1. SUSY Model Building Stuart Raby SUSY 2007 Karlsruhe, Germany July 30, 2007

2. Outline  Introduction  Dynamical SUSY breaking  “Little” hierarchy problem, etc.  SUSY GUTs  UV completions  Conclusions

3. Supersymmetric Standard Model Motivation ?? Solve hierarchy problem M Z /M Pl ~ 10 -16 SM - fine-tuning ~ 10 -32 SUSY Dynamical “technically natural”

4. SUSY GUTs Motivation ??  Charge quantization  Family structure  Gauge coupling unification It works !! M GUT ~ 10 16 GeV w/ M SUSY ~ 1 TeV !!  Neutrino masses See-Saw scale ~ (.01 -.1 ) M GUT

5. Minimal Supersymmetric Standard Model Q, U c, D c, L, E c, N c Fermions + Sfermions V i ( i =1,2,3 ) gauge bosons + gauginos H u, H d Higgs + Higgsinos Spectrum R parity, Family reflection sym. or Matter parity

6. Minimal Supersymmetric Standard Model Soft SUSY breaking Over 100 arbitrary parameters – squark & slepton masses gaugino masses quadratic & cubic scalar int’s SUSY flavor problem “Little” hierarchy problem  & B  problems

7. SUSY Model Building “Little” hierarchy prob. Flavor problem  problem CP problem Doublet – triplet splitting GUT breaking

8. SUSY Model Building Good mechanism

9. SUSY Model Building Better

10. SUSY Model Building Best

11. Dynamical SUSY breaking Intriligator, Seiberg & Shih; Dine, Feng & Silverstein; Kitano, Ooguri & Ookouchi; Argurio, Bertolini, Franco & Kachru; Murayama & Nomura; Dine & Mason; Brummer; Bai, Fan & Han; Dudas, Mourad & Nitti; Gomes-Reino & Scrucca; Amariti, Girardello & Mariotto; Essig, Sinha & Torroba; Ahn; Serone & Westphal; Cho & Park; Abel, Dumford, Jaeckel & Khoze; Tatar & Wetenhall; van den Broek; Ferretti; Pastras; Ooguri, Ookouchi & Park; Kawano, Ooguri & Ookouchi

12. Dynamical SUSY breaking Meta-stable SUSY breaking vacua in Global SUSY are quite probable ! Dynamical SUSY breaking is easy !! See talk by Murayama

13. Kachru, Kallosh, Linde & Trivedi; Choi, Falkowski, Nilles, Olechowski, Pokorski; Endo, Yamaguchi & Yoshioka; Choi, Jeong & Okumura; Falkowski, Lebedev & Mambrini; Kitano & Nomura; Lebedev, Nilles & Ratz; Lebedev, Loewen, Mambrini, Nilles & Ratz; Acharya, Bobkov, Kane, Kumar & Vaman (Shao); Randall & Sundrum; Giudice, Luty, Murayama & Rattazzi Meta-stable SUSY breaking vacua in Local SUSY/string theory are generic !

14. SUSY breaking mechanisms  Meta-stable SUSY breaking vacua are ubiquitous w/ Cosmologically long life-times i. Gravity mediated SUSY breaking ii. Gauge mediated “ iii. Anomaly mediated “ + variations on the above Eg. gaugino, moduli, dilaton mediation

15. “Little” hierarchy problem m h > 114.4 GeV

16. RG running from M GUT ( tan  = 10 ) Can also minimize fine – tuning with light gluino !! Fine tuning ~ 10 -2 - 10 -3 Compared to 1 part in 10 32 in SM

17. Title of talk17 Some suggested solutions  problem “Little” hierarchy

18. Title of talk18 Gauge Messenger model Dermisek & Kim (+ Kim)

19. Title of talk19

20. Title of talk20 Bottom Line Gauge mediation w/gauge messengers solves flavor problem 5 – 10 % fine tuning gravitino LSP stau NLSP X Needs UV completion X Doesn’t address  problem

21. Title of talk21 Sweet Spot SUSY Ibe & Kitano Gauge & Gravity mediation M mess ~ 10 -3 M GUT solves flavor problem F/M mess >> F/M Pl solves && B pp roblems Giudice & Masiero UV completion w/ GUT breaking & Higgs D-T splitting X Doesn’t solve “Little” hierarchy Gravitino LSP mass ~ 1 GeV

22. Title of talk22 Mirage Mediation Choi, Falkowski, Nilles, Olechowski, Pokorski, Jeong, Okumura, Lebedev, Mambrini, Ratz, Kobayashi, Endo, Yamaguchi, Yoshioka, Loewen Based on Type II Superstring Moduli stabilization & SUSY breaking Kachru, Kallosh, Linde & Trivedi Gravity (Modulus) & anomaly mediation == anomaly : Modulus SUSY breaking ratio

23. Title of talk23  ~ 1

24. Title of talk24 TeV scale Mirage Mediation Choi, Jeong, Kobayashi & Okumura ; Kitano & Nomura 

25. Title of talk25 TeV scale Mirage Mediation Choi, Jeong, Kobayashi & Okumura ; Kitano & Nomura

26. Title of talk26 Bottom Line  Preserves gauge coupling unification at M GUT ~ 10 16 GeV  Gaugino masses unify BUT typically below the GUT scale  Cures neg. slepton mass squared problem of pure anomaly mediation an address “Little” hierarchy problem X Solution to Flavor prob - model dependent 

27. Title of talk27 Gaugino Code Nilles & Choi  mSugra - GMSB pattern  anomaly pattern  mirage pattern  gauge messenger pattern

28. Title of talk28  “Little” hierarchy problem   problem  fermion masses suggest Higgs special !! Higgs “portal” on BMSSM physics Patt & Wilczek; O’Connell, Ramsey-Musolf & Wise

29. Title of talk29 NMSSM Ellis, Gunion, Haber, Roszkowski & Zwirner; Drees; Ellwanger, Rauch, Traubenberg & Savoy; Pandita; King & White; Franke & Fraas; Dine, Seiberg & Thomas Higgs may be heavier than LEP bound even with light stop due to added mass shift

30. Title of talk30 NMSSM Dermisek& Gunion Higgs may be lighter than LEP bound BUT has new ‘invisible’ decay modes OR

31. Title of talk31 MSSM at Large tan  Talk by Heinemeyer m h = 115 GeV, m A = 160 GeV Br( B s ->    ))  Talk by Belyaev m h = 60 GeV Br( h -> b b ) Br( h ->  )

32. Title of talk32 SUSY GUTs Charge quanization & Fermion masses SO(10) special 16 : Q, U c, D c, L, E c, N c 10 : H u, H d, T, T c Doublet – Triplet splitting ?? GUT symmetry breaking ?? Proton decay ??

33. Title of talk33 Fermion Masses in SO(10) 16 10 16top, bottom, tau,  Yukawa unification Mohapatra, Babu, Senjanovic, Bajc, Aulakh, Chen, Mahanthappa, … “Minimal” SO(10) Model

34. Title of talk34 “Minimal” SO(10) Model Albright, Anderson, Babu, Barr, Barbieri, Berezhiani, Blazek, Carena, Dermisek, Dimopoulos, Hall, Pati, Raby, Romanino, Rossi, Starkman, Wagner, Wilczek, Wiesenfeldt, Willenbrock II Possible UV completion to strings !!

35. Title of talk35 SO(10) x [ D 3 x U(1) family sym. ] Yukawa Unification for 3 rd Family Dermisek & Raby hep-ph/0507045 Dermisek, Harada & S.R. hep-ph/0606055

36. Title of talk36 SO(10) x [ D 3 x U(1) family sym. ] Yukawa Unification for 3 rd Family Fits fermion masses and mixing angles well Requires soft SUSY breaking para’s Blazek, Dermisek & Raby PRL 88 (2002)

37. Title of talk37 small

38. Title of talk38 Recent analysis of DR Model “Challenging SO(10) SUSY GUTs with family symmetries through FCNC processes” Albrecht, Altmannshofer, Buras, Guadagnoli,& Straub See talk by Altmannshofer

39. Title of talk39 compare to SM - 27 parameters MSSM - 32 parameters 24 parameters at GUT scale Global   analysis of DR Model

40. Title of talk40 UV completion 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

41. Title of talk41 E 6 Orbifold GUT on M 4 x S 1 /(Z 2 xZ 2 ’) Kobayashi, SR & Zhang

42. Title of talk42 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

43. Title of talk43 E 8 x E 8 Heterotic string in 10D Compactify 6D on (T 2 ) 3 Then mod by Z 6 = (Z 3 x Z 2 ) and Add Wilson lines Z 6 embedded in E 8 x E 8 gauge lattice as shift V 6 : consistent with mod. inv. !

44. Title of talk44 First consider (T 2 ) 3 /Z 3 + W 3 [Wilson line in SU 3 torus] Massless modes From Untwisted sector + (G 2, SU 3 ) twisted sector E 6 GUT in 5D

45. Title of talk45 Heterotic strings in 10 dimensions 3 family models See talks by Nilles, Kyae, Luedeling, Lebedev & Wingerter Bouchard, Braun, Buchmuller, Cleaver, Donagi, Faraggi, Hamaguchi, He, Kobayashi, Lebedev, Ludeling, Nanopoulos, Nilles, Ovrut, Pantev, Pokorski, Raby, Ramos-Sanchez, Ratz, Reinbacher, Ross, Vaudrevange, Waldram, Wingerter, Zhang

46. Title of talk46 Conclusions  SUSY Model Building focus on “Little” hierarchy,  a nd B  p roblems  Still no Standard Model of SUSY breaking BUT metastable vacua are generic – easier !  Higgs & gauginos “Portal” on BMSSM  UV completion from MSSM to SUSY GUTs to Orbifold GUTs to Heterotic string - In Progress