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Contributions to ρ parameter from heavy gauge bosons

in Littlest Higgs model with T-parity

hep-ph/0602157

Masaki Asano

Shigeki Matsumoto, Nobuchika Okada, Yasuhiro Okada

The Graduate University for Advanced Studies

Collaborated with

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In the Standard Model

The existence have been established.cold dark matter candidate

WIMP Neutral Stable Massive

http://map.gsfc.nasa.gov/

Beyond Standard Model

Dark Matter Problem

Fine-tuning Problem

There is no WIMP in the Standard Model

Constrained by EW Precision Test R.Barbieri and A.Strumia (’00)

Little Hierarchy Problem

Once we consider the low-energy cutoff scenario,

There is no fine-tuning problem, if Λ ～ 1TeV

related to quadratic divergence to the Higgs mass term.

,δm2 ～ Λ2 :cutoff scalem02 +δm2

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In this model, there are allowed parameter region for WMAP.

Candidate of the beyond SM Supersymmetric Model with R-Parity ・・・

This model can solve the little hierarchy problem and has a dark matter candidate.

We improve the estimation of the constraints from EWPM, and show that the entire WMAP allowed region can be consistent with EWPM

Is this region consistent with electroweak precision measurements (EWPM) ?In this study

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Introduction Littlest Higgs Model with T-parity Allowed Region

WMAP ConstraintsElectroweak Precision Measurements

Result Summary

lan

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In the Littlest Higgs Model with T-parity

Little Higgs Mechanism• Higgs is the pseudo Nambu-Goldstone boson

• Quadratic divergences to the Higgs mass term completely vanish at one-loop level.

Wh h

g2 +WH

h h– g2

e.g.

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

T-parityTo avoid constraints from EWPM, T-parity has been introduced.

Lightest T-odd particle becomes a dark matter candidate.

SM particles T-even New particles T-odd

H. C. Cheng, I. Low (’03)

ZH

SM particle

Little Hierarchy Problem is solved by

Dark Matter Probrem is solved by

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ittlest Higgs Model with T-parity

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LHT is based on a non-linear sigma model describing SU(5)/SO(5) symmetry breaking.

UEM(1)

SO(5) SU(2)×U(1)⊃

gauge group

〈 h 〉

SU(5) [SU(2)×U(1)]⊃ 2

absorbed H, ΦH

Littlest Higgs Model with T-parity

VEV14 NG bosons

f ~ TeV

non-linear σ field

I. Low(’04)

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Particles

fermion sector

SM gauge bosonHeavy gauge boson mWH f ∝

gauge sector [SU(2)×U(1)]1+ [SU(2)×U(1)]2

additional singlet UL1 ,UL2 ,UR1 and UR2 are also introduced.

SM fermion Heavy fermion

top sector

Higgs sectorHiggs doubletTriplet Higgs

HΦH mφH f ∝

mψH f ∝Vector like mass term

T-odd, T-even

Yukawa of SM-top and additional singlets

Yukawa of heavy fermion

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new heavy T-even top new heavy T-odd topSM top

If t-T+ mixing large, R becomes large.: R indicate the amplitude of t-T+ mixing.

Yukawa of SM-top and additional singlets

U1 U2uSM

U+ U-uSM

tSM T+ T-

top sector

mT+ f ∝ mT- f ∝

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J.Hubisz and P.Meade (‘05) Relic abundance of dark matter

Lightest T-odd particle: AH

0.1

1

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(TeV

)W, Z

hAH

WH , ZH

Φ

Spectrum

T-even T-odd

Lightest T-oddmain

~g’2/v

~mW2/v

AH annihilates into W, Z

Each branch can be expressed as a function of f & mh

U-branch

L-branch

Allowed region for WMAP at 2σlevelRelic density depends only on f & mh

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llowed region

for Electroweak precision constraints

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main contributions to S, T ( Δρ), U parameters are ∝Top-sector

J. Hubisz, P. Meade, A. Noble and M. Perelstein JHEP01(2006)135

Constraints from EWPM

earlier study

Heavy gauge boson contributions are also important.

Top-sector contributions

∝ R2 (indicate the amplitude of t-T+ mixing ),

If t-T+ mixing is suppressed, this contribution becomes small.

But our , heavy gauge contribution is .

says

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top-sector

SM couplings will receive correction.We should calculate the SM top loops as well as T+ loops.

There is the

The negative contribution from a heavy Higgs can be partially cancelled by the positive contribution from the T+.

Higgs

When t-T+ mixing is suppressed ( is small), this is small

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heavy gauge boson contribution

This contribution arises from the mass splitting of the WH.

we have used for check of the gauge invariance of our result.

WH mass splitting appears from (v/f)4 order in the Σ expansion.

New result

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Expansion of the non-linear sigma field

we should derive The mixing term between gauge bosons and derivatives of

NG bosons from the kinetic term.

Due to the EW symmetry breaking, kinetic terms of NG fields are not canonically normalized. Complex of higher order expansion

Redefinition of these NG fields

Procedure of the gauge fixing

Finally, we can determine gauge fixing functions to cancel the mixing term.

mixing term

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TVH1

TVH2

TVH3

TVH4

TVH5

TVH6

TVH1

TVH2

TVH3

TVH4

TVH5

TVH6

Up to the order of (v/f)4, the logarithmic divergent correction is completely canceled! (gauge invariant)

Heavy gauge contribution is

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esult

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Allowed region

Contour plot of constraint for EWPM

Entire WMAP allowed region can be consistent with the EWPM.

L

U

Large fmh is large

WMAP

: If t-T+ mixing large, R becomes large.

Allowed region

at each point,mh is determined to satisfy WMAP

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Entire WMAP allowed region can be consistent with the EWPM.

ummary

Littlest Higgs model with T-parity can solve the little hierarchy problem and has a dark matter candidate.

Once we consider WMAP allowed region, f & mAH is determined by the mh (in each branch).

Large mh region is allowed.