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 Scenario2. Little Higgs signals at LHC & ILC3. Summary

～ Papers ～

～ Contents ～

1. Little Hierarchy Scenario

Kolde & Murayama, hep-ph/0003170 When the tuning < 10%,ΛSM < O(1)TeV (mh = 120 GeV)

Corrections to mh

If coefficient ci is O(1), ΛSM > O(10)TeV (mh = 120 GeV)

EW Observables

Barbieri & Strumia, 1998

E1 TeV 10 TeV???

Little Hierarchy Problem

Need some mechanism to control the Higgs mass!

1/11

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 mh

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

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 mh

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)

2/11

1. Little Hierarchy Scenario

W,Z WH,ZH

h

h h

h+

+ + ht

t

t

TQuadratically divergent corrections to mh are completely cancelled at 1-loop level!

Diagrammatic view point・ Global symmetry

imposed・ Collective sym. breaking

New particles introduced. (Little Higgs partners)

T

E1 TeV100 GeV 10 TeV

SM Nonlinear sigma modelConstructing models

3/11

1. Little Hierarchy Scenario

– F2/4 + LYukawa – V(H, F)

+ Kinetic terms of fermions

Lagrangian

No quadratically divergent |H|2 term at 1-loop level.

- - -

- - -

- - -

- - -

Triplet

H

H

H

T+

SU(5) SO(5)[SU(2)xU(1)]2 SU(2)xU(1)

4/11

1. Little Hierarchy Scenario

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.

H. C. Cheng, I. Los, J. High Energy Phys. (2003, 2003)

- - -

- - -

- - -

- - -

Triplet

H

H

H

T-parity

T+ T–

4/11

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–

Model Parameters of the LHT f : VEV of the SU(5) SO(5) breakingl2 : 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

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) breakingl2 : 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

Masses of new particles are proportional to f.

Masses of SM particles are proportional to v.

O (f)

O (v)

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)

Main annihilation mode: AH AH h WW or ZZ1. 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)

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

Wh2 of dark matter

5/11

1. Little Hierarchy Scenario

U-branch

Constraints from EWPM?

6/11

1. Little Hierarchy Scenario

Constraints from EWPM?

L-branch

6/11

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 l2 = 1.15 mh = 134 GeVmT+ = 834 GeVmT- = 664 GeV mAH = 81.9 GeVmWH = 368 GeVmZH = 369 GeV

Representative point

6/11

Constraints from EWPM?

L-branch

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, sothat colored new particlesare copiously produced! T+ & T- productions!

MadGraph/Event (Event generation)

PYTHIA (Hadronization)

PDG4 (Detector Response)

T+ pair production

Reconstructing twoT+-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

S.M., T. Moroi, K. Tobe, Phys.Rev.D78 (2008)

LHC is a hadron collider, sothat colored new particlesare 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

2. Littlest Higgs Signals at LHC & ILC

H1H2

Top partner productions

S.M., T. Moroi, K. Tobe, Phys.Rev.D78 (2008)

LHC is a hadron collider, sothat colored new particlesare copiously produced! T+ & T- productions!

MadGraph/Event (Event generation)

PYTHIA (Hadronization)

PDG4 (Detector Response)

Top reconstruction via hemisphere analysis. End points of MT2 depend on mT- & mAH

(within about 20 GeV accuracy.)

T- pair production

S.M., Nojiri, Nomura (2007)

0 100 200

7/11

2. Littlest Higgs Signals at LHC & ILC

f = 580 ± 33 GeV Cosmological connections

f (GeV)

l2

From T+ pair prod.From T+ single prod.From T- pair prod.

1s3s

8/11

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 thatheavy particles are producedwith clean environment. WH, ZH, AH productions!

Physsim (Event generation)

PYTHIA (Hadronization)

JSF Q-sim. (Detector Response)

ZHAH production @ 500 GeV

Energy distribution of h End points depend on mAH & mZH

mAH = 83.2 ± 13.3 GeV mZH = 366. ± 16. GeV f = 576. ± 25. GeV

s = 1.9 fb

9/11

500 fb-1

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 thatheavy particles are producedwith clean environment. WH, ZH, AH productions!

Physsim (Event generation)

PYTHIA (Hadronization)

JSF Q-sim. (Detector Response)

ZHAH production @ 1 TeV

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

s = １２１ fb

9/11

500 fb-1

2. Littlest Higgs Signals at LHC & ILC

Probability densitySimulation results + Higgs mass

Annihilation X-section<sv>(mAH, mh) WDMh2

Probability density ofthe dark matter relics WDMh2

WMAPPlanck

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

11/113. 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.

Back Up

The LH Lagrangian

Pseudo NG bosons Breaking directions

– F2/4 + LYukawa – V(H, F)

Non-linear s field

+ Kinetic terms of fermions

The LH Lagrangian

Gauge interactions [SU(2) x U(1)]2

– F2/4 + LYukawa – V(H, F)

Gauge couplings: g1, g’1, g2, g’2

The LH Lagrangian

– F2/4 + LYukawa – V(H, F)

Top Yukawa interactions

Top Yukawa: l1

U quark mass: l2

tL

tR

Particle contents in Gauge, Higgs, and top sectors

4 gauge bosons : B1, W1 , B2, W2

Σ= (24 – 10) pions :

SM gauges : A, W±, ZHeavy gauges : AH, WH

±, ZH

SM Higgs : h Triplet Higgs : Φ

After breakings

SM top quark : t , Heavy top : T = (U , UR)T

g1, g’1, g2, g’2

l1, l2

Parameters

f

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: 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)

[Asano, S.M, N.Okada, Y.Okada (2006)]

[J. Hubisz, P. Meade, Phys. Rev. D71, 035016 (2005) ]

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.

Wh2(mAH(f), mh)

Representative point for simulation study

(1) Observables (mw sinqW, Gl, WDMh2) vs. Model parameters (f, l2, mh)(2) 2mh

2/mt > O(0.1-1), where mt is the top-loop contribution to mh.

Considering EW precision & WMAP constraints

f = 580 GeV l2 = 1.15 mh = 134 GeVmAH = 81.9 GeVmWH = 368 GeVmZH = 369 GeVmT+ = 834 GeVmT- = 664 GeV mF = 440 GeV(mLH = 410 GeV)

[J. Hubisz, P. Meade, A. Noble, M. Perelstein, JHEP0601 (2006)]

T+ pair production at the LHC

SM BG: tt–production! (460 pb)-

At the parton levelSignal = bbqqlν

- - 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 = mW

2. There are 6-fold ambiguity in the reconstruction of T+-system.The combination to minimize

~ Output ~Distribution of

~ Strategy to reduce BG ~

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 ~

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 mT+ determination ~

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 levelSignal = bqlν

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

~ Strategy to reduce BG ~

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.

~ Results ~ ~ Cut used in the analysis ~

~ Discussion ~

T+ single production at the LHC

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 sin2β, will be determined with 10-20%. Parameter “sinβ”, which is given by a combinationof f & λ2, will be determined with 5-10% accuracy!

T+ single production at the LHC

T– pair production at the LHC

SM BG: tt–production! (460 pb)-

At the parton levelSignal = (bqqAH)×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 AH is undetectable, direct masurements of T– & AH are difficult. MT2 variable!

~ Output ~Distribution of MT2

~ Strategy to reduce BG ~

T– decays into t + AH with 100 % branching ratio

H1H2

“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

~ Results (Point 2) ~ ~ Cut used in the analysis ~

~ Discussion ~

T– pair production at the LHC

0 100 200

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!

~ Results (Point 2) ~

~ Conclusion ~~ Accuracy MT2

(max) determination ~

Using the distribution of the MT2 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, usingusing

when . Theoretically, the end-point is 664 GeV.