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Little Higgs Dark M atter & Its Collider Signals

Little Higgs Dark M atter & Its Collider Signals. Shigeki Matsumoto (University of Toyama ). ～ Papers ～. ・ 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.

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Little Higgs Dark M atter & Its Collider Signals

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  1. Little Higgs Dark Matter & Its Collider Signals Shigeki Matsumoto (University of Toyama) ～Papers ～ ・ 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. ～Contents ～ Little Higgs Scenario Little Higgs signals at LHC & ILC Summary

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

  3. 2/11 1. Little Hierarchy Scenario Little Higgs Scenario ・ Higgs boson = Pseudo NG boson ・ Explicit breaking = Collective symmetry breaking E Generation of mh Origin of mh = Interactions which break G. New Physics with G ( ⊃ Gauge group ), which is slightly broken 10 TeV Usual breaking: When the interaction “L1“ breaks the symmetry G, and generates mh, then (mh)2～ (ΛSM)2/(16π2) ～ (1 TeV)2 (1-loop diagrams) SSB: G  G’, where G’ ( ⊃ SU(2) x U(1)Y ) 1 TeV Electroweak breaking SU(2) x U(1)Y U(1)EM (Standard Model) 100 GeV

  4. 2/11 1. Little Hierarchy Scenario Little Higgs Scenario ・ Higgs boson = Pseudo NG boson ・ Explicit breaking = Collective symmetry breaking E Generation of mh Origin of mh = Interactions which break G. New Physics with G ( ⊃ Gauge group ), which is slightly broken 10 TeV Collective symmetry breaking: When the Interactions “L1“ & “L2“ (partially) break G, and the Higgs boson is “pseudo” NG boson when both interactions exist, (mh)2～ (ΛSM)2/(16π2)2 ～ (100 GeV)2 (2-loop diagrams) SSB: G  G’, where G’ ( ⊃ SU(2) x U(1)Y ) 1 TeV Electroweak breaking SU(2) x U(1)Y U(1)EM (Standard Model) 100 GeV

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

  6. 4/11 1. Little Hierarchy Scenario - - - H SU(5)  SO(5) [SU(2)xU(1)]2SU(2)xU(1) - - - H H - - - - - - T+ Triplet Lagrangian – F2/4 + LYukawa– V(H, F) + Kinetic terms of fermions No quadratically divergent |H|2 term at 1-loop level.

  7. 4/11 1. Little Hierarchy Scenario H. C. Cheng, I. Los, J. High Energy Phys. (2003, 2003) - - - H T-parity - H - - H - - - - - - T– T+ Triplet Constraints from EWPM Littlest Higgs model suffers from EWP constraints. ～ Imposition of the Z2-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.

  8. 4/11 1. Little Hierarchy Scenario H. C. Cheng, I. Los, J. High Energy Phys. (2003, 2003) - - - H T-parity - H - - H - - - - - - T– T+ Triplet Constraints from EWPM • Model Parameters of the LHT • f : VEV of the SU(5)  SO(5) breaking • l2: Mass of the top-partners (in units of f) • kx: Mass of the T-odd partner of “x”(in units of f) • Higgs mass mh is treated as a free parameter

  9. 4/11 1. Little Hierarchy Scenario H. C. Cheng, I. Los, J. High Energy Phys. (2003, 2003) Masses of new particles are proportional to f. O (f) O (v) Masses of SM particles are proportional to v. Constraints from EWPM • Model Parameters of the LHT • f : VEV of the SU(5)  SO(5) breaking • l2: Mass of the top-partners (in units of f) • kx: Mass of the T-odd partner of “x”(in units of f) • Higgs mass mh is treated as a free parameter

  10. 5/11 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) J. Hubisz, P. Meade, Phys. Rev. D71, 035016 (2005) Main annihilation mode:AH AH  h  WW or ZZ 1. AHAHh vertex is given by the SM gauge coupling. 2. Annihilation cross section depends on mAH & mh.  Relic abundance of AH: Wh2(mAH(f), mh) Little Higgs dark matter is singlet and spin 1 particle. The dark matter mass:80-400 GeV The Higgs mass:110-800 GeV Wh2 of dark matter Asano, S.M, N.Okada, Y.Okada (2006)

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

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

  13. 6/11 1. Little Hierarchy Scenario Constraints from EWPM? L-branch Representative point f = 580 GeVl2 = 1.15 mh = 134 GeVmT+ = 834 GeVmT-= 664 GeV mAH= 81.9 GeVmWH = 368 GeVmZH = 369 GeV 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.

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

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

  16. 7/11 2. Littlest Higgs Signals at LHC & ILC Top partner productions LHC is a hadron collider, sothat colored new particlesare copiously produced!  T+ & T- productions! MadGraph/Event (Event generation) PYTHIA (Hadronization) PDG4 (Detector Response) H1 H2 S.M., T. Moroi, K. Tobe, Phys.Rev.D78 (2008) T- pair production 200 100 0 Top reconstruction via hemisphere analysis. End points of MT2 depend on mT- & mAH (within about 20 GeV accuracy.) S.M., Nojiri, Nomura (2007)

  17. 8/11 2. Littlest Higgs Signals at LHC & ILC From T+ pair prod. From T+ single prod. From T- pair prod. l2 3s 1s f (GeV) f = 580 ± 33 GeV  Cosmological connections

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

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

  20. 10/11 2. Littlest Higgs Signals at LHC & ILC Probability density Simulation results + Higgs mass Planck WMAP ILC(1000) LHC Annihilation X-section <sv>(mAH, mh)  WDMh2 ILC(500) Probability density of the dark matter relics WDMh2 LHC: Abut 10% accuracy (Model-dependent analysis) ILC(500): Better than 10% accuracy (Model-independent analysis) ILC(1000): 2% accuracy!! (Model-independent analysis)

  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 s1/2 = 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 s1/2 = 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. – F2/4 + LYukawa– V(H, F) + Kinetic terms of fermions The LH Lagrangian Non-linear s field Pseudo NG bosons Breaking directions

  24. – F2/4 + LYukawa – V(H, F) The LH Lagrangian Gauge interactions [SU(2) x U(1)]2 Gauge couplings: g1, g’1, g2, g’2

  25. – F2/4 + LYukawa – V(H, F) The LH Lagrangian Top Yukawa interactions tR tL Top Yukawa: l1 U quark mass: l2

  26. 4 gauge bosons: B1, W1 , B2, W2 Σ= (24 – 10) pions : Particle contents in Gauge, Higgs, and top sectors SM gauges : A, W±, Z Heavy gauges : AH, WH±, ZH SM Higgs : h Triplet Higgs : Φ After breakings Parameters g1, g’1, g2, g’2 SM top quark : t , Heavy top : T = (U, UR)T l1, l2 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) [J. Hubisz, P. Meade, Phys. Rev. D71, 035016 (2005) ] Main annihilation mode:AH AH  h  WW or ZZ. 1. AHAHh vertex is given by the SM gauge coupling. 2. Annihilation cross section depends on mAH & mh.  Relic abundance of AH: Wh2(mAH(f), mh) Wh2(mAH(f), mh) When mh < 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. [Asano, S.M, N.Okada, Y.Okada (2006)]

  28. Representative point for simulation study Considering EW precision & WMAP constraints [J.Hubisz, P. Meade, A. Noble, M. Perelstein, JHEP0601 (2006)] (1) Observables (mwsinqW, Gl, WDMh2) vs. Model parameters (f, l2, mh) (2) 2mh2/mt > O(0.1-1), where mt is the top-loop contribution to mh. f = 580 GeVl2 = 1.15 mh = 134 GeVmAH = 81.9 GeVmWH = 368 GeVmZH = 369 GeVmT+ = 834 GeVmT-= 664 GeV mF = 440 GeV (mLH = 410 GeV)

  29. T+ pair production at the LHC - SM BG: tt–production! (460 pb) At the parton levelSignal = bbqqlν ~ Strategy to reduce BG ~ - - • Reconstruct Two T+-system: T+(lep) & T–(had) using the fact that the missing momentum • pT is due to the neutrino emission and • (pl + pν)2 = mW2. There are 6-fold ambiguity in the reconstruction of T+-system. • The combination to minimize ~ Output ~ Distribution of

  30. T+ pair production at the LHC ~ Cut used in the analysis ~ ~ Results ~ ~ Discussion ~ 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+.

  31. T+ pair production at the LHC ~ Accuracy of the mT+ determination ~ 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 ~ Conclusion ~ The difference between the position of the peak and the input value of mT+ is, typically, 10-20 GeV! ~ Results ~

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

  33. T+ single production at the LHC ~ Cut used in the analysis ~ ~ Results ~ ~ Discussion ~ 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 sin2βis large enough!  From the cross section, we will be able to determine sinβ.

  34. T+ single production at the LHC ~ Accuracy of sinβ determination ~ ~ Conclusion ~ 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. The cross section, which is proportional to sin2β, will be determined with 10-20%. Parameter “sinβ”, which is given by a combinationof f & λ2, will be determined with 5-10% accuracy! ~ Results (Point 2) ~

  35. T– pair production at the LHC H1 H2 T– decays into t + AH with 100 % branching ratio - SM BG: tt–production! (460 pb) At the parton levelSignal = (bqqAH)×2 ~ Strategy to reduce BG ~ 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 AH is undetectable, direct masurements of T– & AH are difficult.  MT2 variable! ~ Output ~ Distribution of MT2

  36. T– pair production at the LHC ~ Cut used in the analysis ~ ~ Results (Point 2) ~ 0 100 200 ~ Discussion ~ “MT2 variable” is a powerful tool to determine mT+ and mAH, which is defined by with being the postulated AH mass. Then, the end point of MT2 distribution is

  37. T– pair production at the LHC ~ Accuracy MT2(max) determination ~ ~ Conclusion ~ End-point of the distribution of MT2 is determined by a combination of mT+ , mAH, 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 mAH & mT+! We have also checked that there is no contamination of the BG around End-point! Using the distribution of the MT2 with , the upper end-point will be determined with 10-20 GeV accuracy (at Point 2)! ~ Results (Point 2) ~ With the use of quadratic function to estimate the end-point, using using when . Theoretically, the end-point is 664 GeV.

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