With SUSY towards the LHC

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1 With SUSY towards the LHC Hans Peter Nilles Bethe Center for Theoretical Physics Universität Bonn SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 1/86

2 Outline Prehistory Hierarchy problem How to hide the hidden sector Gravity mediation Some support from string theory The quest for unification Where are we now? LHC as a gluino factory the gaugino code crosschecks for unification SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 2/86

3 Early history Supersymmetry was discovered in the 1970 s. The early work concentrated on field theory aspects of SUSY, including Wess-Zumino model and gauge theories, Superspace formalism, spontaneous F- and D-term Susy breakdown, local supersymmetry. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 3/86

4 Early history Supersymmetry was discovered in the 1970 s. The early work concentrated on field theory aspects of SUSY, including Wess-Zumino model and gauge theories, Superspace formalism, spontaneous F- and D-term Susy breakdown, local supersymmetry. Some attempts in particle physics model building were pioneered by Fayet in the framework of D-term susy breakdown. (Fayet, 1970 s) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 3/86

5 Hierarchy problem Around the same time Grand Unified Theories (GUTs) came into the game and emphasized the so-called hierarchy problem with solutions like Technicolour. (Weinberg, Susskind, 1970 s) Susy entered the stage because of the nonrenormalization theorems possibility of dynamical susy breakdown (Witten, 1981) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 4/86

6 Hierarchy problem Around the same time Grand Unified Theories (GUTs) came into the game and emphasized the so-called hierarchy problem with solutions like Technicolour. (Weinberg, Susskind, 1970 s) Susy entered the stage because of the nonrenormalization theorems possibility of dynamical susy breakdown (Witten, 1981) Early attempts in model building turned out to be difficult because of obstacles in spontaneous Susy breakdown (Dimopoulos, Raby; Dine, Fischler, Srednicki, 1981) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 4/86

7 MSSM The minimal particle content of the susy extension of the standard model contains chiral superfields Q, Ū, D for quarks and partners L, Ē for leptons and partners H, H Higgs supermultiplets SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 5/86

8 MSSM The minimal particle content of the susy extension of the standard model contains chiral superfields Q, Ū, D for quarks and partners L, Ē for leptons and partners H, H Higgs supermultiplets with superpotential W = QH D + Q HŪ + LHĒ + µh H. Also allowed (but problematic) are Ū D D + QL D + LLĒ. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 5/86

9 Soft susy breakdown We consider the MSSM with explicit soft susy breakdown terms as this is compatible with the supersymmetric solution to the hierarchy problem. (Girardello, Grisaru, 1981) This scheme now is characterized by two problems and two predictions. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 6/86

10 Soft susy breakdown We consider the MSSM with explicit soft susy breakdown terms as this is compatible with the supersymmetric solution to the hierarchy problem. (Girardello, Grisaru, 1981) This scheme now is characterized by two problems and two predictions. Still we would need to understand the origin of the soft susy breakdown terms, but there remain four obstacles to be removed. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 6/86

11 Two predictions The evolution of gauge coupling constants is modified M GUT is raised by an order of magnitude (because of the presence of the gauginos), sin 2 θ W SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 7/86

12 Two predictions The evolution of gauge coupling constants is modified M GUT is raised by an order of magnitude (because of the presence of the gauginos), sin 2 θ W There is an upper bound on the mass of the lightest Higgs boson (since the Higgs boson self-coupling is determined by the the gauge couplings) m h M Z at tree level m h 130 GeV for m top 175 GeV SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 7/86

13 Two problems The Higgs bilinear term µh H is allowed by susy: why is µ small compared to the GUT-scale? why is µ of order of the soft mass terms? SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 8/86

14 Two problems The Higgs bilinear term µh H is allowed by susy: why is µ small compared to the GUT-scale? why is µ of order of the soft mass terms? We have to distinguish between L and H to avoid fast proton decay Ū D D + QL D + LLĒ have to be forbidden need some discrete symmetry: R-parity But there is a reward: a stable particle (LSP) as dark matter candidate. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 8/86

15 Four obstacles for model building In spontaneous breakdown of susy we have STrM 2 = 0 at tree level for F-term breaking, SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 9/86

16 Four obstacles for model building In spontaneous breakdown of susy we have STrM 2 = 0 at tree level for F-term breaking, no (renormalizable) gaugino masses at tree level, SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 9/86

17 Four obstacles for model building In spontaneous breakdown of susy we have STrM 2 = 0 at tree level for F-term breaking, no (renormalizable) gaugino masses at tree level, accidential R-symmetry has to be broken explicitely to avoid a harmful R-axion (and allow gaugino masses), SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 9/86

18 Four obstacles for model building In spontaneous breakdown of susy we have STrM 2 = 0 at tree level for F-term breaking, no (renormalizable) gaugino masses at tree level, accidential R-symmetry has to be broken explicitely to avoid a harmful R-axion (and allow gaugino masses), the vacuum energy E vacuum is too large. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 9/86

19 Four obstacles for model building In spontaneous breakdown of susy we have STrM 2 = 0 at tree level for F-term breaking, no (renormalizable) gaugino masses at tree level, accidential R-symmetry has to be broken explicitely to avoid a harmful R-axion (and allow gaugino masses), the vacuum energy E vacuum is too large. We need a (weakly coupled) hidden sector and well as supergravity SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 9/86

20 Gravity Mediation All of these problems can be solved by gravity mediation MSSM as observable sector, hidden sector breaks susy spontaneously gravitational interactions as messenger. (HPN, Phys. Lett. 115B, 1982) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 10/86

21 Gravity Mediation All of these problems can be solved by gravity mediation MSSM as observable sector, hidden sector breaks susy spontaneously gravitational interactions as messenger. Soft breaking terms can be computed explicitely m 3/2 Λ 3 /MPlanck 2 F/M Planck, soft (mass) terms m 0, m 1/2, A and B. (HPN, Phys. Lett. 115B, 1982) (Arnowitt, Chamseddine, Nath, PRL 49, 1982; Barbieri, Ferrara, Savoy, PL 119B, 1982; HPN, Srednicki, Wyler, PR 120B, 1982; Hall, Lykken, Weinberg, PRD 27, 1982) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 10/86

22 The golden era With these developments of gravity mediation: successful model building was possible, a wider fraction of theoretical physicsts became optimistic concerning the realization of SUSY at the weak scale. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 11/86

23 The golden era With these developments of gravity mediation: successful model building was possible, a wider fraction of theoretical physicsts became optimistic concerning the realization of SUSY at the weak scale. One was tempted to say: Experiments within the next five to ten years will enable us to decide whether supersymmetry at the weak interaction scale is a myth or reality. This statement is still true today! SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 11/86

24 Early string theory With the developments in string theory the optimism was still growing heterotic E 8 E 8, hidden and observable E 8 sector, gaugino condensation in the hidden sector. (Derendinger, Ibanez, HPN, 1985; Dine, Rohm, Seiberg, Witten, 1985) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 12/86

25 Early string theory With the developments in string theory the optimism was still growing heterotic E 8 E 8, hidden and observable E 8 sector, gaugino condensation in the hidden sector. (Derendinger, Ibanez, HPN, 1985; Dine, Rohm, Seiberg, Witten, 1985) A new variant of gravity mediation emerged dilaton and/or modulus mediation. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 12/86

26 LEP I Results from LEP were eagerly awaited in The first stage of LEP gave us: no direct sign for SUSY, but indirect sign from evolution of gauge coupling constants the resurrection of (SUSY-) GUTs A large fraction of the community got excited about susy: all was set for the discovery at LEP II But there was no clear answer. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 13/86

27 MSSM (supersymmetric) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 14/86

28 Standard Model SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 15/86

29 LEP II The results of LEP II gave support for grand unification, Higgs mass m h > 114 GeV, electroweak precision data consistent with Standard Model, rather low Higgs mass preferred. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 16/86

30 LEP II The results of LEP II gave support for grand unification, Higgs mass m h > 114 GeV, electroweak precision data consistent with Standard Model, rather low Higgs mass preferred. No direct sign for susy, but encouragement... A large part of parameter space is gone. We are living in a corner of parameter space ( little hierarchy problem ) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 16/86

31 What keeps us going? unification of coupling constants dark matter candidate from R-parity electroweak precision data (S, T seem to fit) (g 2) µ as a hint alternatives look much worse SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 17/86

32 What keeps us going? unification of coupling constants dark matter candidate from R-parity electroweak precision data (S, T seem to fit) (g 2) µ as a hint alternatives look much worse Where are we now? many different models many different mediation schemes We need the LHC to judge. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 17/86

33 The future is the LHC Mediation schemes: gravity mediation (m soft m 3/2 ) anomaly mediation (m soft m 3/2 ) gauge mediation (m soft m 3/2 ) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 18/86

34 The future is the LHC Mediation schemes: gravity mediation (m soft m 3/2 ) anomaly mediation (m soft m 3/2 ) gauge mediation (m soft m 3/2 ) Meanwhile we have to guess what might happen. This personal guideline is based on simplicity motivation from Grand Unification theoretical input (from string theory) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 18/86

35 Questions What can we learn from strings for particle physics? Can we incorporate particle physics models within the framework of string theory? SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 19/86

36 Questions What can we learn from strings for particle physics? Can we incorporate particle physics models within the framework of string theory? Recent progress: explicit model building towards the MSSM Heterotic brane world local grand unification F-theory constructions moduli stabilization and Susy breakdown fluxes and gaugino condensation mirage mediation SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 19/86

37 Mediation schemes Supersymmetry is broken in a hidden sector and we have a variant of so-called gravity mediation tree level dilaton/modulus mediation (Derendinger, Ibanez, HPN, 1985; Dine, Rohm, Seiberg, Witten, 1985) radiative corrections in case of a sequestered hidden sector (e.g. anomaly mediation) (Ibanez, HPN, 1986; Randall, Sundrum, 1999) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 20/86

38 Mediation schemes Supersymmetry is broken in a hidden sector and we have a variant of so-called gravity mediation tree level dilaton/modulus mediation (Derendinger, Ibanez, HPN, 1985; Dine, Rohm, Seiberg, Witten, 1985) radiative corrections in case of a sequestered hidden sector (e.g. anomaly mediation) (Ibanez, HPN, 1986; Randall, Sundrum, 1999) The importance of the mechanism to adjust the cosmological constant has only been appreciated recently (Choi, Falkowski, HPN, Olechowski, Pokorski, 2004) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 20/86

39 Basic Questions origin of the small scale? stabilization of moduli? SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 21/86

40 Basic Questions origin of the small scale? stabilization of moduli? Recent progress in moduli stabilization via fluxes in warped compactifications of Type IIB string theory (Dasgupta, Rajesh, Sethi, 1999; Giddings, Kachru, Polchinski, 2001) generalized flux compactifications of heterotic string theory (Becker, Becker, Dasgupta, Prokushkin, 2003; Gurrieri, Lukas, Micu, 2004) combined with gaugino condensates and uplifting (Kachru, Kallosh, Linde, Trivedi, 2003; Löwen, HPN, 2008) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 21/86

41 AdS vacuum SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 22/86

42 Uplifting à la KKLT Add a supersymmetry breaking term to the potential V = D (T + T ) n t (S + S ) n s SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 23/86

43 Uplifting à la KKLT Add a supersymmetry breaking term to the potential V = D (T + T ) n t (S + S ) n s and adjust the coefficient D to obtain a local minimum with the desired fine tuned vacuum energy. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 23/86

44 Uplifting à la KKLT Add a supersymmetry breaking term to the potential V = D (T + T ) n t (S + S ) n s and adjust the coefficient D to obtain a local minimum with the desired fine tuned vacuum energy. This leads to local minimum at finite T global minimum for T height of barrier given by gravitino mass SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 23/86

45 Uplifted vacuum SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 24/86

46 Uplifted vacuum SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 24/86

47 Uplifted vacuum SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 25/86

48 Fluxes and gaugino condensation Is there a general pattern of the soft mass terms? We always have (from flux and gaugino condensate) W = something exp( X) where something is small and X is moderately large. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 26/86

49 Fluxes and gaugino condensation Is there a general pattern of the soft mass terms? We always have (from flux and gaugino condensate) W = something exp( X) where something is small and X is moderately large. In fact in this simple scheme X log(m Planck /m 3/2 ) providing a little hierarchy. (Choi, Falkowski, HPN, Olechowski, Pokorski, 2004) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 26/86

50 Mixed Mediation Schemes The contribution from Modulus Mediation is therefore suppressed by the factor X log(m Planck /m 3/2 ) 4π 2. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 27/86

51 Mixed Mediation Schemes The contribution from Modulus Mediation is therefore suppressed by the factor X log(m Planck /m 3/2 ) 4π 2. Thus the contribution due to radiative corrections becomes competitive, leading to mixed mediation schemes. The simplest case for radiative corrections leads to anomaly mediation competing now with the suppressed contribution of modulus mediation. For reasons that will be explained later we call this scheme MIRAGE MEDIATION (Loaiza, Martin, HPN, Ratz, 2005) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 27/86

52 The little hierarchy m X X m 3/2 X 2 m soft is a generic signal of such a scheme moduli and gravitino are heavy gaugino mass spectrum is compressed (Choi, Falkowski, HPN, Olechowski, 2005; Endo, Yamaguchi, Yoshioka, 2005; Choi, Jeong, Okumura, 2005) such a situation occurs if SUSY breaking is e.g. sequestered on a warped throat (Kachru, McAllister, Sundrum, 2007) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 28/86

53 Mirage Unification Mirage Mediation provides a characteristic pattern of soft breaking terms. To see this, let us consider the gaugino masses M 1/2 = M modulus + M anomaly as a sum of two contributions of comparable size. M anomaly is proportional to the β function, i.e. negative for the gluino, positive for the bino thus M anomaly is non-universal below the GUT scale SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 29/86

54 Evolution of couplings Αi log 10 Μ GeV SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 30/86

55 The Mirage Scale 1600 Mi GeV M 3 M 2 M log 10 Μ GeV (Lebedev, HPN, Ratz, 2005) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 31/86

56 The Mirage Scale (II) The gaugino masses coincide above the GUT scale at the mirage scale µ mirage = M GUT exp( 8π 2 /ρ) where ρ denotes the ratio of the contribution of modulus vs. anomaly mediation. We write the gaugino masses as M a = M s (ρ + b a g 2 a) = m 3/2 16π 2 (ρ + b ag 2 a) and ρ 0 corresponds to pure anomaly mediation. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 32/86

57 The Mirage Scale (III) The gaugino masses coincide above the GUT scale at the mirage scale µ mirage = M GUT exp( 8π 2 /ρ) There is a different notation used in the literature using a parameter α where the mirage scale is µ mirage = M GUT ( m3/2 M Planck ) α/2 α 0 corresponds to pure gravity mediation and α log ( m3/2 M Planck ) 1/ρ SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 33/86

58 Constraints on the mixing parameter 120 tanβ 5 signμ 1 m t 172 GeV 100 m3 2 TeV TACHYONS t 1 LSP ALLOWED 20 0 m h 114 GeV Ρ (Löwen, HPN, Ratz, 2006) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 34/86

59 Constraints on ρ 120 tanβ 30 signμ 1 m t 172 GeV 100 m3 2 TeV TACHYONS t 1 LSP ALLOWED 20 0 m h 114 GeV Ρ (Löwen, HPN, Ratz, 2006) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 35/86

60 The MSSM hierarchy problem The scheme predicts a rather high mass scale heavy gravitino rather high mass for the LSP-Neutralino SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 36/86

61 The MSSM hierarchy problem The scheme predicts a rather high mass scale heavy gravitino rather high mass for the LSP-Neutralino One might worry about a fine-tuning to obtain the mass of the weak scale around 100 GeV from m 2 Z 2 = µ 2 + m2 H d m 2 H u tan 2 β tan 2 β 1 and there are large corrections to m 2 H u... (Choi, Jeong, Kobayashi, Okumura, 2005), SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 36/86

62 Evolution of Higgs masses 8 2 m H TeV 2 i m Hu 2 m Hd log 10 Μ GeV SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 37/86

63 Fine tuning ( ) δ RG m 2 H u 3y2 t Λ 8π 2 (m2 + m et 2 ) ln 1 et 2 m e t, where m 2 et is of order TeV and Λ M GUT. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 38/86

64 Fine tuning ( ) δ RG m 2 H u 3y2 t Λ 8π 2 (m2 + m et 2 ) ln 1 et 2 m e t, where m 2 et is of order TeV and Λ M GUT. We thus need a fine-tuning on the right hand side of m 2 Z 2 = µ 2 + m2 H d m 2 H u tan 2 β tan 2 β 1, to obtain the (small) Z-mass. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 38/86

65 Fine tuning ( ) δ RG m 2 H u 3y2 t Λ 8π 2 (m2 + m et 2 ) ln 1 et 2 m e t, where m 2 et is of order TeV and Λ M GUT. We thus need a fine-tuning on the right hand side of m 2 Z 2 = µ 2 + m2 H d m 2 H u tan 2 β tan 2 β 1, to obtain the (small) Z-mass. This fine tuning depends on ρ. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 38/86

66 The MSSM hierarchy problem? The influence of the various soft terms is given by m 2 Z 1.8µ M M m 2 H u + 0.9m 2 q (3) L + 0.7m 2 0.6A u (3) t M M 2 M R + SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 39/86

67 The MSSM hierarchy problem? The influence of the various soft terms is given by m 2 Z 1.8µ M M m 2 H u + 0.9m 2 q (3) L + 0.7m 2 0.6A u (3) t M M 2 M R + Mirage mediation improves the situation especially for small ρ because of a reduced gluino mass and a compressed spectrum of supersymmetric partners (Choi, Jeong, Kobayashi, Okumura, 2005) explicit model building required (Kitano, Nomura, 2005; Lebedev, HPN, Ratz, 2005; Pierce, Thaler, 2006; Dermisek, Kim, 2006; Ellis, Olive, Sandick, 2006; Martin, 2007) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 39/86

68 Explicit schemes I The different schemes depend on the mechanism of uplifting: uplifting with anti D3 branes (Kachru, Kallosh, Linde, Trivedi, 2003) ρ 5 in the original KKLT scenario leading to a mirage scale of approximately GeV This scheme leads to pure mirage mediation: gaugino masses and scalar masses both meet at a common mirage scale SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 40/86

69 Constraints on ρ 120 tanβ 30 signμ 1 m t 172 GeV 100 m3 2 TeV TACHYONS t 1 LSP ALLOWED 20 0 m h 114 GeV Ρ (Löwen, HPN, Ratz, 2006) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 41/86

70 The Mirage Scale 1600 Mi GeV M 3 M 2 M log 10 Μ GeV (Lebedev, HPN, Ratz, 2005) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 42/86

71 Explicit schemes II uplifting via matter superpotentials (Lebedev, HPN, Ratz, 2006) allows a continuous variation of ρ leads to potentially new contributions to sfermion masses SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 43/86

72 Explicit schemes II uplifting via matter superpotentials (Lebedev, HPN, Ratz, 2006) allows a continuous variation of ρ leads to potentially new contributions to sfermion masses gaugino masses still meet at a mirage scale soft scalar masses might be dominated by modulus mediation similar constraints on the mixing parameter SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 43/86

73 Constraints on the mixing parameter m3 2 TeV No EWSB g LSP tanβ 5 signμ 1 m t 175 GeV Χ 10 Below LEP Ρ (V. Löwen, 2007) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 44/86

74 Constraints on the mixing parameter 50 tanβ 5 signμ 1 m t 175 GeV 40 m3 2 TeV Ρ 900 (V. Löwen, 2007) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 45/86

75 Constraints on the mixing parameter m3 2 TeV No EWSB g LSP tanβ 5 signμ 1 m t 175 GeV Χ 10 Below LEP Ρ (V. Löwen, 2007) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 46/86

76 Constraints on the mixing parameter tanβ 30 Η 4 Η No EWSB Χ LSP WMAP 40 g LSP m3 2 TeV WMAP 10 0 Below LEP ς SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 47/86

77 Explicit schemes III This relaxed mirage mediation is rather common for schemes with F-term uplifting (Intriligator, Shih, Seiberg; Gomez-Reino, Scrucca; Dudas, Papineau, Pokorski; Abe, Higaki, Kobayashi, Omura; Lebedev, Löwen, Mambrini, HPN, Ratz,2006) although pure mirage mediation is possible as well SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 48/86

78 Explicit schemes III This relaxed mirage mediation is rather common for schemes with F-term uplifting (Intriligator, Shih, Seiberg; Gomez-Reino, Scrucca; Dudas, Papineau, Pokorski; Abe, Higaki, Kobayashi, Omura; Lebedev, Löwen, Mambrini, HPN, Ratz,2006) although pure mirage mediation is possible as well Main message predictions for gaugino masses are more robust than those for sfermion masses mirage (compressed) pattern for gaugino masses rather generic SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 48/86

79 Obstacles to D-term uplifting In supergravity we have the relation D F W which implies that KKLT AdS minimum cannot be uplifted via D-terms. (Choi, Falkowski, HPN, Olechowski, 2005) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 49/86

80 Obstacles to D-term uplifting In supergravity we have the relation D F W which implies that KKLT AdS minimum cannot be uplifted via D-terms. (Choi, Falkowski, HPN, Olechowski, 2005) Moreover in these schemes we have F m 3/2 M Planck and D m 2 3/2. So if m 3/2 M Planck the D-terms are irrelevant. (Choi, Jeong, 2006) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 49/86

81 Explicit schemes IV In the heterotic case, we have hidden sector gaugino condensation potential run-away behaviour of the dilaton SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 50/86

82 Explicit schemes IV In the heterotic case, we have hidden sector gaugino condensation potential run-away behaviour of the dilaton Stabilization of dilaton via nontrivial corrections to Kähler potential downlifting via matter superpotentials (Barreiro, de Carlos, Copeland, 1998) (Löwen, HPN, 2008) Again the uplifting sector becomes dominant at tree level SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 50/86

83 Hidden Sector Susy Breakdown 25 # of models log 10 GeV m 3/2 = Λ 3 /M 2 Planck (with Λ = µ exp( 1/g2 hidden (µ))) from hidden sector gaugino condensation (Lebedev, HPN, Raby, Ramos-Sanchez, Ratz, Vaudrevange, Wingerter, 2006B) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 51/86

84 Run-away potential N 4 A 4.9 d 0 p 0 b V Re S SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 52/86

85 Corrections to Kähler potential 2 N 4 A 4.9 d p 1.1 b V Re S (Barreiro, de Carlos, Copeland, 1998) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 53/86

86 Sequestered sector uplifting 6 N 4 A 4.9 C V Re S (Lebedev, HPN, Ratz, 2006; Löwen, HPN, 2008) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 54/86

87 Metastable Minkowski vacuum V Re C Re S 1.95 (Löwen, HPN, 2008) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 55/86

88 Downlift (Löwen, HPN, 2008) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 56/86

89 Constraints on the mixing parameter tanβ 5 Η 4 Η No EWSB Χ LSP m3 2 TeV g LSP WMAP WMAP Below LEP ς (Löwen, HPN, 2008) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 57/86

90 Some important messages Please keep in mind: the uplifting mechanism plays an important role for the pattern of the soft susy breaking terms predictions for gaugino masses are more robust than those for sfermion masses dilaton/modulus mediation suppressed in many cases mirage pattern for gaugino masses rather generic SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 58/86

91 The string signatures We might consider the following schemes: Type II string theory Heterotic string theory M-theory on manifolds with G 2 holonomy F-theory SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 59/86

92 The string signatures We might consider the following schemes: Type II string theory Heterotic string theory M-theory on manifolds with G 2 holonomy F-theory Questions: are there distinct signatures for the various schemes? can they be identified with LHC data? (Choi, HPN, 2007) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 59/86

93 What to expect from the LHC At the LHC we scatter protons on protons, i.e. quarks on quarks and/or gluons on gluons Thus LHC will be a machine to produce strongly interacting particles. If TeV-scale susy is the physics beyond the standard model we might expect LHC to become a GLUINO FACTORY with cascade decays down to the LSP neutralino. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 60/86

94 The Gaugino Code First step to test these ideas at the LHC: look for pattern of gaugino masses Let us assume the low energy particle content of the MSSM measured values of gauge coupling constants g1 2 : g2 2 : g3 2 1 : 2 : 6 The evolution of gauge couplings would then lead to unification at a GUT-scale around GeV SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 61/86

95 Formulae for gaugino masses ( Ma ) g 2 a TeV = M (0) a + M (1) a loop + M (1) a gauge + M (1) a string M a (0) = 1 2 F I I f a (0) M a (1) loop = 1 F C 16π 2b a C 1 8π 2 Ca m F I I ln(e K0/3 Z m ) m M (1) a string = 1 8π 2FI I Ω a SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 62/86

96 The Gaugino Code Observe that evolution of gaugino masses is tied to evolution of gauge couplings for MSSM M a /g 2 a does not run (at one loop) This implies robust prediction for gaugino masses gaugino mass relations are the key to reveal the underlying scheme 3 CHARACTERISTIC MASS PATTERNS (Choi, HPN, 2007) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 63/86

97 SUGRA Pattern Universal gaugino mass at the GUT scale SUGRA pattern: M 1 : M 2 : M 3 1 : 2 : 6 g1 2 : g2 2 : g2 3 as realized in popular schemes such as gravity-, modulus- and gaugino-mediation This leads to LSP χ 0 1 predominantly Bino G = M gluino /m χ as a characteristic signature of these schemes. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 64/86

98 Anomaly Pattern Gaugino masses below the GUT scale determined by the β functions anomaly pattern: M 1 : M 2 : M : 1 : 9 at the TeV scale as the signal of anomaly mediation. For the gauginos, this implies LSP χ 0 1 predominantly Wino G = M gluino /m χ Pure anomaly mediation inconsistent, as sfermion masses are problematic in this scheme (tachyonic sleptons). SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 65/86

99 Mirage Pattern Mixed boundary conditions at the GUT scale characterized by the parameter ρ (the ratio of anomaly to modulus mediation). M 1 : M 2 : M 3 1 : 1.3 : 2.5 for ρ 5 M 1 : M 2 : M 3 1 : 1 : 1 for ρ 2 The mirage scheme leads to LSP χ 0 1 predominantly Bino G = M gluino /m χ 0 1 < 6 a compact gaugino mass pattern. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 66/86

100 The Mirage Scale (III) The gaugino masses coincide above the GUT scale at the mirage scale µ mirage = M GUT exp( 8π 2 /ρ) There is a different notation used in the literature using a parameter α where the mirage scale is µ mirage = M GUT ( m3/2 M Planck ) α/2 α 0 corresponds to pure gravity mediation and α log ( m3/2 M Planck ) 1/ρ SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 67/86

101 Gaugino Masses 3 Ma M0 1 Α Modulus M 3 M 2 M 1 Anomaly Α SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 68/86

102 Scalar Masses 1.5 L q L 1 e R m i 2 M Α Modulus Anomaly Α SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 69/86

103 Scalar Masses q L m i 2 M Α Modulus L Anomaly 0.1 e R Α SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 70/86

104 Gravity mediation 1.4 Α q L mi M u R d R 0.4 L 0.2 e R m 0 m 1 2 SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 71/86

105 Mirage Mediation 1.4 Α mi M q L d R u R 0.4 L e R m 0 m 1 2 SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 72/86

106 Constraints on α (pure mirage) 60 tanβ 30 Η i t LSP TACHYONS m3 2 TeV Below LEP Α SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 73/86

107 Constraints on α (modified mirage) tanβ 30 Η i 3 60 m3 2 TeV t LSP Χ LSP g LSP No EWSB Χ LSP 0 Below LEP Below LEP Α SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 74/86

108 Various string schemes Type IIB with matter on D7 branes: mirage mediation (Choi, Falkowski, HPN, Olechowski, 2005) Type IIB with matter on D3 branes: anomaly mediation? (Choi, Falkowski, HPN, Olechowski, 2005) Heterotic string with dilaton domination: mirage mediation (Löwen, HPN, 2008) Heterotic string with modulus domination: string thresholds might spoil anomaly pattern (Derendinger, Ibanez, HPN, 1986) M theory on G 2 manifold : Kähler corrections might spoil mirage pattern (Acharya, Bobkov, Kane, Kumar, Shao, 2007) SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 75/86

109 Uncertainties String thresholds Kähler corrections M (1) a string = 1 8π 2FI I Ω a M a (1) loop = 1 F C 16π 2b a C 1 8π 2 Ca m F I I ln(e K0/3 Z m ) m Intermediate thresholds M (1) a gauge = 1 8π 2 Φ C Φ a F X Φ M Φ SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 76/86

110 SUGRA Pattern Universal gaugino mass at the GUT scale msugra pattern: M 1 : M 2 : M 3 1 : 2 : 6 g1 2 : g2 2 : g2 3 as realized in popular schemes such as gravity-, modulus- and gaugino-mediation This leads to LSP χ 0 1 predominantly Bino G = M gluino /m χ as a characteristic signature of these schemes. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 77/86

111 Loop Mediation If the tree level masses vanish we have contributions from radiative corrections M a (1) loop = 1 F C 16π 2b a C 1 8π 2 Ca m F I I ln(e K0/3 Z m ) m Which can be written as a sum M (1) a loop = M (1) a anomaly + M (1) a Kähler where the first term is proportional to b a = (33/5, 1, 3) and the second to b a = (33/5, 5, 3). SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 78/86

112 Anomaly Pattern Gaugino masses below the GUT scale are determined by the β functions anomaly pattern: M 1 : M 2 : M : 1 : 9 at the TeV scale as the signal of anomaly mediation. For the gauginos, this implies LSP χ 0 1 predominantly Wino G = M gluino /m χ Pure anomaly mediation inconsistent, as sfermion masses are problematic in this scheme (tachyonic sleptons). SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 79/86

113 Kähler Pattern Gaugino masses below the GUT scale determined by the β functions Kähler pattern: M 1 : M 2 : M : 5 : 9 at the TeV scale as the signal of Kähler mediation. For the gauginos, this implies LSP χ 0 1 predominantly Bino G = M gluino /m χ 0 1 < 3 Kähler mediation depends on a parameter φ (the vev of a hidden sector field) We again expect problems with tachyons. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 80/86

114 Loop Pattern is a combination of Anomaly and Kähler contribution Loop pattern: M 1 : M 2 : M 3 ( φ) : (1 + 5φ) : ( 9 + 9φ) at the TeV scale as the signal loop mediation. For the gauginos, this implies LSP χ 0 1 could be Bino or Wino gluino could be rather light as well The loop scheme will have problems with tachyons and needs additional contributions to scalar masses. In any case we seem to need tree level contributions to scalar (and gaugino) masses. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 81/86

115 Mirage Pattern Mixed boundary conditions at the GUT scale characterized by the parameter α: the ratio of modulus to anomaly mediation. M 1 : M 2 : M 3 1 : 1.3 : 2.5 for α 1 M 1 : M 2 : M 3 1 : 1 : 1 for α 2 The mirage scheme leads to LSP χ 0 1 predominantly Bino G = M gluino /m χ 0 1 < 6 a compact gaugino mass pattern. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 82/86

116 Mirage Scale Α 1 m TeV Φ M 1 Mass TeV 0.8 M Μ GeV M 3 SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 83/86

117 Loop Mirage Scale Α 1 m TeV Φ M Mass TeV 1 M Μ GeV M 3 SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 84/86

118 Keep in mind In the calculation of the soft masses we get the most robust predictions for gaugino masses Modulus Mediation: (fww with f = f(moduli)) If this is supressed we might have loop contributions, e.g. Anomaly Mediation as simplest example SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 85/86

119 Keep in mind In the calculation of the soft masses we get the most robust predictions for gaugino masses Modulus Mediation: (fww with f = f(moduli)) If this is supressed we might have loop contributions, e.g. Anomaly Mediation as simplest example How much can it be suppressed? So we might expect log(m 3/2 /M Planck ) a mixture of tree level and loop contributions. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 85/86

120 Conclusion Gaugino masses can serve as a promising tool for an early test for supersymmetry at the LHC Rather robust predictions 3 basic and simple patterns (Sugra, anomaly, mirage) Mirage pattern rather generic With some luck we might find such a simple scheme at the LHC and measure the ratio G = M gluino /m χ 0 1! Let us hope for a bright future of SUSY at the LHC. SUSY + LHC, Corfu Summer Institute, Corfu, September 2010 p. 86/86

With SUSY towards the LHC

With SUSY towards the LHC Hans Peter Nilles Bethe Center for Theoretical Physics Universität Bonn SUSY + LHC, MariaLaach09, Bautzen, September 2009 p. 1/59 Outline Prehistory Hierarchy problem How to hide