Moduli stabilization, SUSY breaking and the Higgs sector Tatsuo Kobayashi

1. Moduli stabilization, SUSY breaking and the Higgs sector Tatsuo Kobayashi １．Introduction 2. KKLT scenario 3．Generalized KKLT scenario 4. TeV scale mirage mediation 5. Summary based on Choi, Jeong, T.K., Okumura, hep-ph/0508029, 0612258 Abe, Higaki, T.K., hep-th/0511160, 0512232, 060506095 Abe, Higaki, T.K., Omura, hep-th/0612035 Abe, T.K., Omura, hep-ph/0703044 Abe, Kim, T.K., Shimizu, in preparation

2. 1. Introduction Several mediation mechanisms of SUSY breaking Supergravity mediation (mSUGRA) (moduli-dilaton mediation) Gauge mediation Anomaly mediation New type of mechanism Mirage mediation phenomenological aspects ⇒ Y.G.Kim’s talk This talk covers theoretical side. Mirage mediation can be realized in string-derived supergravity. TeV scale mirage is quite interesting, and leads to a unique pattern of s-spectrum.

3. String phenomenology Superstring theory is a promising candidate for unified theory including gravity. Superstring theory has several moduli fields including the dilaton. Moduli correspond to the size and shape of compact space. VEVs of moduli fields  couplings in low-energy effective theory, e.g. gauge and Yukawa couplings Thus, it is important to stabilize moduli VEVs at realistic values from the viewpoint of particle physics as well as cosmology Actually, lots of works have been done so far.

4. Moduli stabilization and SUSY breaking Low-energy effective theory = supergravity Moduli-stabilizing potential may break SUSY. When Moduli-mediated SUSY breaking is dominant unless couplings between the visible sector and moduli fields are suppressed by some reason. This is the conventional approach. Gaugino masses and sfermion masses are comparable with the gravitino mass. (Ratios are fixed by supergravity Lagrangian.) For example, when gauge kinetic functions and Kahler metric are universal, that leads to the spectrum of mSUGRA.

5. Moduli stabilization and SUSY breaking The magnitude of moduli F-components depend on moduli stabilization mechanism. When F/M is smaller than the gravitino mass, another contribution is also important or rather dominant. ⇒　Different spectrum of s-particles

6. KKLT scenario Kachru, Kallosh, Linde, Trivedi, ‘03 They have proposed a new scenario for moduli stabilization leading to de Sitter (or Minkowski) vacua, where all of moduli are stabilized. Soft SUSY breaking terms Choi, Falkowski, Nilles, Olechowski, Pokorski ’04, CFNO ‘05  a unique patter of soft SUSY breaking terms Modulus med. and anomaly med. are comparable.  Mirage (unification) scale Mirage Mediation Choi, Jeong, Okumura, ‘05  little SUSY hierarchy (TeV scale mirage mediation) Choi, Jeong, T.K., Okumura, ’05, ‘06

7. More about moduli stabilization a generic KKLT scenario with moduli-mixing superpotential ⇒various mirage scale Abe, Higaki, T.K., ’05 Choi, Jeong, ’06 Choi, Jeong, T.K., Okumura, ‘06 F-term uplifting Dudas, Papineau, Pokorski, ’06 Abe, Higaki, T.K., Omura, ’06 Kallosh, Linde, ’06 Abe, Higaki, T.K, in preparation

8. 2. KKLT scenario This scenario consists of three steps in type IIB. • Flux compactification Giddings, Kachru, Polchinski, ‘01 The dilaton S and complex structure moduli U are assumed to be stabilized by the flux-induced superpotential while the Kaher moduli T remain not stabilized. (It is stabilized in the next step.)

9. 2) Non-perturbative effect We add T-dependent superpotential induced by e.g. gaugino condensation. Scalar potential T is stabilized at DTW=0 • SUSY Anti de Sitter vacuum V < 0 Moduli mass

10. 3) Uplifting We add uplifting potential generated by e.g. anti-D3 brane at the tip of warp throat The value of D can be suppressed by the warp factor. We fine-tune such that VF+VL = 0 (or slightly positive)  SUSY breaking de Sitter/Minkowski vacuum T is shifted slightly from the point DTW=0

11. Uplifting hidden sector non-perturbative effect T anti D3 (SUSY breaking source) visible sector

12. Uplifting V SUSY breaking total potential T before uplifting SUSY point

13. Mirage mediation If aT = O(1), moduli-mediation is dominant However, when aT=O(10), moduli mediation and anomaly mediation are comparable, that is, Mirage mediation.

14. Mirage mediation Mirage mediation = (modulus med.) + (Anomaly med.) the mirage scale

15. Mirage mediation For scalar masses, we can obtain the same behavior. Scalar masses (Mx) = mixture of (modulus med.) and (Anomaly med.). However, at the mirage scale, RG effect and Anomaly med. are cancelled each other.

16. Soft SUSY breaking Modulus med. and anomaly med. are comparable. It is useful to define the ratio, AM/modulus med. An interesting aspect is the mirage scale, where anomaly med. at the cut-off scale and RG effects between the cut-off scale and the mirage scale cancel each other. Original KKLT  α=1 Mirage scale = intermediate scale α=2 ⇒ TeV scale mirage

17. example Suppose that the modulus mediation leads to the s-spectrum of mSUGRA. α=0 ⇒usual mSUGRA α=2 ⇒ TeV scale mirage

18. 3. Generalized KKLT scenario 3-1. moduli-mixing superpotential In several string models, gauge kinetic function f is obtained as a linear combination of two or more fields. IIA intersecting D-branes/IIB magnetized D-branes Lust, et. al. ’04 Gaugino condensation  W = exp[-a f] Moduli mixing superpotential S is assumed to be stabilized already.

19. Moduli mixing Abe, Higaki, T.K., ’05 Choi, Jeong, ‘06 Moduli mixing superpotential ⇒change F-term of T after uplifting Gauge kinetic function of the visible sector ⇒change ratio of gaugino mass to F-term Both change a value of α

20. Our model Choi, Jeong, T.K. Okumura, ‘06 m,n,k,p are discrete. S is replace by its VEV. We also add the same uplifting potential.

21. 3.2 F-term uplifting Dudas, et. al. ’06, Abe, Higaki, T.K., Omura ’06 Kallosh, Linde, ‘06 Can we realize uplifting by a spontaneous SUSY breaking ? If the potential minimum corresponds to non-vanishing DXW, F-term of X uplifts the vacuum energy. Any g(x) is OK, e.g. the Intriligator-Seiberg-Shih model.

22. Spectra in F-term uplifting 1) When Fx is sequestered from the visible sector like anti-D3 brane in the original KKLT, modulus mediation and anomaly mediation are comparable, i.e. mirage mediation. 2) When contact terms between the visible matter fields and X are not suppressed sfermion masses ←Fx gaugino masses ←mirage mediation sfermion masses >> gaugino masses by O(10)

23. 3.3 light dilaton S Abe, Higaki, T.K., ’05, ‘06 If the dilaton S has no SUSY mass at DSWflux=0, S is not stabilized at the first step. We have to stabilize both S and T at the second step. Our model There is a solution for the SUSY condition, DSW=DTW=0 However, that is a saddle point. Near this point, there is SUSY breaking minimum with negative vacuum energy.

24. F-terms before uplifting after uplifting Dilaton-moduli dominant SUSY breaking different pattern from the mirage mediation Why the SUSY point is unstable ?

25. S-T mixing racetrack model before uplifting Uplifting

26. 4.TeV-scale mirage mediation: solution for the fine-tuning problem TeV scale mirage mediation leads to the unique pattern of s-particle spectrum, gaugino masses degenerate around 1 TeV sfermion masses degenerate around 1 TeV the little hierarchy between the stop mass and the Higgs soft mass is naturally realized at TeV scale. In this type of models, there is no fine-tuning problem.

27. 4.1 the fine-tuning problem Higgs sector Supersymmetric mass terms in superpotential SUSY scalar potential = (F-term potential) + (D-term potential) Soft SUSY-breaking mass terms No quartic term in soft SUSY breaking terms

28. Higgs sector ( fine-tuning) The Higgs potential Higgs VEVs

29. The lightest Higgs mass RG effect

30. The fine-tuning problem Fine-tuning

31. Favored pattern of mass parameters If we can realize “naturally” the following little hierarchy that would be favorable from a simple bottom-up viewpoint to avoid the fine-tuning problem. That is possible in the mirage mediation.

32. 4.2 TeV-scale mirage mediation By choosing discrete values, n,m,p,k, we can obtain α=2 ⇒Mirage scale = TeV scale If the modulus mediation leads to the little hierarchy between the stop mass and the Higgs soft mass is naturally realized at TeV scale. In this type of models, there is no fine-tuning problem.

33. TeV-scale mirage mediation Low-energy spectra (I) (II) They can relax the fine-tuning problem. They have unique patterns. It is interesting to study more their phenomenological aspects.

34. LSP Higgsisno << bino, wino LSP = Higgsino-like Dark matter ??? Thermal relic density is rather small

35. 4.3 More about fine-tuning: bottom-up approach Abe, T.K.,Omura, ‘07 Soft Higgs mass Cancellation between gluino mass and wino mass is important, but bino mass is not so important. gluino and wino masses are comparable at Mz.

36. fine-tuning:bottom-up approach Abe, T.K.,Omura, ‘07 r2 = M2/M3, r1= M1/M3 at Mx Favorable region r2=4 , -3 < r1 < 10

37. Extended model:partial TeV scale mirage Everything is the same as the previous one, except U(1) gauge kinetic function. We take U(1) gauge kinetic function different from SU(3) and SU(2) ones such that they lead to the gauge coupling unification.

38. Extended model LSP = mixture between higgsino and bino ⇒ different phenomenology, e.g. dark matter Further study would be interesting Abe, Kim, T.K., Shimizu, in preparation

39. Summary We have studied KKLT type models with moduli-mixing superpotential. Soft SUSY breaking terms in generalized models have a rich structure. in general mixture of modulus mediation and anomaly mediation with a certain ratio, i.e. mirage mediation sometimes modulus med. >> anomaly med. or modulus med. << anomaly med.  further study TeV scale partial mirage model also important, e.g. for the fine-tuning problem and dark matter physics