1. SUSY at the LHC Yeong Gyun Kim (Sejong U. & KAIST) HPC Asia 2007 (September. 9-12, 2007 Seoul, Korea)

2. Introduction (weak scale supersymmetry) LHC signature of Mirage mediation Tau polarization in SUSY cascade decay Contents

3. We are entering exciting period in particle physics. The LHC is about to explore for the first time the TeV energy scale. The origin of EWSB ? The nature of dark matter ? Supersymmetry ? Extra dimensions ?

4. Weak scale supersymmetry - Provides a solution for the naturalness problem - Complies with gauge coupling unification - Lightest Supersymmetric Particles (LSP) a natural candidate for non-baryonic Dark Matter

5. Minimal Supersymmetric Standard Model (MSSM) SM fields plus an extra Higgs doublet and their superpartners SU(3) x SU(2) x U(1) gauge symmetry and Renormalizability R-parity conservation (to avoid fast proton decay) ( B: baryon number, L: lepton number S: spin ) = +1 for ordinary particles = -1 for their superpartners Soft Supersymmetry Breaking Sparticles are produced in pairs The Lightest SUSY Particle (LSP) is STABLE

6.  Precise measurement of SUSY particle masses  Reconstruction of the SUSY theory (SUSY breaking mechanism) Measurement of SUSY masses  SUSY events always contain two invisible LSPs  No masses can be reconstructed directly  One promising approach  Identify particular decay chain and measure kinematic endpoints using visible particles (functions of sparticle masses)

7. When a long decay chain can be identified, various combinations of masses can be measured in a model independent way

8. The SPS 1a benchmark scenario A favorable scenario both for LHC and ILC M_gluino = 595 GeV M_qL= 534 GeV, M_uR = 522 GeV M_N2 = 177 GeV, M_N1 = 96 GeV M_eR = 143 GeV, M_eL= 202 GeV (M_eR < M_N2)

9.  Dilepton invariant mass distribution after the cut ~ 77 GeV

10.  Other invariant mass edges In total, five endpoint measurements Four invovled sparticle masses can be obtained

11. LHC signature of Mirage Mediation In collaboration with W.Cho, K.Y.Lee, C.Park, Y.Shimizu (KAIST) Ref. JHEP 0704 (2007) 054

12. 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 /4pi 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.

13.  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 gamma i : beta function and anomalous dim.

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

15. A benchmark point for collider study alpha = 1 M 0 = 500 GeV a M =c M =1/2 a H =c H =0 tan(beta)=10 K.Choi, YGK, K.Y.Lee, K.Okumura, Y.Shimizu (2006)

17.  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 )

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

19. Event Selection Cuts.

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

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

22. Gluino and squark mass measurement Di-jet invariant mass

23. Gluino and squark mass measurement Di-jet invariant mass

24. Squark mass measurement Stransverse mass m_qR vs m_N1

25. ‘Model-Independent’ Masses

26.  The mass ratio of gluino to LSP which is quite distinctive from the prediction of other gaugino mass pattern (i.e anomaly, mSUGRA pattern)

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

28. Determination of model parameters

29. Conclusions (of mirage medication part)  We have investigated LHC signature of mirage mediation by performing a Monte Carlo study for a benchmark point.  SUSY particle masses are determined in a model independent way. In particular, the measured ratio well reproduce theoretical input value of the benchmark point. Therefore, the benchmark scenario may be distinguishable experimentally from other SUSY scenarios, for example, in which gaugino masses are unified at GUT scale.  Model parameters were obtained from a global fit to observable and well agree with the input values.

30. Tau Polarization in SUSY Cascade decays In collaboration with S.Y.Choi, K.Hagiwara, K.Mawatari, P.M Zerwas Ref) hep-ph/0612237

31.  Much attention has been paid in the recent past to the SPS1a cascade  So far, cascades have primarily been studied involving first and second generation leptons/sleptons.  Explore how the polarization of tau leptons can be exploited to study R / L chirality and mixing effects in stau and neutralino sector

32. Single pion decays of tau as polarization analyzer At high energies, the fragmentation functions for pions ( z : energy fraction transferred from the polarized tau to the pion. R / L : tau chirality )  Pion from the right-handed polarized tau- is harder than the one from left-handed polarized tau-

33. Neutralino decay  On the contrary, results in soft pions. results in hard pions (for, gauginos)

34.  Invariant mass distribution of tau-tau and pi-pi

35.  Dependence of on the stau mixing angle With fixed SPS1a values of and With pion momentum cut Without pion momentum cut

36.  m (pi-pi) distribution for SUSY (SPS1a) and UED’ SPS1a : LR type UED’ : LL type

37.  m (pi-pi) distribution for SUSY (SPS1a) and UED’ SPS1a : LR type UED’ : LL type

38. Conclusions (tau polarization part)  The analysis of tau polarization in cascade decays provides valuable information on chirality-type and mixing of suspersymmetric particles.  By comparing the distribution of the SUSY cascade with UED-type predictions, the sensitivity of the method has been demonstrated.  Though pi-pi distributions have been analyzed in detail, the techniques can readily be applied to other tau decay modes.