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Measurements of Model Parameters in the Littlest Higgs Model with T-parity in ILC

Investigating the Littlest Higgs model with T-parity, a TeV new physics solution addressing the little hierarchy problem and dark matter. Study focuses on measuring MWH, MZH, MAH and determining VEV.f & other parameters, targeting dark matter relic abundance at ILC. Introduction to LHT, its measurement at ILC, simulation results, and summary are provided. Discusses the hierarchy problem, dark matter, and potential new physics solutions at different energy scales.

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Measurements of Model Parameters in the Littlest Higgs Model with T-parity in ILC

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  1. Measurements of Model Parameters in the Littlest Higgs Model with T-parity in ILC PRD79, 075013  Masaki Asano (Tohoku Univ.) Collaborator: E. Asakawa (Meiji-gakuin Univ.), K. Fujii (KEK), T. Kusano (Tohoku Univ.), S. Matsumoto(Univ. of Toyama), R. Sasaki (Tohoku Univ.), Y. Takubo (Tohoku Univ.), H. Yamamoto (Tohoku Univ.)

  2. Littlest Higgs model with T-parity (LHT) is one of the possibility for TeV new physics.LHT could solve the little hierarchy problem, & contains a dark matter candidate. • SM particles & their partners have same spin. • M_(New particles) ~ f ~ 1 TeV. g W Z A, q l, H SM qH lH, ΦH Partner WH ZH AH, In this study, we estimate… • Measurement accuracy of MWH, MZH, MAH. • Determination of VEV f& other model parameters • Dark matter relic abundance @ ILC.

  3. Introduction • What is the LHT? • How to measure the LHT at ILC? • Simulation results • Summary and discussion Plan

  4. E Planck scale 1019GeV SM is the successful model describing physics below ~ 100 GeV. ～ ～ But… • Hierarchy Problem • Dark Matter If we assume that SM is valid all the way up to the planck scale, there are several problems. EW scale 100GeV • Hierarchy Problem SM • Dark Matter

  5. E Planck scale 1019GeV SM is the successful model describing physics below ~ 100 GeV. ～ ～ But… new physics If we assume that SM is valid all the way up to the planck scale, there are several problems. 1TeV EW scale 100GeV • Hierarchy Problem SM • Dark Matter From naïve disscussion about these problem, mh2 = m02+ Λ2 ~ 0.1 HP: DM: It seems that they suggest the existence of new physics at TeV scale & the new physics solve these problem. Such new physics models have been proposed: SUSY, Little Higgs , …

  6. Hierarchy Problem Fine-tuning! mh2 = + m02 Λ2 correction related to quadratic divergence to the Higgs boson mass term. E Planck scale 1019GeV ～ ～ EW scale 100GeV

  7. Hierarchy Problem mh2 = + m02 Λ2 correction related to quadratic divergence to the Higgs boson mass term. E solution Planck scale 1019GeV • low energy cut off scenario ～ ～ If Λ ～ 1 TeV, there are no fine-tuning! New phys scale 1TeV EW scale 100GeV

  8. Hierarchy Problem mh2 = + m02 Λ2 correction related to quadratic divergence to the Higgs boson mass term. E solution Planck scale 1019GeV • low energy cut off scenario ～ ～ If Λ ～ 1 TeV, there are no fine-tuning! But… LEP experiments require New phys scale 5TeV … R.Barbieri and A.Strumia (’00) 1TeV Little hierarchy problem ! EW scale 100GeV

  9. Little Hierarchy Problem mh2 = + m02 Λ2 correction E solution Planck scale 1019GeV ～ ～ Little Higgs 10TeV • Little Higgs model Λ~4πf Even if Λ ～ 10 TeV, there are still no fine-tuning! 5TeV Global sym. breaking Because of … VEV f 1TeV Little Higgs mechanism • collective symmetry breaking (VEV f ) • induces cancelation EW scale 100GeV

  10. Little Higgs model with T-parity is solution of little hierarchy problem! Even if Λ ~ 10TeV, there are still no fine-tuning, • Little Higgs mechanism Collective symmetry breaking (VEV f ) N. Arkani-Hamed, A. G. Cohen, H. Georgi (’01) • Higgs boson is regarded as Pseudo NG bosonof a global symmetry at some higher scale. • Explicit breaking of the global symmetry is specially arranged to cancel quadratic divergent corrections to mhat 1-loop level by new gauge bosons and fermions. W WH h h + h h – g2 g2 Λ can be ~10 TeV without fine-tuning! • T-parity H. C. Cheng, I. Low (’03) In order to avoid constraints from EWPM, Z2 symmetry called T-parity are introduced. SM SM SM SM ⇔ SM, New ⇔ - New SM ZH (Heavy photon AH) The model contains dark matter candidate!

  11. What is the LHT?

  12. In order to Implement the Little Higgs Mechanism… gauge group • Littlest Higgs model with T-parity is based on the non-linear sigma model breakingSU(5)/SO(5)symmetry breaking. • The subgroup [SU(2)×U(1)]2in SU(5) isgauged, which is broken down to the SM gauge group by vev f. VEV [SU(2)×U(1)]2 f ~ O(1) TeV [SU(2)×U(1)]SM 〈 h 〉 Uem(1) [Arkani-Hamed, Cohen, Katz and Nelson (2002)] gauge couplings (SU(2)) Kinetic term of non-linear sigma model …, The global sym. is explicitly broken by gauge &Yukawa coupling but only collectively: Each of the gauged subgroup [SU(2)×U(1)]icommute with different subgroup of G that acts on the Higgs field non-linearly. Thus, if any one of gauge couplings of [SU(2)×U(1)]i is zero, the Higgs boson is an exact Nambu-Goldstone boson due to the restoration of the global symmetry. Since there are one gauge coupling in 1-loop diagram, the quadratic divergence is vanished in 1-loop level! W WH h h + h h – g2 g2

  13. In order to Implement the Little Higgs Mechanism… gauge group • Littlest Higgs model with T-parity is based on the non-linear sigma model breakingSU(5)/SO(5)symmetry breaking. • The subgroup [SU(2)×U(1)]2in SU(5) isgauged, which is broken down to the SM gauge group by vev f. VEV [SU(2)×U(1)]2 f ~ O(1) TeV [SU(2)×U(1)]SM 〈 h 〉 Uem(1) [Arkani-Hamed, Cohen, Katz and Nelson (2002)] Particle contents Cancel! t h Fermion sector Gauge-Higgs sector cancel A, W±, Z, h t T b… t + h cancel T AH, WH±, ZH, Φ T Top sector h + Due to the cancelation of quadratic divergences, partners are introduced. In the fermion sector, only top partner is required to cancel the quadratic divergences because other fermion Yukawa couplings are small.

  14. In order to Implement the Little Higgs Mechanism… gauge group • Littlest Higgs model with T-parity is based on the non-linear sigma model breakingSU(5)/SO(5)symmetry breaking. • The subgroup [SU(2)×U(1)]2in SU(5) isgauged, which is broken down to the SM gauge group by vev f. VEV [SU(2)×U(1)]2 f ~ O(1) TeV [SU(2)×U(1)]SM 〈 h 〉 Uem(1) [Arkani-Hamed, Cohen, Katz and Nelson (2002)] Particle contents Cancel! t h Fermion sector Gauge-Higgs sector cancel A, W±, Z, h t T b… t + h cancel T-parity T-parity T-parity T AH, WH±, ZH, Φ tH TH bH… T Top sector h + [SU(2)×U(1)]1 [SU(2)×U(1)]2 In order to implement the T-parity… T-odd partners are introduced for each fermions.

  15. How to measure the LHT at ILC?

  16. In order to verify the Little Higgs model, we should measure the Little Higgs mechanism! O (f) Gauge-Higgs sector Top sector cancel A, W±, Z, h t T b… O (v) 500 GeV cancel AH, WH±, ZH, Φ tHTH bH… Dark Matter mass spectrum

  17. In order to verify the Little Higgs model, we should measure the Little Higgs mechanism! O (f) Gauge-Higgs sector Top sector cancel A, W±, Z, h t T b… O (v) 500 GeV cancel AH, WH±, ZH, Φ tHTH bH… Dark Matter mass spectrum 1. Top sector • can be measured at LHC. • too heavy to produced at ILC. S. Matsumoto, T. Moroi, K. Tobe (08) and …….

  18. In order to verify the Little Higgs model, we should measure the Little Higgs mechanism! O (f) Gauge-Higgs sector Top sector cancel A, W±, Z, h t T b… O (v) 500 GeV cancel AH, WH±, ZH, Φ tHTH bH… Dark Matter mass spectrum 1. Top sector • can be measured at LHC. • too heavy to produced at ILC. S. Matsumoto, T. Moroi, K. Tobe (08) and ……. 2. Gauge sector Q. H. Cao, C. R. Chen (07) • can be produced at ILC! • cannot measure masses at LHC • masses depend only on vev f! We should measure the gauge sector in the LHT at ILC.

  19. O (f) In the gauge sector, Which mode can be measured at the ILC ? O (v) 500 GeV e- AH • can produce easily • mAH + mAH< 500 GeV • No signal eH e+ Dark Matter AH 19 • can produce @ 500 GeV: • mAH + mZH < 500 GeV • cross section is small AH e- eH e+ ZH • ~1 fb e- WH γ, Z • It is difficult to produce @ 500 GeV • cross section is large e+ WH ~ 100 fb

  20. Representative point of our simulation

  21. １ ∝ Dark matter annihilation Relic density ~g’2/v • Main DM annihilation mode: • AHAH h  WW(or ZZ) • The relic density depends only on f & mh! ~mW2/v • M. A, S. Matsumoto, N. Okada,Y. Okada PhysRevD.75.063506 Relic abundance Dark matter (AH) Shaded area is WMAP allowed region . DM abundance is determined by the Higgs mass & vev f. At this WMAP allowed region, the model also satisfys other experimental constraints! WMAP allowed region

  22. Mode &Representative point Which particle can produced at the ILC ? → It depends on VEV f . Because heavy gauge boson massed depend only on vev f. e+e- AHZH If f is larger than ~800GeV, the hierarchy problem appears again. e+e- WHWH • M. A, S. Matsumoto, N. Okada,Y. Okada PhysRevD.75.063506 Relic abundance Dark matter (AH) Shaded area is WMAP allowed region . DM abundance is determined by the Higgs mass & vev f. At this WMAP allowed region, the model also satisfys other experimental constraints! Fine-tuning Λ ~ 4π f > 10TeV WMAP allowed region

  23. Mode &Representative point Which particle can produced at the ILC ? → It depends on VEV f . Because heavy gauge boson massed depend only on vev f. e+e- AHZH e+e- WHWH • M. A, S. Matsumoto, N. Okada,Y. Okada PhysRevD.75.063506 Relic abundance Dark matter (AH) Shaded area is WMAP allowed region . DM abundance is determined by the Higgs mass & vev f. At this WMAP allowed region, the model also satisfys other experimental constraints! Fine-tuning Λ ~ 4π f > 10TeV New gauge bosons are too heavy mWH+mWH > 1TeV mAH + mZH > 500GeV WMAP allowed region

  24. Mode &Representative point Which particle can produced at the ILC ? → It depends on VEV f . Because heavy gauge boson massed depend only on vev f. e+e- AHZH e+e- WHWH • M. A, S. Matsumoto, N. Okada,Y. Okada PhysRevD.75.063506 Relic abundance Mass spectrum f 580 eH 410 ZH 369 WH 368 AH 82 Higgs 134 Fine-tuning Λ ~ 4π f > 10TeV New gauge bosons are too heavy mWH+mWH > 1TeV Point I (GeV) mAH + mZH > 500GeV WMAP allowed region Sample points satisfy all experimental & cosmological constraints.

  25. Simulation results

  26. 1.Event generation MadGraph : for LHT process Physsim : for SM process - helicity amplitude calculation, gauge boson polarization effect - phase space integration and generationof parton 4-momenta • Integrated luminosity 500 fb-1 • Cross section 1.05 fb 2.Hadronization PYTHIA - parton showering and hadronization 3.Detector simulation JSFQuickSimulator - create vertex-detector hits - smear charged-track parameters in central tracker - simulate calorimeter signals as from individual segments @ 500 GeV ILC @ 1 TeV ILC e+e- AHZH  AHAH h e+e- WHWH  AHAHWW • Integrated luminosity 500 fb-1 • Cross section 120 fb

  27. Event @ 500 GeV ILC e+e-AHZH AHAH hAHAH jj • Large missing energy • 2 jet in final state AHAH bb as the signal event

  28. Event @ 500 GeV ILC Signal e+e-AHZH AHAH hAHAH jj Background • Large missing energy • 2 jet in final state AHAH bb as the signal event

  29. Event @ 500 GeV ILC Signal e+e-AHZH AHAH hAHAH jj Background • Large missing energy • 2 jet in final state AHAH bb as the signal event Selection Cut Ptmiss>80(GeV) 100(GeV)<mh<140(GeV) P_t^miss > 80GeV :missing transverse momentum 100 < mh <140 GeV : reconstracted Higgs mass we can calculate mass of AH and ZH by using the edge of the Higgs energy distribution.

  30. @ 500 GeV ILC <Higgs energy distribution> An energy distribution of Higgs from ZHAH after subtraction of the backgrounds, whose number of events was estimated by independent background samples. The distribution is fitted by a polynomial function convoluted with an error function. • mAH= 83.2 ±13.3 GeV, mZH = 366. ±16. GeV Results • f = 576. ±25. GeV 4.3 %

  31. Event @ 1 TeV ILC e+e- WHWH  AHAHWW • Large missing energy • 4 jet in final state AHAH qqqq as the signal event

  32. Event @ 1 TeV ILC e+e- WHWH  AHAHWW Signal Background • Large missing energy • 4 jet in final state Selection Cut Ptmiss>84(GeV) E_W < 500GeV : energy of W cW2 < 26 : c2 for W± reconstruction from jets PTmiss > 84 GeV/c : Missing transverse momentum cW2 < 26

  33. @ 1 TeV ILC <Wenergy distribution> An energy distribution of W’s from WHWH after subtraction of the backgrounds, whose number of events was estimated by independent background samples. The distribution is fitted by a polynomial function convoluted with an error function. • mAH= 81.58 ±0.67 GeV, mWH = 368.3 ±0.63 GeV Results High accuracy ! • f = 580 ±0.69 GeV 0.1 %

  34. Other parameters Cross section Heavy lepton mass! @ 500 GeV ILC @ 1 TeV ILC Heavy lepton masses depend on Yukawa k_l. k_l can be determined with 22.1% accuracy at 500 GeV, 0.5% accuracy at 1 TeV.

  35. Other parameters Cross section Heavy lepton mass! Production angle of WH± WHis spin 1 particle! Angular distribution of jets from W± The dominance of the longitudinal mode! The coupling arises from EWSB!

  36. j1 W+ q W+ WH- j2 WH+ W+ W- WH+ e+ AH AH e- WH- W- Distribution of production angles of WH+ Production angle of WH± WH± candidates are reconstructed as cornaround W±. If WH+ and WH- are assumed as back-to-back, there are 2 solutions for WH± candidates. In this mode, however , 2 solutions should be close to true WH±. j1 j2 This shape shows WH± spin as spin-1. q Angular distribution of jets Angular distribution of jets <Rest frame of W+> Angular distribution of jets in the helicity-frame of the W± carries information on the polarization of the W±. W±helicity as longitudinal mode.

  37. Other parameters Cross section Heavy lepton mass! Production angle of WH± WHis spin 1 particle! 100% RH polarization Angular distribution of jets from W± The dominance of the longitudinal mode! The coupling arises from EWSB! Beam polarization WH has SU(2)L charge, but no U(1)Y charge!

  38. Cosmological impact

  39. Cosmological Impact Connection between ILC & cosmology The DM relic density depends only on f & mh in this model. Probability density Simulation results : f, +mh DM annihilation cross section σv (f, mh) Probability density of DM relics • DM abundance will be determined toO(10%) and O(1%) levels @ 500 GeV and 1 TeV. • These accuracies are compatible to those of current & future experiments.

  40. Summary & Discussion

  41. Summary • Littest Higgs model with T-parity (LHT) is one of attractive models for physics beyond the SM. • Heavy gauge boson masses are determined with good accuracy in a model-independent way • @ 500 GeV ILC, using e+e- → AHZH. • @ 1 TeV ILC, using e+e- → WHWH. • Once the model are determined, we also obtain the VEV f & other model parameters. • Results obtained from the collider experiments will be compared to those from astrophysical experiments(PLANCK) ILC will play essential role to understand the thermal history of the Universe.

  42. http://map.gsfc.nasa.gov/ Dark Matter WIMP One of the most plausible candidate: (Weakly Interacting Massive Particles) WIMP candidates spin model • ηI 0 Inert Doublet • χ0 ½ SUSY • AH 1 Littlest Higgs … The spin of DM candidate comes in a variety of types. How to distinguish the DM nature in different new physics models? X0 We use X- W- W+ X+ X0 LH Dark matter Charged new particle In order to measure mass & spin of new particles at ILC.

  43. For example, X0 • SUSY X- W- X0: Neutralino spin ½ W+ X+ X+: Chargino spin ½ X0

  44. For example, X0 • SUSY X- W- X0: Neutralino spin ½ W+ X+ X+: Chargino spin ½ X0 Since WIMP DM is interact SM particle weakly, the DM will interact W+- gauge boson. To conserve the charge and Z2-symmetry, the interaction also includes Charged New Particles. W+ X0

  45. For example, X0 • SUSY X- W- X0: Neutralino spin ½ W+ X+ X+: Chargino spin ½ X0 Since WIMP DM is interact SM particle weakly, the DM will interact W+- gauge boson. To conserve the charge and Z2-symmetry, the interaction also includes Charged New Particles. W+ X+ X0

  46. For example, X0 • SUSY X- W- X0: Neutralino spin ½ W+ X+ X+: Chargino spin ½ X0 Since WIMP DM is interact SM particle weakly, the DM will interact W+- gauge boson. To conserve the charge and Z2-symmetry, the interaction also includes Charged New Particles. W+ X+ X0 Other WIMP scenario will also have this mode!

  47. X0 • SUSY X- W- X0: Neutralino spin ½ W+ X+ X+: Chargino spin ½ X0 AH • Littlest Higgs with T-parity WH- W- AH: Heavy Photon spin 1 W+ WH+: Heavy W boson spin 1 WH+ AH ηＩ • Inert Doublet model η- W- ηＩ: Neutral Inert Higgs spin 0 W+ η+ η+: Charged Inert Higgs spin 0 ηＩ

  48. X0 X- From this mode, W- W+ we will measure X+ X0 masses mass relation between X0 & X+- will confirm the model. Angular distribution of charged new particles X± X+- spin Angular distribution of jets from W± polarization The decay vertex structure Inert Higgs We will study this mode for three models in order to distinguish the dark matter nature.

  49. Angular distribution in three models @ Inert Doublet SUSY Little Higgs N. Okada Since, angular distribution is different from each models, this is the powerful probe of the dark matter nature. Keisuke Fujii (KEK)   Katsumasa Ikematsu (KEK) Rei Sasaki (Tohoku U.) Taikan  Suehara (ICEPP, U. of Tokyo) Yosuke Takubo (Tohoku U.)  Ryo Yonamine (Sokendai) R.S. Hundi (U. of Hawaii) Hideo Itoh (KEK) Shigeki Matsumoto (Toyama U.) Nobuchika Okada (KEK) We need full simulation for each models in next step . Generic WIMP study!

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