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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 ~ 1. 2. 3. Little Higgs Scenario Little Higgs signals at LHC & ILC Summary 1/11 1. Little Hierarchy Scenario Corrections to mh EW Observables 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 1 TeV ??? E 10 TeV Need some mechanism to control the Higgs mass! 1. Little Hierarchy Scenario Little Higgs Scenario ・ Higgs boson = Pseudo NG boson ・ Explicit breaking = Collective symmetry breaking E 10 TeV 1 TeV 100 GeV Generation of mh New Physics with G ( ⊃ Gauge group ), which is slightly broken SSB: G G’, where G’ ( ⊃ SU(2) x U(1)Y ) Electroweak breaking SU(2) x U(1)Y U(1)EM (Standard Model) Origin of mh = Interactions which break G. 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) 2/11 1. Little Hierarchy Scenario 2/11 Little Higgs Scenario ・ Higgs boson = Pseudo NG boson ・ Explicit breaking = Collective symmetry breaking E 10 TeV Generation of mh New Physics with G ( ⊃ Gauge group ), which is slightly broken 1 TeV SSB: G G’, where G’ ( ⊃ SU(2) x U(1)Y ) 100 GeV Electroweak breaking SU(2) x U(1)Y U(1)EM (Standard Model) Origin of mh = Interactions which break G. 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) 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 h t + h T + h t T Quadratically divergent corrections to mh are completely cancelled at 1-loop level! Constructing models SM Nonlinear sigma model E 100 GeV 1 TeV 10 TeV 4/11 1. Little Hierarchy Scenario - - - H - H H SU(5) SO(5) [SU(2)xU(1)]2 SU(2)xU(1) - - - - - T+Triplet Lagrangian – F2/4 + LYukawa – V(H, F) + Kinetic terms of fermions No quadratically divergent |H|2 term at 1-loop level. 4/11 1. Little Hierarchy Scenario H. C. Cheng, I. Los, J. High Energy Phys. (2003, 2003) T-parity T+ - - - H - - - H - - - H - - 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. T– 4/11 1. Little Hierarchy Scenario H. C. Cheng, I. Los, J. High Energy Phys. (2003, 2003) T-parity T+ - - - H - - - H - - - H - - 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 T– 1. Little Hierarchy Scenario H. C. Cheng, I. Los, J. High Energy Phys. (2003, 2003) O (f) O (v) Masses of new particles are proportional to f. 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 4/11 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. 1. The dark matter mass: 80-400 GeV Wh2 of dark matter 2. The Higgs mass: 110-800 GeV Asano, S.M, N.Okada, Y.Okada (2006) 5/11 1. Little Hierarchy Scenario Constraints from EWPM? U-branch 6/11 1. Little Hierarchy Scenario Constraints from EWPM? L-branch 6/11 1. Little Hierarchy Scenario Constraints from EWPM? L-branch f = 580 GeV l2 = 1.15 mh = 134 GeV mT+ = 834 GeV mT- = 664 GeV mAH = 81.9 GeV mWH = 368 GeV mZH = 369 GeV Representative point 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. 6/11 2. Littlest Higgs Signals at LHC & ILC Top partner productions LHC is a hadron collider, so that colored new particles are copiously produced! T+ & T- productions! S.M., T. Moroi, K. Tobe, Phys.Rev.D78 (2008) MadGraph/Event (Event generation) PYTHIA PDG4 (Hadronization) (Detector Response) T+ pair production Reconstructing two T+-system, T+(lep) & T–(had) Determination of T+ Mass (with ±20 GeV uncertainty) 7/11 2. Littlest Higgs Signals at LHC & ILC Top partner productions LHC is a hadron collider, so that colored new particles are copiously produced! T+ & T- productions! S.M., T. Moroi, K. Tobe, Phys.Rev.D78 (2008) MadGraph/Event (Event generation) PYTHIA PDG4 (Hadronization) (Detector Response) Single T+ production Reconstructing bW system # of the signal depends on NP! (σ determined with 20% accuracy.) 7/11 2. Littlest Higgs Signals at LHC & ILC Top partner productions LHC is a hadron collider, so that colored new particles are copiously produced! T+ & T- productions! MadGraph/Event (Event generation) PYTHIA S.M., T. Moroi, K. Tobe, Phys.Rev.D78 (2008) PDG4 (Hadronization) (Detector Response) T- pair production H1 H2 Top reconstruction via hemisphere analysis. S.M., Nojiri, Nomura (2007) 0 100 200 End points of MT2 depend on mT- & mAH (within about 20 GeV accuracy.) 7/11 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 8/11 2. Littlest Higgs Signals at LHC & ILC 9/11 Heavy gauge boson productions ILC is a e+e- collider, so that heavy particles are produced with clean environment. WH, ZH, AH productions! E. Asakawa, M. Asano, K. Fujii, T. Kusano, S. M., R. Sasaki, Y. Takubo, and H. Yamamoto, PRD79, 2009. Physsim (Event generation) PYTHIA (Hadronization) JSF Q-sim. (Detector Response) ZHAH production @ 500 GeV 500 fb-1 s = 1.9 fb Energy distribution of h End points depend on mAH & mZH mAH = 83.2 ± 13.3 GeV mZH = 366. ± 16. GeV f = 576. ± 25. GeV 2. Littlest Higgs Signals at LHC & ILC 9/11 Heavy gauge boson productions ILC is a e+e- collider, so that heavy particles are produced with clean environment. WH, ZH, AH productions! E. Asakawa, M. Asano, K. Fujii, T. Kusano, S. M., R. Sasaki, Y. Takubo, and H. Yamamoto, PRD79, 2009. Physsim (Event generation) PYTHIA (Hadronization) JSF Q-sim. (Detector Response) ZHAH production @ 1 TeV 500 fb-1 s = 121 fb Energy distribution of W End points depend on mAH & mZH mAH = 81.58 ± 0.67 GeV mWH = 368.3 ± 0.63 GeV f = 580± 0.69 GeV 10/11 2. Littlest Higgs Signals at LHC & ILC Probability density Simulation results + Higgs mass Planck WMAP Annihilation X-section <sv>(mAH, mh) WDMh2 Probability density of the dark matter relics ILC(1000) LHC ILC(500) WDMh2 LHC: Abut 10% accuracy (Model-dependent analysis) ILC(500): Better than 10% accuracy (Model-independent analysis) ILC(1000): 2% accuracy!! (Model-independent analysis) 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. 11/11 Back Up The LH Lagrangian – F2/4 + LYukawa – V(H, F) + Kinetic terms of fermions Non-linear s field Pseudo NG bosons Breaking directions The LH Lagrangian – F2/4 + LYukawa – V(H, F) Gauge interactions [SU(2) x U(1)]2 Gauge couplings: g1, g’1, g2, g’2 The LH Lagrangian – F2/4 + LYukawa – V(H, F) Top Yukawa interactions tR tL Top Yukawa: l1 U quark mass: l2 Particle contents in Gauge, Higgs, and top sectors 4 gauge bosons : B1, W1 , B2, W2 Σ= (24 – 10) pions : After breakings SM gauges : A, W±, Z Heavy gauges : AH, WH±, ZH SM Higgs : h Triplet Higgs : Φ Parameters SM top quark : t , Heavy top : T = (U , UR)T g1, g’1, g2, g’2 f l1, l2 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) [Asano, S.M, N.Okada, Y.Okada (2006)] 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. Representative point for simulation study Considering EW precision & WMAP constraints [J. Hubisz, P. Meade, A. Noble, M. Perelstein, JHEP0601 (2006)] (1) Observables (mw sinqW, 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 GeV l2 = 1.15 mh = 134 GeV mAH = 81.9 GeV mWH = 368 GeV mZH = 369 GeV mT+ = 834 GeV mT- = 664 GeV mF = 440 GeV (mLH = 410 GeV) T+ pair production at the LHC SM BG: tt–production! (460 pb) At the parton- level Signal = bbqqlν ~ Output ~ Distribution of ~ 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 T+ pair production at the LHC ~ Results ~ ~ Cut used in the analysis ~ ~ 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+. T+ pair production at the LHC ~ Accuracy of the mT+ determination ~ We consider the bin ~ Conclusion ~ 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 ~ The difference between the position of the peak and the input value of mT+ is, typically, 10-20 GeV! T+ single production at the LHC SM BG: tt & single t productions! At the parton level Signal = bqlν ~ Output ~ Distribution of ~ 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 reconstruct neutrino momenta & Reject events unless is small. Jet mass is also used to reduce the BG. T+ single production at the LHC ~ Results ~ ~ Cut used in the analysis ~ ~ 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 sin2β is large enough! From the cross section, we will be able to determine sinβ. T+ single production at the LHC ~ Accuracy of sinβ determination ~ 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 ~ The cross section, which is proportional to sin2β, will be determined with 10-20%. Parameter “sinβ”, which is given by a combination of f & λ2, will be determined with 5-10% accuracy! 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 level Signal = (bqqAH)×2 ~ Output ~ Distribution of MT2 ~ 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! T– pair production at the LHC ~ Results (Point 2) ~ 0 100 ~ Cut used in the analysis ~ 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 T– pair production at the LHC ~ Accuracy MT2(max) determination ~ 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! ~ Conclusion ~ 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.