Little Higgs and T Parity Claudia Frugiuele - PowerPoint PPT Presentation

Little Higgs and T Parity Claudia Frugiuele -------------------------- Carleton University 11 May 2010 in collaboration with Thomas Gregoire

------------------------------- Outline ------------------------------- Little Higgs models Strong dynamics and T parity SU(6)/Sp(6) model with a new T-parity

---------------------------------------------------------------------------- Little Higgs models ----------------------------------------------------------------------------

Little Higgs Models(LH): -------------------------------------------------------------------------------------------------- The Higgs is light because it is a pseudo-Goldstone boson in a G/H non linear sigma model ------------------------------------------------------------------------------------------------------ g 2 4 π 2 Λ 2 ∼ (1Tev) 2 m 2 h = > Naive breaking of the the global symmetry G > global symmetry broken Gauge couplings explicitly via collective Yukawa coupling symmetry breaking Quartic coupling

-------------------------- Example: Littlest Higgs -------------------------- >SU(5)/SO(5) non linear sigma model Σ → V Σ V T V ∈ SU (5) Both and   14 Goldstones h ∗ φ † η  χ +  √ √ 1 complex doublet 2 5 2 h T h † 1 complex triplet − 2 η π =  √ √ √  2 5 2 1 real triplet (eaten)   χ T + h η φ l √ √ 1 complex singlet 2 2 5

Collective symmetry breaking ---------------------------------------------------------------------------------------------------- Enlarge the gauge group to implement collective symmetry breaking, new gauge bosons ---------------------------------------------------------------------------------------------------- Gauge structure: SU (2) 1 × SU (2) 2 × U (1) Y  0 0 0    0 0 σ a 2 0 0 0 Q 2 a = Q 1 a = 0 0 0     − σ ∗ 0 0 a 0 0 0 2 L   (6) SU (2) 1 × SU (2) 2 × U (1) Y → SU (2) ew × U (1) Y The Higgs is kept light as the symmetry which protect it is not broken by each singular gauge group, but just by the two of them together. Just one loop logarithmic contribution! g 1 � = 0 g 2 = 0 The higgs is an exact Goldstone g 1 = 0 g 2 � = 0

Electroweak precision measurement (EWPM) ---------------------------------------------------------------------------------------------------- New Tev particle can induce higher dimensional operators dangerous for EWPM New gauge boson

One more ingredient: T-Parity -------------------------- Discrete symmetry ( called T-parity* )imposed to solve problems with EWPM Coefficient of higher dimensional operator loop suppressed. dark matter candidate Lightest T-odd particle stable, *Low, Cheng JHEP09(2003)051

UV Completion Little Higgs models are non linear sigma model with a cutoff Λ ≅ 10 Tev UV completion E n e r SUSY? Another Little Higgs model? Strongly g coupled interaction? y Λ ≅ 10 Tev Little Higgs model

Strongly coupled UV completion Littlest Higgs model SO ( N ) strong interaction SU (5) flavor group Fermionic condensation Σ   ψ 2 Ψ 5 = ψ 0   < Ψ 5 Ψ 5 > = Σ 0 SO ψ ′ 2 ψ 2 ∈ 2 of SU (2) 1 E .Katz et al 2 ∈ 2 ∗ of SU (2) 2 hep-ph 0312287 ψ ′

Strongly coupled UV completion and T parity Hill and Hill* showed that in strong interacting UV completion T-parity is broken by Wess-Zumino- Witten(WZW) terms. Lightest T-odd particle decays promptly Do not contribute to EWPM Situation analogous with the pion decay in QCD! * Hill & Hill Phys. Rev. D 75, 115009 (2007)

Our Goal : to build a LH model with a new definition of T-parity compatible with a strongly coupled UV completion.

--------------------------------------------------------------------------------------------- Strong dynamics and T parity ------------------------------------------------------------------------------------------------

How T-parity is defined in a strongly coupled UV completion? ∼ ′ † ψ 2 → ψ 2 Σ → ΩΣ † Ω † ψ 0 → − ψ † 0   0 0 1   ψ 2 Ω = 0 − 1 0  ∈ SO (5) Ψ 5 =  ψ 0   0 0 1 ψ ′ 2 Not a symmetry of the fermionic kinetic term!

Solution: ψ i → ψ j We can’t implement this symmetry in SU(5) ψ 2 → ψ ′ 2   ψ 2 Ψ 5 = Y = 1 ψ 0   2 Y = − 1 ψ ′ 2 2 Q 1 a → Q 2 a T- parity Y → Y

− ψ 2 → ψ ′ Y = 0 2 Y = 1 ψ 0 → ψ 0 2 This assignment of the hypercharge leads to a charged vacuum

SU(6) SU(6)/Sp(6) vacuum not charged

A new definition of T-parity Exchange Symmetry

------------------------------------------------------------------------------------- SU(6)/Sp(6) with T-parity ---------------------------------------------------------------------------------------

SU(6)/Sp(6) model   The SU (6) broken ( X a ) and unbroken ( T a ) generators   TTT 0 0 − I X a Σ 0 − Σ 0 X T  , a = 0 , Σ 0 = f 0 0 − i σ 2  0 0 T a Σ 0 + Σ 0 T T I a = 0 . � a /f = e 2 i Π a X a /f Σ 0 , Σ = e i Π a X a /f Σ 0 e i Π a X T to write the Goldstone bosons matrix Π in terms 14 Goldstone bosons Two doublet, 2Higgs model (2HM) φ − η h 1 h 2  χ  2 One real triplet h † − h T η 0  1 2  2 Π = One complex and one real singlet   h † h T η 0   2 1 2 χ † φ T − η − h ∗ h ∗ 2 1 2 Low, Skiba, Smith matrix (real triplet), is a real singlet, [ hep-ph/ 0 2 0 7 2 4 3 ]

New exchange T-parity T-parity: Σ → T Σ T T ,   0 0 i σ 2 T ∈ Sp (6) T = 0 0 I   0 0 − i σ 2 Sp(6) is not anomalous Dark matter candidate!

Inert doublet model Our dark matter candidate is contained in the Higgs sector which is an Inert Doublet Model (IDM) Physical scalars: h, H 0 , H ± , A 0 m H 0 < m H ± < m h < m A 0 h looks SM higgs T-odd m H 0 ∼ m H ± Approximate custodial symmetry Small contribution to the T Lightest particle is H0 and it is a parameter good dark matter * E.Dolle, S. Su Candidate for mass around hep-ph 0906.1609 60Gev *

Conclusion & Summary New definition of T parity in a SU(6)/Sp(6) LH model compatible with strong interacting UV completion Dark matter candidate Natural and well motivated inert doublet model UV completion change the structure and the phenomenology of the low energy theory

Work in progress • We are studying the phenomelogy of the model • Parameters space for dark matter • Smoking gun?

Backup

Particle content 10 Tev Even Gauge bosons Odd Gauge bosons, E new fermions, and N 1 Tev scalars E R G Higgs sector Electroweak scale Y H 0 mass around 60 Gev to have the right amount of relic density Two sets of gauge bosons and each SM fermion has a vector‐ like T odd partner. Extra states compared to SU(6)/Sp(6) without T parity

Wess-Zumino-Witten terms • WZW fixed by anomaly structure of the flavor group • In the low energy theory these are complicated terms funcSon of the sigma fields • To simplify we can think about

Inert doublet model 1 | H even | 2 + µ 2 2 | H odd | 2 +˜ λ 1 | H even | 4 +˜ V ( H even , H odd ) = µ 2 λ 2 | H odd | 4 (54) ˜ λ 5 λ 3 | H even | 2 | H odd | 2 +˜ even H odd | 2 + even H odd ) 2 + h.c. ) , + ˜ λ 4 | H † 2 (( H †

------------------------------------------------------------------------------ Fermionic sector ---------------------------------------------------------------------------------

Extra Gauge group Need to enlarge the gauge group to implement T‐parity in a chiral theory SU (2) 1 ⊗ SU (2) 2 ⊗ SU (2) 3 ⊗ U (1) Y , Extra SU(2) not in SU(6) SU (2) 1 ⊗ SU (2) 3 → SU (2) 1+3 , K 1 → V 1 K 1 V † 3 , (2) K 2 → V 2 K 2 V † SU (2) 2 ⊗ SU (2) 3 → SU (2) 2+3 . 3 , transform a s a real triplets under SU

L top = k 1 fQ T Σ † Q c + k 2 f k [ q T u c + h.c. 3 K T 1 ( − i σ 2 q c 1 ) + q T 3 K T 2 q c 2 ] + k 3 u ˜ Vector like partner of the top: One even doublet One odd doublet Two even singlets