contributions to ρ parameter from heavy gauge bosons in littlest higgs model with t-parity
DESCRIPTION
Contributions to ρ parameter from heavy gauge bosons in Littlest Higgs model with T-parity. The Graduate University for Advanced Studies. Masaki Asano. hep-ph/0602157. Collaborated with. Shigeki Matsumoto, Nobuchika Okada, Yasuhiro Okada. In the Standard Model. http://map.gsfc.nasa.gov/. - PowerPoint PPT PresentationTRANSCRIPT
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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.