1. Little Higgs Dark Matter & Its Collider Signals ・ E. Asakawa, M. Asano, K. Fujii, T. Kusano, S. M., R. Sasaki, Y. Takubo, and H. Yamamoto, PRD 79, 2009. ・ S. M, T. Moroi and K. Tobe, PRD 78, 2008. ・ S. M, M. M. Nojiri and D. Nomura, PRD 75, 2007. ・ M. Asano, S. M., N. Okada and Y. Okada, PRD 75, 2007. Shigeki Matsumoto (University of Toyama) 1.Little Higgs Scenario 2.Little Higgs signals at LHC & ILC 3.Summary ～ Papers ～ ～ Contents ～

2. 1. Little Hierarchy Scenario Kolde & Murayama, hep-ph/0003170 When the tuning < 10%, Λ SM < O(1)TeV (m h = 120 GeV) Corrections to m h If coefficient c i is O(1), Λ SM > O(10)TeV (m h = 120 GeV) EW Observables Barbieri & Strumia, 1998 E 1 TeV 10 TeV ??? Little Hierarchy Problem Need some mechanism to control the Higgs mass! 1/11

3. 1. Little Hierarchy Scenario Little Higgs Scenario ・ Higgs boson = Pseudo NG boson ・ Explicit breaking = Collective symmetry breaking New Physics with G ( ⊃ Gauge group ), which is slightly broken Electroweak breaking SU(2) x U(1) Y  U(1) EM (Standard Model) E 1 TeV 100 GeV 10 TeV SSB: G  G’, where G’ ( ⊃ SU(2) x U(1) Y ) Generation of m h Origin of m h = Interactions which break G. Usual breaking: When the interaction “L 1 “ breaks the symmetry G, and generates m h, then (m h ) 2 ～ (Λ SM ) 2 /(16π 2 ) ～ (1 TeV) 2 (1-loop diagrams) 2/11

4. 1. Little Hierarchy Scenario Little Higgs Scenario ・ Higgs boson = Pseudo NG boson ・ Explicit breaking = Collective symmetry breaking New Physics with G ( ⊃ Gauge group ), which is slightly broken Electroweak breaking SU(2) x U(1) Y  U(1) EM (Standard Model) E 1 TeV 100 GeV 10 TeV SSB: G  G’, where G’ ( ⊃ SU(2) x U(1) Y ) Generation of m h Origin of m h = Interactions which break G. Collective symmetry breaking: When the Interactions “L 1 “ & “L 2 “ (partially) break G, and the Higgs boson is “pseudo” NG boson when both interactions exist, (m h ) 2 ～ (Λ SM ) 2 /(16π 2 ) 2 ～ (100 GeV) 2 (2-loop diagrams) 2/11

5. 1. Little Hierarchy Scenario W,Z W H,Z H h h h h + + + h t t t T Quadratically divergent corrections to m h are completely cancelled at 1-loop level! Diagrammatic view point ・ Global symmetry imposed ・ Collective sym. breaking New particles introduced. (Little Higgs partners) T E 1 TeV 100 GeV 10 TeV SM Nonlinear sigma model Constructing models 3/11

6. 1. Little Hierarchy Scenario – F 2 /4 + L Yukawa – V(H,  ) + Kinetic terms of fermions Lagrangian No quadratically divergent |H| 2 term at 1-loop level. - - - - - - - - - -- - Triplet H H H T+T+ SU(5)  SO(5) [SU(2)xU(1)] 2 SU(2)xU(1) 4/11

7. 1. Little Hierarchy Scenario Constraints from EWPM Littlest Higgs model suffers from EWP constraints. ～ Imposition of the Z 2 -symmetry (T-parity) ～ 1. SM particles & Top partner T + are even 2. Heavy Gauge bosons are odd. 3. T-odd partners of matter fields introduced. H. C. Cheng, I. Los, J. High Energy Phys. (2003, 2003) - - - - - - - - - -- - Triplet H H H T-parity T+T+ T–T– 4/11

8. 1. Little Hierarchy Scenario Constraints from EWPM H. C. Cheng, I. Los, J. High Energy Phys. (2003, 2003) - - - - - - - - - -- - Triplet H H H T-parity T+T+ T–T– Model Parameters of the LHT f : VEV of the SU(5)  SO(5) breaking 2 : Mass of the top-partners (in units of f)  x : Mass of the T-odd partner of “x”(in units of f)  Higgs mass m h is treated as a free parameter 4/11

9. 1. Little Hierarchy Scenario Constraints from EWPM H. C. Cheng, I. Los, J. High Energy Phys. (2003, 2003) Model Parameters of the LHT f : VEV of the SU(5)  SO(5) breaking 2 : Mass of the top-partners (in units of f)  x : Mass of the T-odd partner of “x”(in units of f)  Higgs mass m h is treated as a free parameter Masses of new particles are proportional to f. Masses of SM particles are proportional to v. O (f) O (v) 4/11

10. 1. Little Hierarchy Scenario Lightest T-odd Particle is stable due to the T-parity conservation.  Little Higgs Dark Matter! (Heavy photon in the LHT) Main annihilation mode: A H A H  h  WW or ZZ 1. A H A H h vertex is given by the SM gauge coupling. 2. Annihilation cross section depends on m AH & m h.  Relic abundance of A H :  h 2 (m AH (f), m h ) Asano, S.M, N.Okada, Y.Okada (2006) J. Hubisz, P. Meade, Phys. Rev. D71, 035016 (2005) Little Higgs dark matter is singlet and spin 1 particle. 1.The dark matter mass: 80-400 GeV 2.The Higgs mass: 110-800 GeV  h 2 of dark matter 5/11

11. 1. Little Hierarchy Scenario U-branch Constraints from EWPM? 6/11

12. 1. Little Hierarchy Scenario Constraints from EWPM? L-branch 6/11

13. 1. Little Hierarchy Scenario 1. Masses of top partners are about (or less than) 1 TeV!  copiously produced at the LHC. 2. Masses of heavy gauge bosons are several hundred GeV!  can be produced at the ILC. f = 580 GeV 2 = 1.15 m h = 134 GeV m T+ = 834 GeV m T- = 664 GeV m AH = 81.9 GeV m WH = 368 GeV m ZH = 369 GeV Representative point 6/11 Constraints from EWPM? L-branch

14. 2. Littlest Higgs Signals at LHC & ILC Top partner productions S.M., T. Moroi, K. Tobe, Phys.Rev.D78 (2008) LHC is a hadron collider, so that colored new particles are copiously produced!  T + & T - productions! MadGraph/Event (Event generation) PYTHIA (Hadronization) PDG4 (Detector Response) T + pair production Reconstructing two T + -system, T + (lep) & T – (had) Determination of T + Mass (with ±20 GeV uncertainty) 7/11

15. 2. Littlest Higgs Signals at LHC & ILC Top partner productions S.M., T. Moroi, K. Tobe, Phys.Rev.D78 (2008) LHC is a hadron collider, so that colored new particles are copiously produced!  T + & T - productions! MadGraph/Event (Event generation) PYTHIA (Hadronization) PDG4 (Detector Response) Single T + production Reconstructing bW system # of the signal depends on NP! (σ determined with 20% accuracy.) 7/11

16. 2. Littlest Higgs Signals at LHC & ILC H1H1 H2H2 Top partner productions S.M., T. Moroi, K. Tobe, Phys.Rev.D78 (2008) LHC is a hadron collider, so that colored new particles are copiously produced!  T + & T - productions! MadGraph/Event (Event generation) PYTHIA (Hadronization) PDG4 (Detector Response) Top reconstruction via hemisphere analysis. End points of M T2 depend on m T- & m AH (within about 20 GeV accuracy.) T - pair production S.M., Nojiri, Nomura (2007) 0 100 200 7/11

17. 2. Littlest Higgs Signals at LHC & ILC f = 580 ± 33 GeV  Cosmological connections f (GeV) 2 From T + pair prod. From T + single prod. From T - pair prod.   8/11

18. 2. Littlest Higgs Signals at LHC & ILC Heavy gauge boson productions E. Asakawa, M. Asano, K. Fujii, T. Kusano, S. M., R. Sasaki, Y. Takubo, and H. Yamamoto, PRD79, 2009. ILC is a e + e - collider, so that heavy particles are produced with clean environment.  W H, Z H, A H productions! Physsim (Event generation) PYTHIA (Hadronization) JSF Q-sim. (Detector Response) Z H A H production @ 500 GeV Energy distribution of h  End points depend on m AH & m ZH m AH = 83.2 ± 13.3 GeV m ZH = 366. ± 16. GeV  f = 576. ± 25. GeV  = 1.9 fb 9/11 500 fb -1

19. 2. Littlest Higgs Signals at LHC & ILC Heavy gauge boson productions E. Asakawa, M. Asano, K. Fujii, T. Kusano, S. M., R. Sasaki, Y. Takubo, and H. Yamamoto, PRD79, 2009. ILC is a e + e - collider, so that heavy particles are produced with clean environment.  W H, Z H, A H productions! Physsim (Event generation) PYTHIA (Hadronization) JSF Q-sim. (Detector Response) Z H A H production @ 1 TeV Energy distribution of W  End points depend on m AH & m ZH m AH = 81.58 ± 0.67 GeV m WH = 368.3 ± 0.63 GeV  f = 580± 0.69 GeV  = １２１ fb 9/11 500 fb -1

20. 2. Littlest Higgs Signals at LHC & ILC Probability density Simulation results + Higgs mass Annihilation X-section (m AH, m h )   DM h 2 Probability density of the dark matter relics  DM h 2 WMAP Planck LHC ILC(1000) ILC(500) LHC: Abut 10% accuracy (Model-dependent analysis) ILC(500): Better than 10% accuracy (Model-independent analysis) ILC(1000): 2% accuracy!! (Model-independent analysis) 10/11

21. 11/11 3. Summary Little Higgs model with T-parity is one of attractive scenario describing New Physics at TeraScale. It contains a candidate for cold dark matter whose stability is guaranteed by the T-parity (Little Higgs dark matter). The property of the dark matter can be investigated at collider experiments such as LHC & ILC. At LHC, top partners can be detected. From their data, the property of the dark matter can be estimated with a model dependent way. At ILC with s 1/2 = 500 GeV, the property of the dark matter can be determined with model-independent way. Also, the relic abundance can be determined with the accuracy comparable to the WMAP. AT ILC with s 1/2 = 1 TeV, the property of the dark matter can be determined very accurately. For instance, the relic abundance will be determined with the accuracy comparable to PLANCK experiment.

22. Back Up

23. The LH Lagrangian Pseudo NG bosons Breaking directions – F 2 /4 + L Yukawa – V(H,  ) Non-linear  field + Kinetic terms of fermions

24. The LH Lagrangian Gauge interactions [SU(2) x U(1)] 2 – F 2 /4 + L Yukawa – V(H,  ) Gauge couplings: g 1, g’ 1, g 2, g’ 2

25. The LH Lagrangian – F 2 /4 + L Yukawa – V(H,  ) Top Yukawa interactions Top Yukawa: 1 U quark mass: 2 tLtL tRtR

26. Particle contents in Gauge, Higgs, and top sectors 4 gauge bosons : B 1, W 1, B 2, W 2 Σ= (24 – 10) pions : SM gauges : A, W ±, Z Heavy gauges : A H, W H ±, Z H SM Higgs : h Triplet Higgs : Φ After breakings SM top quark : t, Heavy top : T = (U, U R ) T g 1, g’ 1, g 2, g’ 2 1, 2 Parameters f

27. Little Higgs Dark Matter Lightest T-odd Particle is stable due to the T-parity conservation.  Little Higgs Dark Matter! (Heavy photon in the LHT) Main annihilation mode: A H A H  h  WW or ZZ. 1. A H A H h vertex is given by the SM gauge coupling. 2. Annihilation cross section depends on m AH & m h.  Relic abundance of A H :  h 2 (m AH (f), m h ) [Asano, S.M, N.Okada, Y.Okada (2006)] [J. Hubisz, P. Meade, Phys. Rev. D71, 035016 (2005) ] When m h < 150 GeV, then 550 < f < 750 GeV. Masses of heavy gauge bosons are several hundred GeV.  can be produced at ILC. Masses of top partners are about (or less than) 1 TeV  copiously produced at LHC.  h 2 (m AH (f), m h )

28. Representative point for simulation study (1) Observables (m w sin  W,  l,  DM h 2 ) vs. Model parameters (f, 2, m h ) (2) 2m h 2 /  t > O (0.1-1), where  t is the top-loop contribution to m h. Considering EW precision & WMAP constraints f = 580 GeV 2 = 1.15 m h = 134 GeV m AH = 81.9 GeV m WH = 368 GeV m ZH = 369 GeV m T+ = 834 GeV m T- = 664 GeV m  = 440 GeV (m LH = 410 GeV) [J. Hubisz, P. Meade, A. Noble, M. Perelstein, JHEP0601 (2006)]

29. T + pair production at the LHC SM BG: tt–production! (460 pb) - At the parton level Signal = bbqqlν - - Reconstruct Two T + -system: T + (lep) & T – (had) using the fact that the missing momentum p T is due to the neutrino emission and (p l + p ν ) 2 = m W 2. There are 6-fold ambiguity in the reconstruction of T + -system.  The combination to minimize ~ Output ~ Distribution of ~ Strategy to reduce BG ~

30. T + pair production at the LHC The distributions have distinguishable peaks at around the T + mass. SM BG are well below the signal.  From the distribution, we will be able to study the properties of T +. ~ Results ~ ~ Cut used in the analysis ~ ~ Discussion ~

31. T + pair production at the LHC We consider the bin Then, we calculate the # of events in the bin as a function of with being fixed. The peak of the distribution is determined by maximizing the # of events in the bin. We applied the procedure for ~ Results ~ ~ Conclusion ~ ~ Accuracy of the m T+ determination ~ The difference between the position of the peak and the input value of mT+ is, typically, 10-20 GeV!

32. T + single production at the LHC SM BG: tt & single t productions! - At the parton level Signal = bqlν Existence of very energetic jet (b from T + )! With the leading jet, reconstruct T + -system. There are 2-fold ambiguity to reconstruct neutrino momenta  & Reject events unless is small. Jet mass is also used to reduce the BG. ~ Output ~ Distribution of ~ Strategy to reduce BG ~

33. Single T + production occurs not through a QCD process but through a EW process (e.g. W-exchange). Distributions have distinguishable peaks at around the T + mass when sin 2 β is large enough!  From the cross section, we will be able to determine sinβ. ~ Results ~ ~ Cut used in the analysis ~ ~ Discussion ~ T + single production at the LHC

34. We use the side-band method to extract the # of the single production events, (L) (C) (R) after imposing the cuts. Then, cross section for the single T + production can be obtained from the # of events in the signal region. ~ Results (Point 2) ~ ~ Conclusion ~ ~ Accuracy of sinβ determination ~ The cross section, which is proportional to sin 2 β, will be determined with 10-20%. Parameter “sinβ”, which is given by a combination of f & λ 2, will be determined with 5-10% accuracy! T + single production at the LHC

35. T – pair production at the LHC SM BG: tt–production! (460 pb) - At the parton level Signal = (bqqA H )×2 1. Large missing momentum is expected in the signal event due to dark matter emissions. 2. Use the hemisphere analysis to reconstruct the top quark [S.M., Nojiri, Nomura (2007)]. 3. Since A H is undetectable, direct masurements of T – & A H are difficult.  M T2 variable! ~ Output ~ Distribution of M T2 ~ Strategy to reduce BG ~ T – decays into t + A H with 100 % branching ratio H1H1 H2H2

36. “MT2 variable” is a powerful tool to determine m T+ and m AH, which is defined by with being the postulated A H mass. Then, the end point of M T2 distribution is ~ Results (Point 2) ~ ~ Cut used in the analysis ~ ~ Discussion ~ T – pair production at the LHC 0100 200

37. End-point of the distribution of M T2 is determined by a combination of m T+, m AH, and the postulate mass. By looking at the position of the end-point with an appropriate value of, it is possible to get information of m AH & m T+ ! We have also checked that there is no contamination of the BG around End-point! ~ Results (Point 2) ~ ~ Conclusion ~ ~ Accuracy M T2 (max) determination ~ Using the distribution of the M T2 with, the upper end-point will be determined with 10-20 GeV accuracy (at Point 2)! T – pair production at the LHC With the use of quadratic function to estimate the end-point, using when. Theoretically, the end-point is 664 GeV.