Contributions to ρ parameter from heavy gauge bosons in Littlest Higgs model with T-parity

1. Contributions to ρ parameter from heavy gauge bosonsin 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

2. In the Standard Model http://map.gsfc.nasa.gov/ • Dark Matter Problem The existence have been established. cold dark matter candidate • Neutral • Stable • Massive WIMP • Fine-tuning Problem There is no WIMP in the Standard Model Beyond Standard Model related to quadratic divergence to the Higgs mass term. ,δm2～Λ2 :cutoff scale m02 +δm2 • 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 for physics at TeV scale Candidate of the beyond SM • Supersymmetric Model with R-Parity • ・・・ 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. In the Littlest Higgs Model with T-parity Little Higgs Mechanism SM particle N. Arkani-Hamed, A. G. Cohen, H. Georgi (’01) • Higgs is thepseudo Nambu-Goldstone boson ZH e.g. WH W • Quadratic divergences to the • Higgs mass term completely • vanish at one-loop level. h h h h + – g2 g2 T-parity H. C. Cheng, I. Low (’03) To avoid constraints from EWPM, T-parity has been introduced. SM particles T-even New particles T-odd Lightest T-odd particle becomes a dark matter candidate. • Little Hierarchy Problem is solved by • 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, ΦH 〈 h 〉 absorbed UEM(1) non-linear σ field

8. Particles • Yukawa of heavy fermion • Yukawa of SM-top and additional singlets Higgs sector Higgs doublet H ΦH mφH∝ f Triplet Higgs gauge sector [SU(2)×U(1)]1+ [SU(2)×U(1)]2 SM gauge boson mWH∝ f Heavy gauge boson 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. uSM uSM U1 U2 U+ U- tSM T- T+ top sector • Yukawa of SM-top and additional singlets new heavy T-odd top new heavy T-even top SM 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 • Lightest T-odd particle: AH • AH annihilates intoW, Z U-branch ~g’2/v Spectrum 10 T-even T-odd Φ ~mW2/v L-branch WH , ZH main Lightest T-odd 1 (TeV) Relic density depends only on f & mh h AH Allowed region for WMAP at 2σlevel W, Z 0.1 J.Hubisz and P.Meade (‘05) • Each branch can be expressed as a function of f & mh

11. A llowed region for Electroweak precision constraints

12. 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 contributionsare also important. Top-sector contributions ∝ R2 (indicate the amplitude of t-T+ mixing ), If t-T+ mixing is suppressed, this contribution becomes small. new result But our , heavy gauge contribution is . negligible

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

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

17. R esult

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

19. S ummary • Littlest Higgs model with T-parity can solve the little hierarchy problem and has a dark matter candidate. • Entire WMAP allowed region can be consistent with the EWPM. • Once we consider WMAP allowed region, f & mAH is determined by the mh (in each branch). • Large mh region is allowed.