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 Dark Matter Problem WIMP Beyond Standard Model http://map.gsfc.nasa.gov/ 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)

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

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

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

L ittlest Higgs Model with T-parity

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

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

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.

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

for Electroweak precision constraints llowed region for Electroweak precision constraints

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

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

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.

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.

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

R esult

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.

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.