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 eg. New physics at scale M breaks B & L eg. Grand unification M = M GUT eg. Universal large extra dims. M ~ TeV

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  parameter 29 including G N

6. Title of talk6 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 USY GUTs “natural extension of SM”

7. Title of talk7

8. 8 All interactions of fermions & Higgs with gauge bosons fixed by their charges

9. Title of talk9 The MSSM is obtained by defining chiral superfields

10. Grand Unification & Charge Quantization

11. Title of talk11 The two Higgs doublets Quarks & leptons fit into two irreducible reps. Pati-Salam - lepton # = 4 th color Yukawa coupling unification

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

13. Title of talk13 Gauge coupling unification Boundary conditions

14. Title of talk14 Gauge coupling unification Dimopoulos, Raby & Wilczek PRD24, 1681 (1981) LEP data !! Amaldi, de Boer & Furstenau, PLB260, 447 (1991)

15. Title of talk15 

16. Title of talk16 This assumes degenerate squarks and sleptons and degenerate gauginos at GUT scale. If, for example, then can even have. See Raby, Ratz, Schmidt-Hoberg arXiv:0911.4249 [hep-ph]

17. Title of talk17 Proton decay - dim 6 operators

18. Title of talk18

19. Title of talk19

20. Title of talk20 Proton decay - dim 4 operators P

21. Title of talk21

22. Title of talk22 Proton decay - dim 5 operators

23. Title of talk23 c ~ Yukawa couplings minimize LF maximize M T eff

24. Title of talk24 Minimal SU 5 : Proton decays toooo fast !!

25. Title of talk25 Minimal SU 5 excluded ! Caveats:  Family structure is standard   < 0

26. Title of talk26 “Minimal” SO(10) Model Albright, Anderson, Babu, Barr, Barbieri, Berezhiani, Blazek, Carena, Dermisek, Dimopoulos, Hall, Pati, Raby, Romanino, Rossi, Starkman, Wagner, Wilczek, Wiesenfeldt, Willenbrock Possible UV completion to strings !! Effective higher dimension operators, Small rep’s + Many predictions !!

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

28. Title of talk28 Superpotential for charged fermion Yukawa couplings Familon VEVs assumed

29. Title of talk29 SO(10) x [ D 3 x U(1) family sym. ] Yukawa Unification for 3 rd Family Dermisek & Raby PLB 622:327 (2005). 7 real para’s + 4 phases + 3 real Majorana Neutrino masses

30. Title of talk30 Extend to neutrino sector Assume 3 new real para’s

31. Title of talk31 compared to SM - 27 parameters CMSSM - 32 parameters 24 parameters at GUT scale Global   analysis

32. Title of talk32    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  & b  s l + l - m 16 ~ 10 TeV

33. Title of talk33  bs What is the tension ?

34. Title of talk34 Belle arXiv:0904.0770 However …

35. Title of talk35 Albrecht et al. JHEP 0710:055 (2007)

36. Title of talk36 MSO 10 SM & Large tan(  )  Predicts light Higgs with mass of order 120 – 130 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      ]  Suppresses Br( B  ) &  M B s  B X s , X s l + l - tension ?? LHCb

37. Title of talk37 MSO 10 SM & Large tan(  )  predicts light gluinos ~ 300 – 500 GeV  predicts light charginos and neutralinos LHC MSO 10 SM : Beautiful symmetry Many experimental tests !!

38. Title of talk38 Problems of SUSY GUTs  GUT symmetry breaking  Higgs doublet-triplet splitting Missing partner mechanism SU(5) Missing VEV mechanism SO(10)

39. Title of talk39 Outline  4 dimensional SUSY GUTs  5 dimensional orbifold GUTs  String orbifolds orbifold GUTs  Conclusions

40. Title of talk40 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)

41. Title of talk41 Brane states Bulk states 1 st & 2 nd families in bulk Hall & Nomura SU(5) GUT on M x S 1 /(Z 2 x Z’ 2 ) b-  Yukawa unification Suppress proton decay GUT symmetry breaking Higgs D-T splitting via orbifold BCs

42. Title of talk42 5D Orbifold GUT G.C. Unif. & Proton decay > 4D 0 RR M c ~  R < M G < M * Dienes et al., Hall & Nomura, Kim & S.R., Feruglio et al. KK modes

43. Title of talk43 5D Orbifold GUT G.C. Unif. & Proton decay > 4D 0 R M c ~ 1/R < M G < M * Dim 6 amp. ~ 1 / M C 2 MCMC Enhanced !! Brane

44. Title of talk44 5D Orbifold GUT G.C. Unif. & Proton decay > 4D 0 R M c ~ 1/R < M G < M * Dim 6 amp. ~ 1 / M C 2 MCMC Suppressed !! Bul k

45. Title of talk45 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

46. Title of talk46 Outline  4 dimensional SUSY GUTs  5 dimensional orbifold GUTs  String orbifolds orbifold GUTs  Conclusions

47. Title of talk47 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

48. Title of talk48 Road to the MSSM with R-parity Lebedev et al. – 0708.2691[hep-th] MSSM spectrum at low energy Exact R parity Light Higgs Non-trivial charged fermion masses Neutrino masses via See-Saw Find 15 models from orbifold compactification of E(8)xE(8) heterotic string

49. Title of talk49 Compactify E(8)xE(8) heterotic string on (T 2 ) 3 /(Z 3 ) + A 3 only ( R 5 >> l s ) SU(6) orbifold GUT After Z 2 SU(5) brane Z’ 2 = Z 2 + A 2 SU(4)xSU(2) brane BULK

50. Title of talk50 Tree level coupling Bulk states Gauge – Higgs unification ! 3 rd family

51. Title of talk51 “Benchmark” model 1 - Spectrum

52. Title of talk52 Yukawa couplings Effective higher dimension operators !! Neutrino masses via See-Saw !!

53. Title of talk53 Superpotential W has charge 2

54. Title of talk54 Conclusions Evolution of SUSY GUT Model Building Bottom up  4D SUSY GUT + family symmetry test predictions via global    analysis  Lift to 5D ( or 6D ) orbifold GUT Top down  Derive from heterotic string, M or F theory includes Gravity !!