Heterotic Brane world: the Geography of Extra Dimensions
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- Ralf Alexander
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1 Heterotic Brane world: the Geography of Extra Dimensions Hans Peter Nilles Physikalisches Institut, Universität Bonn Bad Honnef, March 08 p.1/101
2 Outline MSSM and Grand Unification Heterotic string compactifications Gauge group geography in extra dimensions Local Grand Unification Benchmark scanario Hidden sector susy breakdown Mirage pattern of soft masses Four explicit schemes The Gaugino Code Outlook Bad Honnef, March 08 p.2/101
3 Bottom-up input Experimental findings suggest the existence of two new scales of physics beyond the standard model M GUT GeV (and M SUSY 10 3 GeV): Bad Honnef, March 08 p.3/101
4 Bottom-up input Experimental findings suggest the existence of two new scales of physics beyond the standard model M GUT GeV (and M SUSY 10 3 GeV): Neutrino-oscillations and See-Saw Mechanism m ν M 2 W /M GUT m ν 10 3 ev for M W 100GeV, Bad Honnef, March 08 p.3/101
5 Bottom-up input Experimental findings suggest the existence of two new scales of physics beyond the standard model M GUT GeV (and M SUSY 10 3 GeV): Neutrino-oscillations and See-Saw Mechanism m ν M 2 W /M GUT m ν 10 3 ev for M W 100GeV, Evolution of couplings constants of the standard model towards higher energies. Bad Honnef, March 08 p.3/101
6 MSSM (supersymmetric) Bad Honnef, March 08 p.4/101
7 Standard Model Bad Honnef, March 08 p.5/101
8 Grand Unification has changed our view of the world, but there are also some problematic aspects of the grand unified picture. Bad Honnef, March 08 p.6/101
9 Grand Unification has changed our view of the world, but there are also some problematic aspects of the grand unified picture. Most notably potential instability of the proton doublet - triplet splitting complicated Higgs sector to break grand unified gauge group spontaneously Bad Honnef, March 08 p.6/101
10 Grand Unification has changed our view of the world, but there are also some problematic aspects of the grand unified picture. Most notably potential instability of the proton doublet - triplet splitting complicated Higgs sector to break grand unified gauge group spontaneously Can we avoid these problems in a more complete theory? Bad Honnef, March 08 p.6/101
11 String theory candidates In ten space-time dimensions... Type I SO(32) Type II orientifolds Heterotic SO(32) Heterotic E 8 E 8 Intersecting Branes U(N) M Bad Honnef, March 08 p.7/101
12 String theory candidates In ten space-time dimensions... Type I SO(32) Type II orientifolds Heterotic SO(32) Heterotic E 8 E 8 Intersecting Branes U(N) M...or in eleven Horava-Witten heterotic M-theory Type IIA on manifolds with G 2 holonomy Bad Honnef, March 08 p.7/101
13 String Theory What do we get from string theory? supersymmetry extra spatial dimensions large unified gauge groups consistent theory of gravity Bad Honnef, March 08 p.8/101
14 String Theory What do we get from string theory? supersymmetry extra spatial dimensions large unified gauge groups consistent theory of gravity These are the building blocks for a unified theory of all the fundamental interactions. But do they fit together, and if yes how? We need to understand the mechanism of compactification of the extra spatial dimensions Bad Honnef, March 08 p.8/101
15 Calabi Yau Manifold Bad Honnef, March 08 p.9/101
16 Orbifold Bad Honnef, March 08 p.10/101
17 Orbifolds Orbifold compactifications combine the success of Calabi-Yau compactification calculability of torus compactification Bad Honnef, March 08 p.11/101
18 Orbifolds Orbifold compactifications combine the success of Calabi-Yau compactification calculability of torus compactification In case of the heterotic string fields can propagate in the Bulk (d = 10 untwisted sector) on 3-Branes (d = 4 twisted sector fixed points) on 5-Branes (d = 6 twisted sector fixed tori) Bad Honnef, March 08 p.11/101
19 Torus T 2 Bad Honnef, March 08 p.12/101
20 Torus T 2 e 2 e 1 Bad Honnef, March 08 p.13/101
21 A Z 2 twist e e 1 Bad Honnef, March 08 p.14/101
22 Orbifolding e 2 e 1 Bad Honnef, March 08 p.15/101
23 Ravioli e 2 e 1 Bad Honnef, March 08 p.16/101
24 Bulk Modes e 2 e 1 Bad Honnef, March 08 p.17/101
25 Winding Modes e 2 e 1 Bad Honnef, March 08 p.18/101
26 Brane Modes e 2 e 1 Bad Honnef, March 08 p.19/101
27 Z 3 Example Bad Honnef, March 08 p.20/101
28 Z 3 Example Action of the space group on coordinates X i (θ k X) i + n α e i α, k = 0, 1, 2, i, α = 1,..., 6 Embed twist in gauge degrees of freedom X I (Θ k X) I I = 1,..., 16 Bad Honnef, March 08 p.20/101
29 Classification of Z 3 Orbifold Very few inequivalent models Bad Honnef, March 08 p.21/101
30 Classification of Z 3 Orbifold Very few inequivalent models Case Shift V Gauge Group Gen ` 1 3, 1 3, 2, 05 `08 3 ` 1 3, 1 3, 2 3, 05 ` 1 3, 1 3, 2 3, 05 ` 1 3, 1 3, 06 ` 2 3, 07 ` 1 3, 1 3, 1 3, 1 3, 2 3, 03 ` 2 3, 07 E 6 SU(3) E 8 36 E 6 SU(3) E 6 SU(3) 9 E 7 U(1) SO(14) U(1) 0 SU(9) SO(14) U(1) 9 Bad Honnef, March 08 p.21/101
31 Classification of Z 3 Orbifold Very few inequivalent models Case Shift V Gauge Group Gen ` 1 3, 1 3, 2, 05 `08 3 ` 1 3, 1 3, 2 3, 05 ` 1 3, 1 3, 2 3, 05 ` 1 3, 1 3, 06 ` 2 3, 07 ` 1 3, 1 3, 1 3, 1 3, 2 3, 03 ` 2 3, 07 E 6 SU(3) E 8 36 E 6 SU(3) E 6 SU(3) 9 E 7 U(1) SO(14) U(1) 0 SU(9) SO(14) U(1) 9 as a result of the degeneracy of the matter multiplets at the 27 fixed points Bad Honnef, March 08 p.21/101
32 Classification of Z 3 Orbifold Very few inequivalent models Case Shift V Gauge Group Gen ` 1 3, 1 3, 2, 05 `08 3 ` 1 3, 1 3, 2 3, 05 ` 1 3, 1 3, 2 3, 05 ` 1 3, 1 3, 06 ` 2 3, 07 ` 1 3, 1 3, 1 3, 1 3, 2 3, 03 ` 2 3, 07 E 6 SU(3) E 8 36 E 6 SU(3) E 6 SU(3) 9 E 7 U(1) SO(14) U(1) 0 SU(9) SO(14) U(1) 9 as a result of the degeneracy of the matter multiplets at the 27 fixed points We need to lift this degeneracy... Bad Honnef, March 08 p.21/101
33 Z 3 Orbifold with Wilson lines Torus shifts embedded in gauge group as well X I X I + V I + n α A I α Bad Honnef, March 08 p.22/101
34 Z 3 Orbifold with Wilson lines Torus shifts embedded in gauge group as well X I X I + V I + n α A I α further gauge symmetry breakdown number of generations reduced Bad Honnef, March 08 p.22/101
35 Bottom-up input Gauge couplings meet at GeV in the framework of the Minimal Supersymmetric Standard Model (MSSM) Bad Honnef, March 08 p.23/101
36 Bottom-up input Gauge couplings meet at GeV in the framework of the Minimal Supersymmetric Standard Model (MSSM) See-saw mechanism for neutrino sector favours the interpretation of a family of quarks and leptons as a 16 dimensional spinor representation of SO(10) Bad Honnef, March 08 p.23/101
37 Bottom-up input Gauge couplings meet at GeV in the framework of the Minimal Supersymmetric Standard Model (MSSM) See-saw mechanism for neutrino sector favours the interpretation of a family of quarks and leptons as a 16 dimensional spinor representation of SO(10) gauge and Higgs bosons appear in split multiplets Bad Honnef, March 08 p.23/101
38 Bottom-up input Gauge couplings meet at GeV in the framework of the Minimal Supersymmetric Standard Model (MSSM) See-saw mechanism for neutrino sector favours the interpretation of a family of quarks and leptons as a 16 dimensional spinor representation of SO(10) gauge and Higgs bosons appear in split multiplets Can we incorporate this into a string theory description? Bad Honnef, March 08 p.23/101
39 Five golden rules Family as spinor of SO(10) Incomplete multiplets N = 1 superymmetry in d = 4 Repetition of families from geometry Discrete symmetries of stringy origin (HPN, 2004) Bad Honnef, March 08 p.24/101
40 Five golden rules Family as spinor of SO(10) Incomplete multiplets N = 1 superymmetry in d = 4 Repetition of families from geometry Discrete symmetries of stringy origin (HPN, 2004) Such a scheme should incorporate the successful structures of SO(10)-GUTs avoid (some of) the problems Bad Honnef, March 08 p.24/101
41 Five golden rules Family as spinor of SO(10) Incomplete multiplets N = 1 superymmetry in d = 4 Repetition of families from geometry Discrete symmetries of stringy origin (HPN, 2004) Such a scheme should incorporate the successful structures of SO(10)-GUTs avoid (some of) the problems We need more general constructions to identify remnants of SO(10) in string theory... Bad Honnef, March 08 p.24/101
42 Candidates In ten space-time dimensions... Type I SO(32) Type II orientifolds Heterotic SO(32) Heterotic E 8 E 8 Intersecting Branes U(N) M Bad Honnef, March 08 p.25/101
43 Candidates In ten space-time dimensions... Type I SO(32) Type II orientifolds Heterotic SO(32) Heterotic E 8 E 8 Intersecting Branes U(N) M...or in eleven Horava-Witten heterotic M-theory Type IIA on manifolds with G 2 holonomy Bad Honnef, March 08 p.25/101
44 Remnants of SO(10) symmetry If we insist on the spinor representation of SO(10) we are essentially left with heterotic E 8 E 8 or SO(32) go beyond the simple example of the Z 3 orbifold Bad Honnef, March 08 p.26/101
45 Remnants of SO(10) symmetry If we insist on the spinor representation of SO(10) we are essentially left with heterotic E 8 E 8 or SO(32) go beyond the simple example of the Z 3 orbifold The Z 3 orbifold had fixed points but no fixed tori, leading to difficulties to incorporate a correctly normalized U(1)-hypercharge accomodate satisfactory Yukawa couplings Bad Honnef, March 08 p.26/101
46 Remnants of SO(10) symmetry If we insist on the spinor representation of SO(10) we are essentially left with heterotic E 8 E 8 or SO(32) go beyond the simple example of the Z 3 orbifold The Z 3 orbifold had fixed points but no fixed tori, leading to difficulties to incorporate a correctly normalized U(1)-hypercharge accomodate satisfactory Yukawa couplings From this point of view, the Z 2N or Z N Z M orbifolds do look more promising Bad Honnef, March 08 p.26/101
47 Z 2 Z 2 Orbifold Example θ 1 θ 2 θ 3 Bad Honnef, March 08 p.27/101
48 Z 2 Z 2 Orbifold Example θ 1 θ 2 θ 3 3 twisted sectors (with 16 fixed tori in each) lead to a geometrical picture of... Bad Honnef, March 08 p.27/101
49 Intersecting Branes Bad Honnef, March 08 p.28/101
50 Z 2 Z 2 classification Case Shifts Gauge Group Gen. 1 ` 1 2, 1, 06 ` `0, 2, 1 2, 05 `08 E 6 U(1) 2 E 8 48 ` 1 2, 1, 06 ` `0, , 1 2, 04, 1 `1, 0 7 E 6 U(1) 2 SO(16) , 0 6 `08 5 4, 1 7 ` 1 4 2, 1 2, 06 SU(8) U(1) E 7 SU(2) , 0 5, 1 `1, `0, 2, 1 2, 05 E 6 U(1) 2 SO(8) , 1 3 2, 1, 0 3 ` 1 2, 1 2, 1, 05 `1, , 1 7 ` 1 4 2, 1 2, 06 SU(8) U(1) SO(12) SU(2) 2 0 Bad Honnef, March 08 p.29/101
51 Z 2 Z 2 with Wilson lines θ 1 A 3 θ 2 A 3 θ 3 Again, Wilson lines can lift the degeneracy... Bad Honnef, March 08 p.30/101
52 Three family SO(10) toy model A 16 θ 1 A A 1 A 3 A 4 A 6 θ 2 A 3 A 5 A 2 A 6 θ 3 16 A 1 A 5 Localization of families at various fixed tori Bad Honnef, March 08 p.31/101
53 Zoom on first torus... e 2 θ 1 e 1 e 2 θ 2 e 2 e 1 θ 3 e 1 Interpretation as 6-dim. model with 3 families on branes Bad Honnef, March 08 p.32/101
54 second torus... e 4 θ 1 e 4 e 3 e 4 θ 2 e 3 e 3 θ families on branes, one in (6d) bulk... Bad Honnef, March 08 p.33/101
55 Three family SO(10) toy model A 16 θ 1 A A 1 A 3 A 4 A 6 θ 2 A 3 A 5 A 2 A 6 θ 3 16 A 1 A 5 Localization of families at various fixed tori Bad Honnef, March 08 p.34/101
56 third torus θ 1 e 6 e 6 θ 2 e 6 e 5 e 5 θ 3 e family on brane, two in (6d) bulk. Bad Honnef, March 08 p.35/101
57 Geography Many properties of the models depend on the geography of extra dimensions, such as the location of quarks and leptons, the relative location of Higgs bosons, Bad Honnef, March 08 p.36/101
58 Geography Many properties of the models depend on the geography of extra dimensions, such as the location of quarks and leptons, the relative location of Higgs bosons, but there is also a localization of gauge fields E 8 E 8 in the bulk smaller gauge groups on various branes Observed 4-dimensional gauge group is common subroup of the various localized gauge groups! Bad Honnef, March 08 p.36/101
59 Calabi Yau Manifold Bad Honnef, March 08 p.37/101
60 Orbifold Bad Honnef, March 08 p.38/101
61 Localized gauge symmetries SU(4) 2 SU(6) SU(2) SO(10) SU(6) SU(2) Bad Honnef, March 08 p.39/101
62 Standard Model Gauge Group SU(4) 2 SU(3) 2 SU(6) SU(2) SU(3) 2 SU(4) SU(2) 2 SU(5) SU(4) SU(2) 2 SO(10) SU(5) SU(6) SU(2) Bad Honnef, March 08 p.40/101
63 Model building We can easily find models with gauge group SU(3) SU(2) U(1) 3 families of quarks and leptons doublet-triplet splitting N = 1 supersymmetry (Förste, HPN, Vaudrevange, Wingerter, 2004) (Kobyashi, Raby, Zhang, 2004) (Buchmüller, Hamaguchi, Lebedev, Ratz, 2004, 2005) Bad Honnef, March 08 p.41/101
64 Model building We can easily find models with gauge group SU(3) SU(2) U(1) 3 families of quarks and leptons doublet-triplet splitting N = 1 supersymmetry (Förste, HPN, Vaudrevange, Wingerter, 2004) But explicit model building is tedious: removal of exotic states R parity correct hypercharge (Kobyashi, Raby, Zhang, 2004) (Buchmüller, Hamaguchi, Lebedev, Ratz, 2004, 2005) Bad Honnef, March 08 p.41/101
65 Model building (II) We do not yet have a complete understanding of the origin of these specific problems. Bad Honnef, March 08 p.42/101
66 Model building (II) We do not yet have a complete understanding of the origin of these specific problems. Key properties of the models depend on geometry: family symmetries texture of Yukawa couplings number of families local gauge groups on branes electroweak symmetry breakdown Bad Honnef, March 08 p.42/101
67 Model building (II) We do not yet have a complete understanding of the origin of these specific problems. Key properties of the models depend on geometry: family symmetries texture of Yukawa couplings number of families local gauge groups on branes electroweak symmetry breakdown We need to exploit these geometric properties... Bad Honnef, March 08 p.42/101
68 Localized gauge symmetries SU(4) 2 SU(6) SU(2) SO(10) SU(6) SU(2) Bad Honnef, March 08 p.43/101
69 Standard Model Gauge Group SU(4) 2 SU(3) 2 SU(6) SU(2) SU(3) 2 SU(4) SU(2) 2 SU(5) SU(4) SU(2) 2 SO(10) SU(5) SU(6) SU(2) Bad Honnef, March 08 p.44/101
70 Local Grand Unification In fact string theory gives us a variant of GUTs complete multiplets for fermion families split multiplets for gauge- and Higgs-bosons partial Yukawa unification Bad Honnef, March 08 p.45/101
71 Local Grand Unification In fact string theory gives us a variant of GUTs complete multiplets for fermion families split multiplets for gauge- and Higgs-bosons partial Yukawa unification Key properties of the theory depend on the geography of the fields in extra dimensions. This geometrical set-up called local GUTs, can be realized in the framework of the heterotic braneworld. (Buchmüller, Hamaguchi, Lebedev, Ratz, 2004; Förste, HPN, Vaudrevange, Wingerter, 2004) Bad Honnef, March 08 p.45/101
72 Remnants of SO(10) SO(10) is realized in the higher dimensional theory broken in d = 4 incomplete multiplets Bad Honnef, March 08 p.46/101
73 Remnants of SO(10) SO(10) is realized in the higher dimensional theory broken in d = 4 incomplete multiplets There could still be remnants of SO(10) symmetry 16 of SO(10) at some branes correct hypercharge normalization R-parity family symmetries that are very useful for realistic model building... Bad Honnef, March 08 p.46/101
74 Proton decay R-parity from SO(10) memory could avoid dangerous dimension-4 operators Bad Honnef, March 08 p.47/101
75 Proton decay R-parity from SO(10) memory could avoid dangerous dimension-4 operators Proton decay rate via dimension-5 operators reduced because of doublet-triplet splitting Bad Honnef, March 08 p.47/101
76 Proton decay R-parity from SO(10) memory could avoid dangerous dimension-4 operators Proton decay rate via dimension-5 operators reduced because of doublet-triplet splitting Avoid SO(10) brane for first family: suppressed p-decay via dimension-6 operators Bad Honnef, March 08 p.47/101
77 Proton decay R-parity from SO(10) memory could avoid dangerous dimension-4 operators Proton decay rate via dimension-5 operators reduced because of doublet-triplet splitting Avoid SO(10) brane for first family: suppressed p-decay via dimension-6 operators There are lots of opportunities, but there is a strong model dependence Bad Honnef, March 08 p.47/101
78 Unification SO(10) memory provides a reasonable value of sin 2 θ W and a unified definition of hypercharge Bad Honnef, March 08 p.48/101
79 Unification SO(10) memory provides a reasonable value of sin 2 θ W and a unified definition of hypercharge presence of fixed tori allows for sizable threshold corrections at the high scale to match string and unification scale Bad Honnef, March 08 p.48/101
80 Unification SO(10) memory provides a reasonable value of sin 2 θ W and a unified definition of hypercharge presence of fixed tori allows for sizable threshold corrections at the high scale to match string and unification scale Yukawa unification from SO(10) memory for third family (on an SO(10) brane) Bad Honnef, March 08 p.48/101
81 Unification SO(10) memory provides a reasonable value of sin 2 θ W and a unified definition of hypercharge presence of fixed tori allows for sizable threshold corrections at the high scale to match string and unification scale Yukawa unification from SO(10) memory for third family (on an SO(10) brane) no Yukawa unification for first and second family required Bad Honnef, March 08 p.48/101
82 Yukawa textures and family symmetries Yukawa couplings depend on location of Higgs and matter fields Bad Honnef, March 08 p.49/101
83 Yukawa textures and family symmetries Yukawa couplings depend on location of Higgs and matter fields family symmetries arise if different fields live on the same brane Bad Honnef, March 08 p.49/101
84 Yukawa textures and family symmetries Yukawa couplings depend on location of Higgs and matter fields family symmetries arise if different fields live on the same brane Exponential suppression if fields at distant branes Bad Honnef, March 08 p.49/101
85 Yukawa textures and family symmetries Yukawa couplings depend on location of Higgs and matter fields family symmetries arise if different fields live on the same brane Exponential suppression if fields at distant branes family symmetries might also arise if there is a symmetry between various fixed point locations Bad Honnef, March 08 p.49/101
86 Yukawa textures and family symmetries Yukawa couplings depend on location of Higgs and matter fields family symmetries arise if different fields live on the same brane Exponential suppression if fields at distant branes family symmetries might also arise if there is a symmetry between various fixed point locations GUT relations could be partially present, depending on the nature of the brane (e.g. SO(10) brane) Bad Honnef, March 08 p.49/101
87 It s a long way to go Full classification seems to be too difficult (at the moment). Work in progress: Bad Honnef, March 08 p.50/101
88 It s a long way to go Full classification seems to be too difficult (at the moment). Work in progress: SO(32) classification (with SO(10) spinors) (Choi, Groot Nibbelink, Trapletti, 2004) (Ramos-Sanchez, Vaudrevange, Wingerter, 2006) Bad Honnef, March 08 p.50/101
89 It s a long way to go Full classification seems to be too difficult (at the moment). Work in progress: SO(32) classification (with SO(10) spinors) (Choi, Groot Nibbelink, Trapletti, 2004) (Ramos-Sanchez, Vaudrevange, Wingerter, 2006) Z 2 Z 3 Pati-Salam model (Kobyashi, Raby, Zhang, 2004) Bad Honnef, March 08 p.50/101
90 It s a long way to go Full classification seems to be too difficult (at the moment). Work in progress: SO(32) classification (with SO(10) spinors) (Choi, Groot Nibbelink, Trapletti, 2004) (Ramos-Sanchez, Vaudrevange, Wingerter, 2006) Z 2 Z 3 Pati-Salam model (Kobyashi, Raby, Zhang, 2004) Z 2 Z 3 standard model (Buchmüller, Hamaguchi, Lebedev, Ratz, 2005) Bad Honnef, March 08 p.50/101
91 The Higgs-mechanism in string theory......can be achieved via continuous Wilson lines. The aim is: electroweak symmetry breakdown breakdown of Trinification or Pati-Salam group to the Standard Model gauge group rank reduction Continuous Wilson lines require specific embeddings of twist in the gauge group difficult to implement in the Z 3 case more promising for Z 2 twists (Ibanez, HPN, Quevedo, 1987) Bad Honnef, March 08 p.51/101
92 An example We consider a model that has E 6 gauge group in the bulk of a 6d orbifold. The breakdown pattern is E 6 SO(10) via a Z 2 twist SO(10) SU(4) SU(2) SU(2) U(1) via a discrete (quantized) Wilson line SU(4) SU(2) SU(2) SU(3) SU(2) U(1) via a continuous Wilson line (Förste, HPN, Wingerter, 2005) Such 6d models can be embedded in 10d string theory orbifolds. Models with consistent electroweak symmetry breakdown have been constructed. (Förste, HPN, Wingerter, 2006) Bad Honnef, March 08 p.52/101
93 Pati-Salam breakdown e 6 SO(10) U(1) Pati-Salam U(1) SU(6) SU(2) W 6 SU(5) U(1) SU(3) SU(2) U(1) 2 SU(3) SU(2) U(1) 2 SU(3) 2 U(1) SO(10) U(1) Pati-Salam U(1) W 5 SU(6) SU(2) e 5 Bad Honnef, March 08 p.53/101
94 Benchmark Scenario: Z 6 II orbifold (Kobayashi, Raby, Zhang, 2004; Buchmüller, Hamaguchi, Lebedev, Ratz, 2004) Bad Honnef, March 08 p.54/101
95 Benchmark Scenario: Z 6 II orbifold (Kobayashi, Raby, Zhang, 2004; Buchmüller, Hamaguchi, Lebedev, Ratz, 2004) provides fixed points and fixed tori allows for 61 different shifts out of which 2 lead to SO(10) gauge group allows for localized 16-plets for 2 families SO(10) broken via Wilson lines nontrivial hidden sector gauge group Bad Honnef, March 08 p.54/101
96 Selection Strategy criterion V SO(10),1 V SO(10),2 models with 2 Wilson lines 22, 000 7, 800 SM gauge group SO(10) net (3, 2) non anomalous U(1) Y SU(5) generations + vector-like (Lebedev, HPN, Raby, Ramos-Sanchez, Ratz, Vaudrevange, Wingerter, 2006A) Bad Honnef, March 08 p.55/101
97 Decoupling of exotics requires extensive technical work: analysis of Yukawa couplings S n EĒ vevs of S break additional U(1) symmetries our analysis includes n 6 Bad Honnef, March 08 p.56/101
98 Decoupling of exotics requires extensive technical work: analysis of Yukawa couplings S n EĒ vevs of S break additional U(1) symmetries our analysis includes n 6 Requirement of D-flatness vevs of S should not break supersymmetry anomalous U(1) and Fayet-Iliopoulos terms checking D-flatness with method of gauge invariant monomials Bad Honnef, March 08 p.56/101
99 MSSM candidates criterion V SO(10),1 V SO(10),2 SM gauge group SO(10) net (3, 2) non anomalous U(1) Y SU(5) generations + vector-like exotics decouple D-flat solutions (Lebedev, HPN, Raby, Ramos-Sanchez, Ratz, Vaudrevange, Wingerter, 2007) Bad Honnef, March 08 p.57/101
100 The road to the MSSM The benchmark scenario leads to 200 models with the exact spectrum of the MSSM (absence of chiral exotics) local grand unification (by construction) gauge- and (partial) Yukawa unification examples of neutrino see-saw mechanism (Raby, Wingerter, 2007) (Buchmüller, Hamguchi, Lebedev, Ramos-Sanchez, Ratz, 2007) models with R-parity + solution to the µ-problem (Lebedev, HPN, Raby, Ramos-Sanchez, Ratz, Vaudrevange, Wingerter, 2007) hidden sector gaugino condensation Bad Honnef, March 08 p.58/101
101 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) Bad Honnef, March 08 p.59/101
102 Comparison to TypeII braneworld strategy based on geometrical intuition is successful properties of models can trace back the geometry of extra dimensions heterotic versus Type II braneworld bulk gauge group complete chiral multiplets chiral exotics R-parity (B-L and seesaw mechanism) localization of fields at various corners of Calabi-Yau manifold remnants of Grand Unification indicate that we live in a special place of the compactified extra dimensions! Bad Honnef, March 08 p.60/101
103 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) Bad Honnef, March 08 p.61/101
104 Basic Questions origin of the small scale? stabilization of moduli? adjustment of vacuum energy? Bad Honnef, March 08 p.62/101
105 Basic Questions origin of the small scale? stabilization of moduli? adjustment of vacuum energy? 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) Bad Honnef, March 08 p.62/101
106 Fluxes and gaugino condensation Is there a general pattern of the soft mass terms? We have (from flux and gaugino condensate) W = something exp( X) where something is small and X is moderately large. Bad Honnef, March 08 p.63/101
107 Fluxes and gaugino condensation Is there a general pattern of the soft mass terms? We 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) Bad Honnef, March 08 p.63/101
108 Mixed Modulus Anomaly Mediation The universal contribution from Modulus Mediation is therefore suppressed by the factor X log(m Planck /m 3/2 ) Numerically this factor is given by: X 4π 2. Bad Honnef, March 08 p.64/101
109 Mixed Modulus Anomaly Mediation The universal contribution from Modulus Mediation is therefore suppressed by the factor X log(m Planck /m 3/2 ) Numerically this factor is given by: X 4π 2. Thus contributions from radiative corrections such as Anomaly Mediation become competitive, leading to a Mixed Modulus-Anomaly-Mediation scheme. For reasons that will be explained later we call this scheme MIRAGE MEDIATION (Loaiza, Martin, HPN, Ratz, 2005) Bad Honnef, March 08 p.64/101
110 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 mirage unification of gaugino masses (Choi, Falkowski, HPN, Olechowski, 2005; Endo, Yamaguchi, Yoshioka, 2005; Choi, Jeong, Okumura, 2005) Bad Honnef, March 08 p.65/101
111 Evolution of couplings Αi log 10 Μ GeV Bad Honnef, March 08 p.66/101
112 The Mirage Scale 1600 Mi GeV M 3 M 2 M log 10 Μ GeV Bad Honnef, March 08 p.67/101
113 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 Bad Honnef, March 08 p.68/101
114 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. Bad Honnef, March 08 p.69/101
115 Constraints on the mixing parameter 120 tan Β 5 sign Μ 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) Bad Honnef, March 08 p.70/101
116 Constraints on ρ 120 tan Β 30 sign Μ 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) Bad Honnef, March 08 p.71/101
117 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), Bad Honnef, March 08 p.72/101
118 The MSSM hierarchy problem? The influence of the various soft terms is given by m 2 Z 1.8 µ M M m 2 H u m 2 q (3) L m A 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 explicit model building required (Choi, Jeong, Kobayashi, Okumura, 2005) (Kitano, Nomura, 2005; Lebedev, HPN, Ratz, 2005; Pierce, Thaler, 2006; Dermisek, Kim, 2006; Ellis, Olive, Sandick, 2006; Martin, 2007) Bad Honnef, March 08 p.73/101
119 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 Bad Honnef, March 08 p.74/101
120 Constraints on ρ 120 tan Β 30 sign Μ 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) Bad Honnef, March 08 p.75/101
121 The Mirage Scale 1600 Mi GeV M 3 M 2 M log 10 Μ GeV (Lebedev, HPN, Ratz, 2005) Bad Honnef, March 08 p.76/101
122 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 Bad Honnef, March 08 p.77/101
123 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 Bad Honnef, March 08 p.77/101
124 Constraints on the mixing parameter m3 2 TeV No EWSB g LSP tan Β 5 sign Μ 1 m t 175 GeV Χ 10 Below LEP Ρ (V. Löwen, 2007) Bad Honnef, March 08 p.78/101
125 Constraints on the mixing parameter 50 tan Β 5 sign Μ 1 m t 175 GeV 40 m3 2 TeV Ρ 900 (V. Löwen, 2007) Bad Honnef, March 08 p.79/101
126 Constraints on the mixing parameter m3 2 TeV No EWSB g LSP tan Β 5 sign Μ 1 m t 175 GeV Χ 10 Below LEP Ρ (V. Löwen, 2007) Bad Honnef, March 08 p.80/101
127 Explicit schemes III This relaxed mirage mediation is rather common for schemes with F-term uplifting (Gomez-Reino, Scrucca; Dudas, Papineau, Pokorski; Abe, Higaki, Kobayashi, Omura; Lebedev, Löwen, Mambrini, HPN, Ratz,2006) although pure mirage mediation is possible as well Bad Honnef, March 08 p.81/101
128 Explicit schemes III This relaxed mirage mediation is rather common for schemes with F-term uplifting (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 Bad Honnef, March 08 p.81/101
129 Explicit schemes IV In the heterotic case, we have hidden sector gaugino condensation potential run-away behaviour of the dilaton Bad Honnef, March 08 p.82/101
130 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 Bad Honnef, March 08 p.82/101
131 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) Bad Honnef, March 08 p.83/101
132 Run-away potential N 4 A 4.9 d 0 p 0 b V Re S Bad Honnef, March 08 p.84/101
133 Corrections to Kähler potential 2 N 4 A 4.9 d p 1.1 b V Re S (Barreiro, de Carlos, Copeland, 1998) Bad Honnef, March 08 p.85/101
134 Sequestered sector uplifting 6 N 4 A 4.9 C V Re S (Lebedev, HPN, Ratz, 2006; Löwen, HPN, 2008) Bad Honnef, March 08 p.86/101
135 Metastable Minkowski vacuum V Re C Re S 1.95 (Löwen, HPN, 2008) Bad Honnef, March 08 p.87/101
136 Constraints on the mixing parameter tan Β 5 Η 4 Η No EWSB Χ LSP m3 2 TeV g LSP WMAP WMAP 10 0 Below LEP ς (Löwen, HPN, 2008) Bad Honnef, March 08 p.88/101
137 Constraints on the mixing parameter tan Β 30 Η 4 Η No EWSB Χ LSP WMAP m3 2 TeV g LSP WMAP 10 0 Below LEP ς (Löwen, HPN, 2008) Bad Honnef, March 08 p.89/101
138 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) Bad Honnef, March 08 p.90/101
139 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 Bad Honnef, March 08 p.91/101
140 The string signatures We might consider the following schemes: Type IIB string theory Type IIA string theory Heterotic string theory M-theory on manifolds with G 2 holonomy Heterotic M-theory Bad Honnef, March 08 p.92/101
141 The string signatures We might consider the following schemes: Type IIB string theory Type IIA string theory Heterotic string theory M-theory on manifolds with G 2 holonomy Heterotic M-theory Questions: are there distinct signatures for the various schemes? can they be identified with LHC data? (Choi, HPN, 2007) Bad Honnef, March 08 p.92/101
142 The Gaugino Code How can we 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 Bad Honnef, March 08 p.93/101
143 Formulae for gaugino masses ( Ma ) g 2 a TeV = M (0) a + M (1) a anomaly + M (1) a gauge + (1) M a string M a (0) = 1 2 F I I f a (0) M a (1) anomaly = 1 16π 2 b F C a C 1 8π 2 Ca m F I I ln(e K0/3 Z m ) m M (1) a string = 1 8π 2 F I I Ω a Bad Honnef, March 08 p.94/101
144 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) Bad Honnef, March 08 p.95/101
145 msugra Pattern Universal gaugino mass at the GUT scale msugra pattern: M 1 : M 2 : M 3 1 : 2 : 6 g 2 1 : g2 2 : g2 3 as realized in popular schemes such as gravity-, modulus- or dilaton-mediation This leads to LSP χ 0 1 M gluino /m χ predominantly Bino as a characteristic signature of these schemes. Bad Honnef, March 08 p.96/101
146 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 M gluino /m χ Pure anomaly mediation inconsistent, as sfermion masses are problematic in this scheme (tachyonic sleptons). Bad Honnef, March 08 p.97/101
147 Mirage Pattern Mixed boundary conditions at the GUT scale characterized by the parameter ρ (the ratio of modulus to anomaly 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 M gluino /m χ 0 1 < 6 a compressed gaugino mass pattern. Bad Honnef, March 08 p.98/101
148 Uncertainties String thresholds Kähler corrections M (1) a string = 1 8π 2 F I I Ω a M a (1) anomaly = 1 16π 2 b F C 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 Bad Honnef, March 08 p.99/101
149 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) Bad Honnef, March 08 p.100/101
150 Conclusion String theory provides us with new ideas for particle physics model building, leading to concepts such as Local Grand Unification Mirage Mediation Geography of extra dimensions plays a crucial role: localization of fields on branes, presence of sequestered sectors LHC might help us to verify some of these ideas! Bad Honnef, March 08 p.101/101
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