1. 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/
Collaborated with
Shigeki Matsumoto, Nobuchika Okada, Yasuhiro Okada

2. In the Standard Model Dark Matter Problem WIMP Beyond Standard Model
Dark Matter Problem
The existence have been established.
cold dark matter candidate
Neutral
Stable
Massive
WIMP
There is no WIMP in the Standard Model
Beyond Standard Model
Fine-tuning Problem
related to quadratic divergence to the Higgs mass term.
m02 +δm2
,δm2～Λ2 :cutoff scale
Once we consider the low-energy cutoff scenario,
There is no fine-tuning problem, if Λ～1TeV
Little Hierarchy Problem
Constrained by EW Precision Test 
R.Barbieri and A.Strumia (’00)

3. The Littlest Higgs Model with T-parity is a new possibility
Candidate of the beyond SM
Supersymmetric Model with R-Parity
・・・
The Littlest Higgs Model with T-parity is a new possibility
for physics at TeV scale
This model can solve the little hierarchy problem and has a dark matter candidate.
In this model, there are allowed parameter region for WMAP.
Is this region consistent with electroweak precision measurements (EWPM) ?
In this study
We improve the estimation of the constraints from EWPM, and show that the entire WMAP allowed region can be consistent with EWPM

4. P lan Introduction Littlest Higgs Model with T-parity Allowed Region
WMAP Constraints
Electroweak Precision Measurements
Result
Summary

5. Little Higgs Mechanism
In the Littlest Higgs Model with T-parity
Little Hierarchy Problem is solved by
Little Higgs Mechanism
Higgs is the pseudo Nambu-Goldstone boson
Quadratic divergences to the
Higgs mass term completely
vanish at one-loop level. W h g2 + WH
– g2
e.g.
N. Arkani-Hamed, A. G. Cohen, H. Georgi (’01)
T-parity
To 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
Dark Matter Probrem is solved by

6. L
ittlest Higgs Model with T-parity

7. Littlest Higgs Model with T-parity
I. Low(’04)
LHT is based on a non-linear sigma model describing SU(5)/SO(5) symmetry breaking.
gauge group
VEV
14 NG bosons
SU(5) ⊃ [SU(2)×U(1)]2
f ~ TeV
SO(5) ⊃ SU(2)×U(1)
〈 h 〉
H, ΦH
absorbed
UEM(1)
non-linear σ field

8. Particles Higgs sector gauge sector SM gauge boson fermion sector
Higgs doublet ΦH
Triplet Higgs
mφH∝ f
gauge sector
Yukawa of SM-top and additional singlets
Yukawa of heavy fermion
[SU(2)×U(1)]1+ [SU(2)×U(1)]2
SM gauge boson
Heavy gauge boson
mWH∝ f
fermion sector
SM fermion
Heavy fermion
mψH∝ f
top sector
Vector like mass term
additional singlet UL1 ,UL2 ,UR1 and UR2 are also introduced.
T-odd, T-even

9. U1 U2 uSM U+ U- tSM T+ T- top sector
Yukawa of SM-top and additional singlets
SM top
new heavy T-even top
new heavy T-odd top
mT+∝ f
mT-∝ f
: R indicate the amplitude of t-T+ mixing.
If t-T+ mixing  large, R becomes large.

10. Relic abundance of dark matter
J.Hubisz and P.Meade (‘05)
Lightest T-odd particle: AH
0.1 1 10
(TeV)
W, Z h AH
WH , ZH Φ
Spectrum
T-even
T-odd
Lightest T-odd
U-branch
L-branch
Allowed region for WMAP at 2σlevel
Relic density depends only on f & mh
main
~g’2/v
~mW2/v
AH annihilates into W, Z
Each branch can be expressed as a function of f & mh

11. for Electroweak precision constraints
llowed region
for Electroweak precision constraints

12. new result negligible Constraints from EWPM earlier study says
J. Hubisz, P. Meade, A. Noble and M. Perelstein JHEP01(2006)135
main contributions to S, T (∝ Δρ), U parameters are Top-sector
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
new result
negligible

13. Large Higgs mass is allowed
top-sector
There is the
SM couplings will receive correction.
We should calculate the SM top loops as well as T+ loops.
Higgs
The negative contribution from a heavy Higgs can be partially cancelled by the positive contribution from the T+.
Large Higgs mass is allowed
When t-T+ mixing is suppressed ( is small), this is small

14. heavy gauge boson contribution
New result
heavy gauge boson contribution
WH mass splitting appears from (v/f)4 order in the Σ expansion.
This contribution arises from the mass splitting of the WH.
we have used for check of the gauge invariance of our result.

15. difficulty Procedure of the gauge fixing
mixing term
Procedure of the gauge fixing
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
difficulty
Finally, we can determine gauge fixing functions to cancel the mixing term.

16. sum up negligible Heavy gauge contribution is
TVH1
TVH2
TVH3
TVH4
TVH5
TVH6
TVH1
TVH2
TVH3
TVH4
TVH5
TVH6
sum up
Up to the order of (v/f)4, the logarithmic divergent correction is completely canceled! (gauge invariant)
negligible
Heavy gauge contribution is

17. R
esult

18. U Contour plot of constraint for EWPM
mh is large
WMAP
at each point,
mh is determined to satisfy WMAP
Large f
Allowed region
Allowed region
: If t-T+ mixing  large, R becomes large.
Entire WMAP allowed region can be consistent with the EWPM.

19. S ummary Entire WMAP allowed region can be consistent with the EWPM.
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.
Entire WMAP allowed region can be consistent with the EWPM.