Hunting for the Top Partner in the Littlest Higgs Model with - PowerPoint PPT Presentation

Seminar at Univ. of Toyama. June 29, 2007 Daisuke Nomura Hunting for the Top Partner in the Littlest Higgs Model with T-parity at the LHC Daisuke Nomura (KEK, JSPS Postdoc) 0. Introduction on Chiral Lagrangian 1. Little Higgs models and the Littlest Higgs with T-parity (LHT) 2. Collider Signatures of LHT at the LHC 3. Summary In collaboration with S. Matsumoto and M. M. Nojiri , Phys. Rev. D75 (2007) 055006.

Seminar at Univ. of Toyama. June 29, 2007 Daisuke Nomura QCD and Chiral Lagrangian (1) — Chiral Symmetry Breaking (Ref.: e.g. Weinberg’s Textbook, Chap. 19) QCD Lagrangian /q R + 1 4 F aµν F a L = iq L D /q L + iq R D µν ( u L ( u R where ) ) q L/R = 1 ∓ γ 5 D µ = ∂ µ + ig s T a G a q L = , q R = , q, µ , d L d R 2 L is invariant under the global symmetry, SU (2) L × SU (2) R , ( u L ( u L ( u R ( u R ) ) ) ) → exp ( iθ a L σ a ) → exp ( iθ a R σ a ) , d L d L d R d R At low energies ( < ∼ 1 GeV) non-perturbative effects become important, and the vacuum breaks SU (2) L × SU (2) R qq � ∼ Λ 3 QCD (= ( O (100MeV)) 3 ) � ¯ The vacuum is invariant only under SU (2) V (subgroup of SU (2) L × SU (2) R with θ a L = θ a R ) = ⇒ Chiral Symmetry Breaking

Seminar at Univ. of Toyama. June 29, 2007 Daisuke Nomura QCD and Chiral Lagrangian (2) — Nambu-Goldstone Boson Nambu-Goldstone (NG) Theorem When a global continuous symmetry G is spontaneously broken down to a subgroup H , for each generator of the broken symmetry, there exists a corresponding massless boson ( NG boson ), which parametrizes the coset G/H . U (1) example : a complex scalar φ , with a “wine bottle” potential V ( φ ∗ φ ) , L = ∂ µ φ ∗ ∂ µ φ − V ( φ ∗ φ ) , ( G = U (1) , H = { 1 } , G/H = U (1)) . 2000 0 5 -2000 0 -5 -5 0 0 -5 5 5 A massless mode appears in the θ direction (NG boson), which parametrizes G/H = U (1) .

Seminar at Univ. of Toyama. June 29, 2007 Daisuke Nomura QCD and Chiral Lagrangian (3) — How to construct L for NG bosons? ( ) ( ) u u → exp ( iθ a σ a + iξ a σ a γ 5 ) Transformation law for the quark , d d Unbroken generators (=isospin): T a = σ a , Broken generators: X a = σ a γ 5 . Let’s standardize the group element g of G by g = exp( − iξ a X a ) exp( iθ a T a ) . NG bosons ξ a ( x ) parametrize the coset SU (2) L × SU (2) R /SU (2) V . ( π 0 / √ π + ) 2 1 √ σ a ξ a ( x ) = √ π − − π 0 / 2 2 f π g should transform as ( g 1 g 2 ∈ G ) i ( θ V a σ a + θ A exp ( − iξ a ( x ) X a ) = exp ( − iξ ′ a ( x ) X a ) exp ( iθ ′ [ ] exp a σ a γ 5 ) a ( x ) T a ) . By comparing the (1 + γ 5 ) and the (1 − γ 5 ) parts, iθ R exp ( − iξ a ( x ) σ a ) = exp ( − iξ ′ a ( x ) σ a ) exp ( iθ ′ ( ) exp a σ a a ( x ) σ a ) , iθ L exp ( iξ a ( x ) σ a ) = exp ( iξ ′ a ( x ) σ a ) exp ( iθ ′ ( ) exp a σ a a ( x ) σ a ) , U ≡ exp(2 iξ a σ a ) transforms as U → exp( iθ a L σ a ) U exp( − iθ a R σ a ) , so L 2deriv can be constructed as L 2deriv = ( f 2 π / 4) Tr ( ∂ µ U † ∂ µ U ) , which is manifestly invariant under SU (2) L × SU (2) R .

Seminar at Univ. of Toyama. June 29, 2007 Daisuke Nomura Introduction — Little Higgs Hierarchy Problem in the Standard Model . t W H . Radiative corrections to m 2 H diverges as ∼ Λ 2 . ⇔ Physical Higgs mass ∼ m 2 weak . Little Higgs models solve this by • arranging the model so that Higgs = pseudo Nambu-Goldstone boson , and • introducing collective symmetry breaking Under this mechanism, for example, . λf t T λ λ − λ/f . The Λ 2 divergences cancelled.

Seminar at Univ. of Toyama. June 29, 2007 Daisuke Nomura Introduction — Littlest Higgs with T-parity (LHT) Little Higgs (LH) models – Alternative to SUSY models Many variants. ⋆ The “Simplest” LH ( SU (3) × U (1) X → SU (2) L × U (1) Y , Schmaltz) ⋆ The “Minimal Moose” ( [ SU (3) L × SU (3) R /SU (3) V ] 4 , Arkani-Hamed et al.) ⋆ The “Littlest Higgs” ( SU (5) /SO (5) , Arkani-Hamed et al.) LH Models with T-parity (Cheng & Low) – interesting class of models E.g., in SU (5) /SO (5) , two gauged subgroups [ SU (2) × U (1)] 2 ( ⊂ SU (5)) broken down as [ SU (2) × U (1)] 2 → SU (2) L × U (1) Y at scale f T-parity exchanges the two SU (2) × U (1) ’s. � The lightest T-odd particle (LTP) is a candidate for dark matter.

Seminar at Univ. of Toyama. June 29, 2007 Daisuke Nomura Intro. — Littlest Higgs 1. Suppose that SU (5) is broken down to SO (5) by the VEV of Σ (= 15 rep. of SU (5) )), 0 1 0 0 0 1 0 0 0 0 0 1 B C B C � Σ � = 0 0 1 0 0 B C B C 1 0 0 0 0 B C @ A 0 1 0 0 0 2. Introduce NG bosons, (which include the SM Higgs doublet h ). √ √ χ = χ a σ a (triplet) , h : doublet 0 1 h ∗ / φ † χ + η/ (2 5) 2 √ √ √ π a ˆ h ⊤ / h † / π = ˆ T a = 2 − 2 η/ 5 2 A , χ, η : eaten by gauge bosons B C √ √ @ χ ⊤ + η/ (2 φ : 2 × 2 symmetric matrix φ h/ 2 5) 3. Introduce gauge interactions. (This explicitly breaks G .) Gauge [ SU (2) × U (1)] 2 ⊂ SU (5) , which breaks down (by � Σ � ) to the SM gauge group. ( − σ a ∗ / 2 ( 0 ) ) Q a , Q a 1 = 2 = , σ a / 2 0 Y 1 = diag( − 3 , − 3 , 2 , 2 , 2) / 10 , Y 2 = diag(2 , 2 , 2 , − 3 , − 3) / 10 4. Identify the SM gauge group. (In this case, Q a 1 + Q a 2 and Y 1 + Y 2 are the SU (2) L × U (1) Y generators.)

Seminar at Univ. of Toyama. June 29, 2007 Daisuke Nomura Intro. — Collective Symmetry Breaking (Little Higgs Mechanism) What is the point of the whole construction? The global SU (5) symmetry broken by the [ SU (2) × U (1)] 2 gauge symmetry (generated by Q 1 , Y 1 , Q 2 and Y 2 ) √ √ 0 1 h ∗ / φ † χ + η/ (2 5) 2 √ √ √ π a ˆ h ⊤ / h † / ˆ T a = 2 − 2 η/ 5 2 A , B C √ √ @ χ ⊤ + η/ (2 φ h/ 2 5) „ − σ a ∗ / 2 „ 0 « « Q a , Q a 1 = 2 = , σ a / 2 0 Y 1 = diag( − 3 , − 3 , 2 , 2 , 2) / 10 , Y 2 = diag(2 , 2 , 2 , − 3 , − 3) / 10 ⇒ In the g 1 , g ′ = 1 → 0 limit, h becomes an (exactly massless) NG boson. (The potential for h generated only from those diagram which involves both g 1 and g 2 .) ⇒ No m 2 = h generated at 1-loop. g 2 . 2 h h φ h h h h h h g 1 g 1 g 2 g 2 1 . 1

Seminar at Univ. of Toyama. June 29, 2007 Daisuke Nomura Littlest Higgs — Top Sector ⋆ How to include the top Yukawa coupling? 1. Extend the third generation quark SU (2) 1 doublet q 3 = ( u 3 , d 3 ) to an SU (3) 1 triplet χ = ( d 3 , − u 3 , U ) by introducing an EW singlet U . 2. Couple this to Σ( ≡ e 2 iπ a ˆ T a � Σ � ) and another EW singlet u c ′ 3 in an SU (3) 1 invariant way, 3. Add a mass term for U by introducing another EW singlet U c . 3 + λ ′ fUU c + H . c . L t = λfǫ ijk χ i Σ j 4 Σ k 5 u c ′ ( i, j, k = 1 , . . . , 3) √ 2 λq 3 hu c ′ 3 + fU ( λu c ′ 3 + λ ′ U c ) + H . c . = i 4. After integrating out U , we are left with the top Yukawa coupling, √ 2 λλ ′ | λ | 2 + | λ ′ | 2 q 3 hu c L t = 3 + H . c . √ ⋆ Safe from quadratic divergences? In the λ ′ → 0 limit, SU (3) 1 inv., i.e. h = NG boson. = ⇒ effective potential for h generated only from the diagrams which involve both λ 2 and ( λ ′ f ) 2 . = ⇒ m 2 h at most log divergent

Seminar at Univ. of Toyama. June 29, 2007 Daisuke Nomura Signiture of the LHT model at LHC Q. How to probe the LH model at the LHC? A. E.g., search for new particles (in this talk, the T-odd partner of the top-quark, T − ). We studied the process pp → T − T − followed by T − → tB H . ( B H : neutral and stable. Observed as E Tmiss at the LHC.) . . t t g q ¯ T − B H B H T − T − T − T − B H B H q g ¯ ¯ t t . . We simulate this process using CompHEP + Herwig + AcerDET , taking sample parameters favored by EW precision measurements and the WMAP observations. ( M T − = 600 , . . . , 900 GeV, M B H = 100 , . . . , 175 GeV.)

Seminar at Univ. of Toyama. June 29, 2007 Daisuke Nomura Signal and Background Cross section of pp → T − T − X at the LHC: O (1)pb ∼ O (0.1)pb (for our sample parameters) 10 − X ) (pb) 1 0.1 – σ ( pp → T − T 0.01 0.001 500 750 1000 1250 1500 m T − (GeV) cf. Main Background (BG): pp → ttX ( ∼ 400pb ) How to reduce the BG? • Hemisphere Analysis • Look at diff. in M eff vs E Tmiss distributions

Seminar at Univ. of Toyama. June 29, 2007 Daisuke Nomura BG Reduction 1: Hemisphere Analysis Algorithm to group energetic objects ( j , ℓ and γ ’s) into two hemispheres each of which we guess originates from a heavy particle. (CMS collab.) The algorithm is, roughly speaking, ... (i) Identify the hardest jet. (Seed of Hemisphere 1) (ii) Identify the hardest jet in the “opposite” side of the jet found in (i). (Seed of Hemisphere 2) (iii) For all the remaining jets, calculate the “distance” to the seeds, and associate them to the “closer” hemisphere.