Measurements of the model parameter in the Littlest Higgs model with T-parity

Measurements of the model parameterin the Littlest Higgs model with T-parity

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Masaki Asano (ICRR, Univ. of Tokyo)

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.)

arXiv:0901.1081

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In LHT,SM

NEW

H

ΦHWH ZH AHqH lH

q lg W Z A

• Particles & these partners are same spin.• New particles get mass by VEV f ~ 1 TeV.• New gauge boson masses depend only on VEV f.

In this study, we estimate…• measurement accuracy of new heavy gauge boson masses• determination of VEV f & other model parameters• the dark matter relic abundance @ ILC.

Gauge boson Fermion Higgs

Littlest Higgs model with T-parity (LHT) is one of attractive models for TeV new physics. LHT could solve the little hierarchy problem, & contains a dark matter candidate.

Same Spin

• Introduction• What is the LHT?• How to measure the LHT at ILC?• Simulation results• Summary

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Plan

What is the LHT?

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mh2 = m0

2 + Λ2

Fine-tuning!

The SM is the successful model describing physics below ~ 100 GeV.

If we assume that

Hierarchy problem 　　 (related to quadratic divergence to the Higgs mass term)

1002 ⇔ 10000000000000002

But ...

SM is valid all the way up to the GUTs scale, Λ~1015 GeV,

EW scale higgs mass requires

mh2 = m0

2 + Λ2

No fine-tuning


If we require that


1002 ⇔ 10002

But ...

there are no fine-tuning for Higgs mass term,

No fine-tuning Λ ~ 1 TeV

Cut off scale

mh2 = m0

2 + Λ2

No fine-tuning


However…


1002 ⇔ 50002

But ...

LEP experiments require that the cut off scale is larger than 5 TeV!

Λ ~ 1 TeV

R.Barbieri and A.Strumia (’00)

LEP experiments

Cut off scaleLittle Hierarchy problem!

Still fine-tuning appear!

LHT solves little hierarchy problem! Even if Λ ~ 10TeV, there are still no fine-tuning!

Because of …

• Collective symmetry breaking (VEV f )

• T-parity

SM ⇔ SM, New ⇔ - New　　

(Heavy photon AH)

Wh h

g2 +WH

h h– g2

N. Arkani-Hamed, A. G. Cohen, H. Georgi (’01)

H. C. Cheng, I. Low (’03)

In order to avoid constraints from EWPM, Z2 symmetry (T-parity) are introduced.

• Higgs boson: A Pseudo NG boson of a global symmetry at some higher scale.• Explicit breaking of the global symmetry is specially arranged to cancel

quadratic divergent corrections to mh at 1-loop level.

Λ can be ~10 TeV without fine-tuning!(Little Higgs mechanism)

Lightest T-odd particle becomes dark matter candidate!

A, W±, Z, h

AH, WH±, ZH, Φ

t T

cancel

Particle contents

Gauge-Higgs sector

Top sector

Due to the cancelation of quadratic divergences, partners are introduced.In the fermion sector, only top partner is required to cancel the quadraticdivergences because other fermion Yukawa couplings are small.

In order to Implement the Little Higgs mechanism…

• The non-linear sigma model breaking SU(5)/SO(5).• The subgroup [SU(2)×U(1)]2 in SU(5) is gauged, which is broken down

to the SM gauge group by vev f.

Fermion sector

b…cancel

[Arkani-Hamed, Cohen, Katz and Nelson (2002)]

[SU(2)×U(1)]2 [SU(2)×U(1)]SM

[SU(5)] [SO(5)]VEV f ~ O(1) TeV

Global sym.Gauge sym.

A, W±, Z, h

AH, WH±, ZH, Φ

t T

cancel

Particle contents

Gauge-Higgs sector

Top sector

In order to Implement the Little Higgs Mechanism…

• The non-linear sigma model breaking SU(5)/SO(5).• The subgroup [SU(2)×U(1)]2 in SU(5) is gauged, which is broken down

to the SM gauge group by vev f.

Fermion sector

b…cancel

[Arkani-Hamed, Cohen, Katz and Nelson (2002)]

[SU(2)×U(1)]2 [SU(2)×U(1)]SM

[SU(5)] [SO(5)]VEV f ~ O(1) TeV

Global sym.Gauge sym.

T-parity T-parity

tH TH bH…T-parity

T-odd partners are introduced for each fermions.

In order to implement the T-parity…

T-even

T-odd

A, W±, Z, h

AH, WH±, ZH, Φ

t T

cancel

Gauge-Higgs sector

Top sector

Fermion sector

b…cancel

T-parity T-parity

tH TH bH…T-parity

Model parameters

O (f)

O (v)

Dark Matter

• New particle masses are ~ f

• f: VEV of SU(5) -> SO(5)• λ, κ: Yukawa coupling of new fermions• + SM parameters (mh, … )

How to measure the LHT at ILC?

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A, W±, Z, h

AH, WH±, ZH, Φ

t T

cancel

cancelGauge-Higgs sector

Top sector

Fermion sector

b…

tH TH bH…

O (f)

O (v)500 GeV

Dark Matter

• can be measured at LHC. • too heavy to produced at ILC.

• can be produced at ILC!• cannot measure masses at LHC• masses depend only on vev f!

Top sector

Gauge sector

We should measure the gauge sector in the LHT at ILC.

Q. H. Cao, C. R. Chen (07)

S. Matsumoto, T. Moroi, K. Tobe (08)and …….

In order to verify the LHT,we should measure the Little Higgs mechanism!

• can produce @ 500 GeV:

mAH + mZH < 500 GeV• cross section is small• It is difficult to produce

@ 500 GeV• cross section is large

In the gauge sector,

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O (f)

O (v)500 GeV

Dark Matter

1. Using e+e- AHZH @ 500 GeV ILC, Using e+e- WHWH @ 1 TeV ILC, we determine gauge boson masses.2. gauge boson mass vev f3. Cross section heavy lepton mass (eH, νH)4. Production angle of WH WH spin

e+e- AHZH

e+e- WHWH

Representative point of our simulation

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Relic abundance

Mode &Representative point

WMAP allowed region

Dark matter (AH)

M. A, S. Matsumoto, N. Okada,Y. Okada PhysRevD.75.063506

• Main DM annihilation mode: AHAH h WW(or ZZ)

• The relic density depends only on f & mh!

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!

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Relic abundance


WMAP allowed region

Which particle can produced at the ILC ? → It depends on VEV f .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

Dark matter (AH)

Fine-tuning Λ ~ 4π f > 10TeV

If f is larger than ~800GeV, the hierarchy problem appears again.

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Relic abundance


WMAP allowed region

e+e- AHZH

e+e- WHWH



New gauge bosons are too heavy mWH+mWH > 1TeV

mAH + mZH > 500GeV






Dark matter (AH)


e+e- AHZH

e+e- WHWH



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Relic abundance

WMAP allowed region



Mass spectrum

f 580 eH 410 ZH 369 WH 368 AH 82 Higgs 134

Point I (GeV)

Sample points satisfy all experimental & cosmological constraints.

New gauge bosons are too heavy mWH+mWH > 1TeV

mAH + mZH > 500GeV

Simulation results

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1.Event generation

MadGraph : for LHT processPhyssim : for SM process　　　　 - helicity amplitude calculation, gauge boson polarization effect　　　　 - phase space integration and generation of parton 4-momenta2.Hadronization

3.Detector simulation

PYTHIA - parton showering and hadronization

JSFQuickSimulator - create vertex-detector hits - smear charged-track parameters in central tracker - simulate calorimeter signals as from individual segments

@ 500 GeV ILC @ 1 TeV ILCe+e- AHZH AHAH h e+e- WHWH AHAHWW

• Integrated luminosity 500 fb-1

• Cross section 1.9 fb• Integrated luminosity 500 fb-1

• Cross section 121 fb

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Event

Masses of AH and ZH can be determined from edges of Higgs energy distribution.

@ 500 GeV ILC

• Large missing energy

• 2 jet in final state

e+e- AHZH AHAH h

mAH = 83.2 ± 13.3 GeV,

mZH = 366. ± 16. GeV f = 576. ± 25. GeV

Results

Energy distribution of reconstructed Higgs bosons after subtracting BG

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• Large missing energy• 4 jet in final state

Event

@ 1 TeV ILC

e+e- WHWH AHAHWW

Masses of AH and WH can be determined from edges of W energy distribution.

mAH = 81.58 ± 0.67 GeV,

mWH = 368.3 ± 0.63 GeV f = 580 ± 0.69 GeV

ResultsHigh accuracy !

Energy distribution of reconstructed W bosons after subtracting BG

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Production angle of WH±

Angular distribution of jets from W±

Other parametersCross section

Heavy lepton mass!

WH is spin 1 particle!

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!

For details, next Sasaki san’s talk

Cosmological impact

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Cosmological Impact

Simulation results : f + mh

DM annihilation cross section σv (f, mh)

• DM abundance will be determined with O(10%) accuracy @ 500 GeV.• DM abundance will be determined with O(1%) accuracy @ 1 TeV.• It is possible to consistency check of the model using PLANCK.

Probability densityDM relic abundance can be determined at ILC

Probability density of DM relics

Summary

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• Littest Higgs model with T-parity (LHT) is one of attractive models for physics beyond the SM.

• Important model parameter are determined by measurements of heavy gauge boson sector with good accuracy• @ 500 GeV ILC, using e+e- → AHZH .• @ 1 TeV ILC, using e+e- → WHWH.

• Heavy gauge boson masses can be determined by model-independent way.

• The property of dark matter also can be investigated at ILC.

• Results obtained from the collider experiments will be compared to those from astrophysical experiments(PLANCK) 28

Summary

Back up

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e-

e+ AH

AH

eH1. No signal

2. Vertex is suppressed

e+

e- γ, Z

WH

WH

1. Depend only on f

2. Large Cross section

II. LHT at the ILC

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Phase space integration and the generation of parton 4-momenta

helicity amplitudes (effect of gauge boson polarizations properly)

BASES/SPRING

HELAS library

TAUOLA final-state tau leptons (their polarizations correctly)

Detector Parameters

hits by charged particles at the vertex detector and track parameters at the central tracker are smeared according to their position resolutions

realistic simulation of cluster overlapping (calorimeter signals are simulated in individual segments)

Track-cluster matching is performed for the hit clusters at the calorimeter (in order to achieve the best energy flow measurements)

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Event selection

<Cut statistics and breakdown of efficiency>

WW++WW-- and ee++ee--WW++WW-- are effectively reduced by PTmiss cut.

ZZHHZZHH is negligible after W2 cut.

W+W- and W+W-Z remain after 2 cuts.

#event (efficiency)

All events are forced to 4 jets in final stateW

2 < 10 : 2 for W± reconstruction from jets

PTmiss > 50 GeV/c : Missing transverse momentum

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2 21

WW m

WW

m

WWw

mmmm

<Selection cut>

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1) Energy edges of W±

]2[1

]1[1]0[

4

1[], maxmin

par

EEErf

par

EEErfparparEF WW

Werror

432 ]6[]5[]4[]3[1[], WWWWWpoly EparEparEparEparparEF

1) Cheat Emin,Emax

Ffit1 = Ferror(par[1,2]) Get resolution(par[1,2])

2) Cheat Emin,Emax & Fix par[1,2]Ffit2 = Ferror x Fpoly(par[3~9])

Get shape(par[3~9])

3) Fix par[1~9]Ffit3 = Ferror(Emin,max) x Fpoly(Emin,max)

Get edge(Emin,Emax) Calculate mass(mAH,mWH)

<Fit function>

<Fit step>

xdttxErf

0

2)exp(2

)(

edgeEE :, maxmin

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SignalBackground


All events are forced to 2 jets in final state|cosθ|< 0.6 : 2 for angular dist. of Higgs100 < mh <140 GeV : reconstracted Higgs mass

Selection Cut

Event

e+e- AHZH AHAH hAHAH jj

we can calculate mass of AH and ZH by usingthe edge of the Higgs energy distribution.

@ 500 GeV ILC

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• Mass determination mAH = 82.5 ± 7.7 GeV, mZH = 370. ± 12. GeV true(81.85) true(368.2)

• f determination f = 581 ± 17. GeV true(580)

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.

@ 500 GeV ILC

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SignalBackground


All events are forced to 4 jets in final stateW

2 < 10 : 2 for W± reconstruction from jets

PTmiss > 50 GeV/c : Missing transverse momentum

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2 21

WW m

WW

m

WWw

mmmm

Selection Cut

WW++WW-- and ee++ee--WW++WW-- are effectively reduced by PTmiss cut.

ZZHHZZHH is negligible after W2 cut.

W+W- and W+W-Z remain after 2 cuts.

Event

@ 1 TeV ILCe+e- WHWH AHAHWW

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• Mass determination mAH = 81.85 ± 0.65 GeV, mWH = 368.1 ± 0.62 GeV true(81.85) true(368.2)

• f determination f = 580 ± 0.68 GeV true(580)

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.

High accuracy !

@ 1 TeV ILC

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e-

e+WH

+W+

AH

WH-

AH

W-

WH± candidates are reconstructed

as corn around 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

±.W+

W-

WH+WH

-

WH+ of generator

information

Production angle of WH±

This shape shows WH± spin as spin-1spin-1.

Angular distribution of jetsAngular distribution of jets

W+

j1

j2

<Rest frame of W+>

j1j2

W± helicity as longitudinallongitudinal mode.

Measurements of the model parameter in the Littlest Higgs model with T-parity

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