( u u u) ( d d d ) SU(4) SU(2) SU(2) C L R Q u u u ν u u u ν = Q d d d e = d d d e Q = B L + T + T 1 2 ( ) 3 3 EM L R

11 Pati-Salam - lepton # = 4 th color Quarks & leptons fit into two irreducible reps. Q= ( ql), Q= ( ql) SU(4) SU(2) SU(2) u ν q=, l = (4,2,1) (4,1, 2) d e The two Higgs doublets H = ( H H ) (1, 2, 2) d u C L R QHQ λ λ = λ = λ = λ λ t b τ ν τ Yukawa coupling unification Title of talk 11

12 Grand Unification - SO( 10 ) GUT 1 Georgi Fritszch & Minkowski spinor repsn. of SO( 10 ) 10 tensor product of 5 spin ½ w/even no. + signs 5 Title of talk Georgi & Glashow SU(5) 12

13 Gauge coupling unification Boundary conditions at M GUT A A a Y ggta G gst AG + gtaw + g' B 2 µ µ µ µ g,, ' 3 s = g g = g g = g g ' , sin θ G W 2 2 g = g = g = g = = g + g' 8 Title of talk 13

14 Gauge coupling unification Dimopoulos, Raby & Wilczek PRD24, 1681 (1981) LEP data!! Amaldi, de Boer & Furstenau, PLB260, 447 (1991) Title of talk 14

15 ε 3 Title of talk 15

16 This assumes degenerate squarks and sleptons and degenerate gauginos at GUT scale. If, for example, even have ε. 3 0 M3 << M2 M1 then can See Raby, Ratz, Schmidt-Hoberg arxiv: [hep-ph] Title of talk 16

17 Proton decay - dim 6 operators c l i c d a Title of talk 17

18 p + e π 0 Title of talk 18

19 Super Kamiokande bound τ p Br( p e π ) 34 yrs Theory τ p M Br( p e + π ) g m 4 G G p GeV M X α 3 10 GeV yrs Title of talk 19

20 Proton decay - dim 4 operators λ UDD+ λ' Q L D + λ" EL L P p π π ν or ( π π, π π ) Title of talk 20 e

21 Γ p ( λλ' ) m 2 m 5 p 4 λλ' m 2 g G m < 10 GeV λλ' < 10 M G 1TeV matter parity excludes dim 4 operators F -F, H H Title of talk 21

22 Proton decay - dim 5 operators Q QQ L + UU DE p K ν Title of talk 22 +

23 λλ t ( LF) τ µ 16π /2 2 2 m16 + cc Ap ( Kν ) (LF) eff M T M c ~ Yukawa couplings minimize LF maximize M T eff Eg. "Natural" D T splitting W (10 ) 45 G 2 X with M B L ( ) M T 0 M G 1 X 0 0 =, M eff 2 D MG X = MT M G 0 X Thus for eff X << M obtain M >> M G T G Title of talk 23

24 = + + Higgs GUT breaking Higgs 3 eff 3α G M T = ln( ) 5π M G Minimal SU 5 : Proton decays toooo fast!! 33 τ > yrs (92 ktyr) at 90% CL ( p K + ν ) ~ (1/3-3) yrs Theory Title of talk 24

25 Minimal SU 5 excluded! Caveats: 1. Family structure is standard 2. ε 3 < 0 Title of talk 25

26 Minimal SO(10) Model 45 W M Albright, Anderson, Babu, Barr, Barbieri, Berezhiani, Blazek, Carena, Dermisek, Dimopoulos, Hall, Pati, Raby, Romanino, Rossi, Starkman, Wagner, Wilczek, Wiesenfeldt, Willenbrock Effective higher dimension operators, Small rep s + Many predictions!! Possible UV completion to strings!! Title of talk 26

27 3 family SO 10 SUSY Model D 3 x U(1) Family Symmetry Superpotential Yukawa couplings χ 2 analysis Charged fermion masses & mixing Neutrino masses & mixing

28 Superpotential for charged fermion Yukawa couplings W = χ ch. fermions 3 3 a a φ a φ a + χ Mχ χ A16 M M a a a a φ φ 1 = φ2 φ Familon VEVs 0 = φ 2 assumed ( B ) 45 = L MG Title of talk 28

29 7 real para s + 4 phases SO(10) x [ D 3 x U(1) family sym. ] Yukawa Unification for 3 rd Family + 3 real Majorana Neutrino masses Dermisek & Raby PLB 622:327 (2005). Title of talk 29

30 Extend to neutrino sector ( λ λ ) W = 16 N 16 + N 16 neutrino 2 a a ( SNN SNN) a a a S M S M a = = 16 = v a Assume 3 new real para s Title of talk 30

31 Global χ 2 analysis 24 parameters at GUT scale compared to SM - 27 parameters CMSSM - 32 parameters Title of talk 31

32 χ 2 analysis including B physics Albrecht, Altmannshofer, Buras, Guadagnoli, & Straub JHEP 0710:055 (2007) Find good fits to quark, charged lepton & neutrino masses and mixing angles & test flavor violation in b physics some tension between b s γ & b s l + l - m 16 ~ 10 TeV Title of talk 32

33 + What is the tension? ( SM ) χ µ A tan β sign 2 SM 7 t 7 7 C C C b t s A < 0 t χ χ γ C = C + C C SM SM χ + BR(B X l l ) favors C + C + SM s 7 7 at 2 σ Title of talk 33

34 However C = C SM 7 7 B * + K l l Belle arxiv: Title of talk 34

35 Albrecht et al. JHEP 0710:055 (2007) Required SM 7 7 Title of talk 35 C = + C

36 MSO 10 SM & Large tan( β ) Predicts light Higgs with mass of order GeV Predicts lighter 3 rd and heavy 1 st & 2 nd gen. squarks and sleptons (inverted scalar mass hier.) LFV bounds satisfied Enhances Br[ B s µ + µ ] Suppresses Br( B τ ν ) & M B s B X s γ, X s l + l - tension?? LHCb Title of talk 36

37 MSO 10 SM & Large tan( β ) predicts light gluinos ~ GeV predicts light charginos and neutralinos LHC MSO 10 SM : Beautiful symmetry Many experimental tests!! Title of talk 37

38 Problems of SUSY GUTs GUT symmetry breaking Higgs doublet-triplet splitting Missing partner mechanism SU(5) W + M + H + H H + XH H Hu d Missing VEV mechanism SO(10) ( ) 2 ( ) 4 2 W 45 + M 45 + X F X ( S S ) ( S S ) X ( ) + 16' ' ' ' + ' 10' 1 2 Title of talk 38 2

39 Outline 4 dimensional SUSY GUTs 5 dimensional orbifold GUTs String orbifolds orbifold GUTs Conclusions Title of talk 39

40 Orbifold GUTs in 5 or 6 dimensions GUT symmetry breaking Doublet-Triplet splitting Kawamura; Hall & Nomura; Contino, Pilo, Rattazzi & Trincherini; Altarelli, Feruglio & Masina; Dermisek & Mafi; H.D. Kim & Raby; Asaka, Buchmuller & Covi; Lee; Hebecker & March-Russell H.D.Kim, Raby & Schradin JHEP 0505:036 (2005) Title of talk 40

41 Hall & Nomura SU(5) GUT on M x S 1 /(Z 2 x Z 2 ) GUT symmetry breaking Suppress b-τ Yukawa Higgs D-T splitting proton decay unification via orbifold BCs rd 3 family Brane states c ( H + H ) ( c H + H ) 1 st & 2 nd families in bulk Bulk states π R Title of talk 41

42 G.C. Unif. & Proton decay > 4D 5D Orbifold GUT KK modes 0 πr M c ~ 1/πR < M G < M * Dienes et al., Hall & Nomura, Kim & S.R., Feruglio et al. Title of talk 42

43 u G.C. Unif. & Proton decay Enhanced > 4D!! 5D Orbifold u GUT Dim 6 amp. ~ 1 / M C 2 u u } π 0 P 0 R M C Brane e d Proton 0 π + e + M c ~ 1/R < M G < M * γγ Title of talk 43

44 G.C. Unif. & Proton decay Suppressed > 4D!! Dim 6 amp. ~ 1 / M C 2 u 5D Orbifold u GUT u U } π 0 P 0 R M C Bulk E d Proton 0 π + e + M c ~ 1/R < M G < M * γγ Title of talk 44

45 Orbifold GUTs in 5 or 6 dimensions : GUT breaking via Orbifold Parity Higgs doublet - triplet splitting via Orbifold P NO proton decay via Dim 5 operators due to R symmetry Proton decay via Dim 6 operators can be suppressed, BUT typically enhanced (model dependent) Matter localization determines Yukawas Title of talk 45

46 Outline 4 dimensional SUSY GUTs 5 dimensional orbifold GUTs String orbifolds orbifold GUTs Conclusions Title of talk 46

47 UV completion Orbifold GUTs in 5 or 6 dimensions Derived from heterotic string in 10 D Kobayashi, Raby & Zhang; Forste, Nilles, Vaudrevange & Wingerter; Buchmuller, Hamaguchi, Lebedev & Ratz; JE Kim, JH Kim & Kyae; Buchmuller, Ludeling & Schmidt Title of talk 47

48 Road to the MSSM with R-parity Lebedev et al [hep-th] Find 15 models from orbifold compactification of E(8)xE(8) heterotic string MSSM spectrum at low energy Exact R parity Light Higgs Non-trivial charged fermion masses Neutrino masses via See-Saw Title of talk 48

49 Compactify E(8)xE(8) heterotic string on (T 2 ) 3 /(Z 3 ) + A 3 only ( R 5 >> l s ) SU(6) orbifold GUT BULK After Z 2 SU(5) brane Z 2 = Z 2 + A 2 SU(4)xSU(2) brane Title of talk 49

50 Bulk states SU( 6) SU( 5) H + H Gauge Higgs unification! c t ( ) Q = + t + b ( c ν ) τ + L= + b τ Tree level coupling u d 3 rd family Title of talk 50 τ c Q H t u

51 Benchmark model 1 - Spectrum S Title of talk 51

52 Yukawa couplings Effective higher dimension operators!! Neutrino masses via See-Saw!! Title of talk 52

53 4 3 2 R symmetry LR S V Q U D L E V H H R u d Superpotential W has charge 2 Title of talk 53

54 Conclusions Evolution of SUSY GUT Model Building Bottom up 4D SUSY GUT + family symmetry test predictions via global χ 2 analysis Lift to 5D ( or 6D ) orbifold GUT Top down Derive from heterotic string, M or F theory includes Gravity!! Title of talk 54