1. Phenomenlogical Aspects of Mirage Mediation Yeong Gyun Kim (Sejong University) Neutralino Dark Matter in Mirage Mediation (thermal relic density, direct detection) LHC signature of Mirage Mediation

2. Neutralino Dark Matter in Mirage Mediation In collaboration with K.Choi, K.Y.Lee, Y.Shimizu (KAIST) K.Okumura (Kyushu University) JCAP 0612 (2006) 017

3. In KKLT-type moduli stabilization scenario  Modulus mediated contribution to SSB parameters at M GUT Mirage Mediation can be comparable to the anomaly mediated one O (m 3/2 /4p 2 ) when the gravitino mass m 3/2 ~ 10 TeV.  Depending upon the anomaly to modulus mediation ratio the model can lead to a highly distinctive pattern of superpaticle masses at low energy scale.

4.  The soft parameters at M GUT are determined to be where a ijk = a i + a j + a k, and c i parameterize the pattern of the pure modulus mediated soft masses. b a and g i : beta function and anomalous dim.

5.  An interesting consequence of this mixed modulus-anomaly mediation is that soft masses are unified at a mirage messenger scale For instance,

6. A Benchmark Model The original KKLT compactification of IIB theory gives (T : Calabi-Yau volume modulus) modulus Kahler potential modulus superpotential matter Kahler metric gauge kinetic function uplifting potential n i are rational numbers depending on the origin of matter superfield. (e.g, n i =0 for matter fields living on D7 brane)

7. (tanb, M 0 ) plane  Stau LSP in large tanb Stop LSP in small M 0 Neutralino LSP (Bino-like)  Magenta region gives thermal relic density Stop-neutralino coannihil. Stau-neutralino coannihil. Higgs resonance channel M t =172.7 GeV

8. Masses vs. tanbWh 2 vs. tanb (M 0 = 800 GeV)

9. Low energy effective Lagrangian for neutralino-quark int. scalar interaction In most situations the dominant contribution to the spin-independent (scalar) amplitude is the exchange of the two neutral CP-even Higgs bosons. Significant scalar couplings to nuclei arise if the neutralino is a mixed gaugino-higgsino state. Heavy CP-even Higgs coupling to d-type quark is essentially proportional to for Smaller Higgs masses give larger amplitude.

10. Direct detection ( s SI vs. m c ) Higgs and sparticle mass and B(b  sg) bounds are imposed Bino-like LSP m A is rather large m c > ~ 400 GeV small s SI Red points satisfy WMAP bound on relic density

11. More general cases It is possible to generalize the compactification to get different values of the mirage mediation parameters a, a i and c i Treat a as a free parameter while focusing on a = O (1), with various choices of a i and ci  a i =c i =1  a i =c i =1/2  a H =c H =0, a i =c i =1  a H =c H =0, a i =c i =1/2

12. (a, M 0 ) parameter space with a i =c i =1 tanb=10tanb=35 small a : Bino-like, large a : Higgsino-like seperated by stop/stau LSP region, a>2 : No EWSB

13. When a increases, the lightest neutralino is changed from Bino-like to Higgsino-like via Bino-Higgsino mixing region larger a  smaller M 3 (relative to M 1 )  reduced m M 3 ~M 0 (1-0.3 a), while M 1 ~M 0 (1+0.7 a) at GUT scale

14. tanb=10tanb=35 Direct detection ( s SI vs. m c ) Red points satisfy WMAP bound on relic density Varying a with

15. So far, we assumed a i =c i =1. The sparticle specturm, however, depends on the choice of the parameters a i and c i. The choice of a i and c i which decrease X t implies that the reduction of soft masses by X t becomes less significant, as evolved from the GUT to the EW scale. where

16. When m 2 tR and X t decrease  m 2 t1 increases (NO stop LSP) m 2 tR and X t decrease  m t1 decreases (stau LSP) m 2 Hu and X t decrease  |m 2 Hu | decreases (reduction of m) (reduction of m A ) At GUT scale RGE At EW scale 

17. (a, M 0 ) parameter space with a i =c i =1/2 tanb=10tanb=35 small a : Bino-like, large a : Higgsino-like NO stop LSP region, a>1.5 : No EWSB Bino-Higgsino Mixing Region appear !

18. When a increases, the lightest neutralino is changed from Bino-like to Higgsino-like via Bino-Higgsino mixing region m ~ M 1 around a ~ 1 tanb=10tanb=35

19. tanb=10tanb=35 Direct detection ( s SI vs. m c ) Red points satisfy WMAP bound on relic density

20. m 2 tR remains the same  m 2 t1 increases X t decrease (NO stop LSP) m 2 tR remains the same  m t1 increases X t decrease (NO stau LSP) m 2 Hu and X t decrease  |m 2 Hu | similar m 2 Hd and X t,b decrease  m 2 Hd decreases (Small m A ) At GUT scale RGE At EW scale When a H =c H =0 and a i =c i =1

21. (a, M 0 ) parameter space with a H =c H =0 and a i =c i =1 tanb=10tanb=35 small a : Bino-like, large a : Higgsino-like NO stop LSP region, NO stau LSP region Bino-Higgsino Mixing Region appear

22. When a increases, the lightest neutralino is changed from Bino-like to Higgsino-like via Bino-Higgsino mixing region m ~ M 1 around a ~ 1.5 tanb=10 tanb=35

23. tanb=10tanb=35 and Direct detection ( s SI vs. m c )

24. m 2 tR and X t decrease  m 2 t1 increases (NO stop LSP) m 2 tR and X t decrease  m t1 decreases (stau LSP) m 2 Hu and X t decrease  |m 2 Hu | decreases (reduction of m) (reduction of m A ) At GUT scale RGE At EW scale  When a H =c H =0 and a i =c i =1/2

25. (a, M 0 ) parameter space with a H =c H =0 and a i =c i =1/2 tanb=10 tanb=35 small a : Bino-like, large a : Higgsino-like NO stop LSP region, a>~2 : No EWSB Bino-Higgsino Mixing Region appear

26. tanb=10tanb=35 and Direct detection ( s SI vs. m c )

27. Summary of neutralino DM  Depending upon the model parameters, especially the anomaly to modulus mediation ratio, the nature of the LSP is changed from Bino-like neutralino to Higgsino-like one via Bino-Higgsino mixing region.  For the Bino-like LSP, the standard thermal production mechanism can give a right amount of relic DM density through pseudo-scalar Higgs resonance effect or the stau-neutralino or stop-neutralino coannihilation process.  Neutralino DM might be detected by near future direct detecting experiments, especially in the case of Bino-Higgsino mixed LSP.

28. LHC signature of Mirage Mediation In collaboration with W.Cho, K.Y.Lee, C.Park, Y.Shimizu (KAIST)

29. A benchmark point for collider study alpha = 1 M0 = 500 GeV aM=cM=1/2 aH=cH=0 tan(beta)=10

30.  Mirage benchmark point alpha=1, M 0 =500 GeV, a M =c M =1/2, a H =c H =0, tanb=10 (M1=367 GeV, M2=461 GeV, mu=475 GeV at EW scale) m_gluino= 884 GeV, m_dL=776 GeV, m_t1=545 GeV m_N1 = 355 GeV, m_N2 = 416 GeV, m_eR = 382 GeV  The cascade decay is open ! (m_N2 > m_eR)  Cross section for SUSY events ~ 6 pb We generated SUSY events ( ~ 30 fb -1 luminosity) using PYTHIA (event generator) + PGS (detector simulation)  (cf. mSUGRA )

31. Precision measurements of sparticle masses at the LHC When the cascade decay is open, a clean SUSY signal is l l + jets + missing events.

32. Di-lepton invariant mass distribution for the mirage point1 with 30 fb -1 lumi. M ll (max) ~ 60 GeV well matched with the generated value

33. Various distributions for the mirage point m_squark, m_slepton, m_N2, and m_N1 can be determined.

34. Gluino and squark mass measurement Di-jet invariant mass Stransverse mass

35.  The mass ratio of gluino to LSP which is quite distinctive from the prediction of GUT unification of gaugino masses. ‘Model-Independent’ Masses

36. Backup slides

37.  Gluino, squark and slepton masses  M 0, alpha and c_i  Neutralino masses  Mu (EW scale), tan(beta)  c_H and tan(beta) Determination of model parameters

38. (Bachacou, Hinchliffe, Paige 2000) (for “point 5”, M=300 GeV and m=100 GeV) etc.

39. Moduli-induced gravitino problem M.Endo,K.Hamaguchi,F.Takahashi (2006) N.Nakamura, M.Yamaguchi (2006) Recently, it is shown that the branching ratio of the modulus decay into the gravitino is generically quite large. which causes serious problems after the modulus decay. In this work, we just assume that this problem is avoided by some mechanism and the thermal production of DM is realized. Then we investigate theraml relic density and direct detection rate of neutralino DM.