TeV scale mirage mediation for natural little hierarchy

1. TeV scale mirage mediation for natural little hierarchy Ken-ichi Okumura Kyushu University In collaboration with Kiwoon Choi, Kwang-Sik Jeong, Tatsuo Kobayashi

2. Low energy supersymmetry is the most attractive extension of the SM • Solution of gauge hierarchy problem • Gauge coupling unification is predicted • EW symmetry is broken radiatively • Lightest SUSY particle (LSP) is stable with R-parity →Dark Matter • Light higgs boson (～100 GeV) ←EW precision test Supersymmetry must be broken softly at 100 GeV～1TeV 　　　　　　　　　　　　　　　　　　　←hierarchy problem How to communicate SUSY breaking to visible sector is most relevant to phenomenology.

3. Mirage mediation = Moduli mediation ＋ Anomaly mediation Mirage mediation K.Choi, A.Falkowski, H.P.Nilles, M.Olechowski, and S.Pokorski K.Choi, A.Falkowski, H.P.Nilles and M.Olechowski M.Endo, K.Yoshioka, M.Yamaguchi K.Choi, K-S.Jeong, KO similar order Tree level effect in SUGRA 1-loop effect in SUGRA A class of string inspired models (e.g. KKLT) realizes such a situation generally. Modulus mediation Anomaly Phenomenological consequence is totally different from each of mediation schemes. Our world SUSY breaking

4. Plan of talk • Mirage mediation • Mirage unification of soft masses • Little SUSY hierarchy problem and TeV scale mirage mediation • Conclusion

5. Mirage mediation is generic consequence of modulus stabilization Mirage mediation is a consequence of two simple assumptions: • Gauge coupling modulus (or dilation) is stabilized by • non-perturbative effect. • ii) SUSY is broken by a brane-localized source sequestred • from observable sector. e.g. KKLT-type modulus stabilization Bulk CY SUSY breaking brane Warped throat Visible sector of 4D cut-off

6. 4D effective action “Volume” From sequestered SUSY breaking brane Gauge modulus From T-independent flux or T-independent gaugino condensation From T-dependent instanton effects or T-dependent gaugino condensation Independently of the detail of SUSY breaking, in low energy limit, Should be tuned to make final vacuum energy density to be nearly zero

7. Little hierarchies from modulus stabilization Little hierarchy structure is a generic consequences of the two assumption Anomaly mediation Modulus mediation

8. Mirage unification of soft masses K.Choi, K-S. Jeong, KO (2005) Just below the unification scale Anomaly mediated contributions Modulus mediated contributions

9. Modulus mediated contributions : rational numbers ~ # of extra dimensions Discretized in unit of gaugino mass (up to small corrections).

10. Renormalization group runningof gaugino mass Compare formulas at scale μ, Because quantum correction in modulus contribution has exactly same form as anomaly mediation, they cancel at scale, ←This does not depend on the choice of gauge group Their sum can be rewritten as, Anomaly mediation only shifts the mediation scale of modulus mediation!

11. No new fields (other than modulus) below the unification scale. Gaugino unification is “mirage” , not physical threshold.

12. Renormalization group running of A term and soft mass For the first and second generations (y =0) and Yukawa coupling which satisfy the following relation, We obtain similar expressions,

13. Compared other SUSY breaking scenarios, e.g. mSUGRA, GMSB, AMSB, Mirage mediation gives more compressed superparticles spectrum Dark matter Y.G. Kim’s talk Light higgsino and pseudo scalar Higgs

14. little SUSY hierarchy problem Log running of from the cut-off M_Z scale is natural tuning Tension ! The lightest Higgs boson mass > 114 GeV Tree < M_Z^2 Loop

15. Radiative EW symmetry breaking

16. Example in CMSSM Fine-tuning parameter Worse than a few % !

17. TeV scale mirage mediation for natural little hierarchy K.Choi, K-S.Jeong, T.Kobayashi, KO (2005) R.Kitano, Y.Nomura (2005) Suppose and With , can be naturally close to even when

19. Argument by A.Pierce and J.Thaler (2006) For the models described above, It is likely that a brane-localized source of SUSY breaking gives , so T T

20. But this difficulty of obtaining can be avoided in models with modulus-(heavy) dilaton mixing vev of heavy dilaton fixed by flux are relatively rational number ( Im(S): axionic ). can be achieved even for a sequestered SUSY breaking brane stabilized at the end of throat (n_P = 0). ( General aspects of modulus-dilaton mixing : Talk by T.Higaki & H.Abe )

21. Natural Bμfrom nonperturbative effects Forbid by symmetry which is broken by nonperturbative effects We naturally have, and are rational numbers. Discrete choice realizes .

22. Two possibilities for in the little hierarchy In the above model, and pattern (I) requires fine-tuning beyond the control of the model.

23. SM Higgs mass bound can be evaded with tuning less tan 10%.

24. Conclusion • Mirage mediation is generic in modulus stabilization. • Compressed SUSY spectrum leads to distinctive phenomenology. -> Talk by Y.G.Kim for dark matter • TeV mirage mediation can be realized with sequestered SUSY breaking brane by modulus-dilaton mixing. • Better than 10% tuning in EW symmetry breaking is compatible with MSSM. (and gauge coupling unification)