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 L = iqLD /qL + iqRD /qR + 1 4F aµνF a

µν

where qL = ( uL dL ) , qR = ( uR dR ) , qL/R = 1 ∓ γ5 2 q, Dµ = ∂µ + igsT aGa

µ,

L is invariant under the global symmetry, SU(2)L × SU(2)R, ( uL dL ) → exp (iθa

Lσa)

( uL dL ) , ( uR dR ) → exp (iθa

Rσa)

( uR dR ) At low energies (< ∼ 1 GeV) non-perturbative effects become important, and the vacuum breaks SU(2)L × SU(2)R ¯ qq ∼ Λ3

QCD (= (O(100MeV))3)

The vacuum is invariant only under SU(2)V (subgroup of SU(2)L × SU(2)R with θa

L = θa 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 = ∂µφ∗∂µφ − V (φ∗φ), (G = U(1), H = {1}, G/H = U(1)).

• 5

5

• 5

5

• 2000

2000

• 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?

Transformation law for the quark ( u d ) → exp (iθaσa + iξaσaγ5) ( u d ) , Unbroken generators (=isospin): Ta = σa, Broken generators: Xa = σaγ5. Let’s standardize the group element g of G by g = exp(−iξaXa) exp(iθaT a). NG bosons ξa(x) parametrize the coset SU(2)L × SU(2)R/SU(2)V . σaξa(x) =

1 √ 2fπ

( π0/ √ 2 π+ π− −π0/ √ 2 ) g should transform as (g1g2 ∈ G) exp [ i(θV

a σa + θA a σaγ5)

] exp (−iξa(x)Xa) = exp (−iξ′

a(x)Xa) exp (iθ′ a(x)Ta) .

By comparing the (1 + γ5) and the (1 − γ5) parts, exp ( iθR

a σa

) exp (−iξa(x)σa) = exp (−iξ′

a(x)σa) exp (iθ′ a(x)σa) ,

exp ( iθL

a σa

) exp (iξa(x)σa) = exp (iξ′

a(x)σa) exp (iθ′ a(x)σa) ,

U ≡ exp(2iξaσa) transforms as U → exp(iθa

Lσa)U exp(−iθa Rσa), so L2deriv can be

constructed as L2deriv = (f 2

π/4) Tr(∂µU †∂µU), 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 m2

H diverges as ∼ Λ2. ⇔ Physical Higgs mass ∼ m2 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,

. .

λ λ t λf −λ/f T The Λ2 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))),

Σ = B B B B B @ 1 1 1 1 1 1 C C C C C A

• 2. Introduce NG bosons, (which include the SM Higgs doublet h).

π = ˆ πa ˆ Ta = B @ χ + η/(2 √ 5) h∗/ √ 2 φ† h⊤/ √ 2 −2η/ √ 5 h†/ √ 2 φ h/ √ 2 χ⊤ + η/(2 √ 5) 1 C A , χ = χaσa (triplet), h : doublet χ, η : eaten by gauge bosons φ : 2 × 2 symmetric matrix

• 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. Qa

1 =

( −σa∗/2 ) , Qa

2 =

( 0 σa/2 ) , Y1 = diag(−3, −3, 2, 2, 2)/10, Y2 = diag(2, 2, 2, −3, −3)/10

• 4. Identify the SM gauge group. (In this case, Qa

1 + Qa 2 and Y1 + Y2 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 Q1, Y1, Q2 and Y2)

ˆ πa ˆ Ta = B @ χ + η/(2 √ 5) h∗/ √ 2 φ† h⊤/ √ 2 −2η/ √ 5 h†/ √ 2 φ h/ √ 2 χ⊤ + η/(2 √ 5) 1 C A , Qa

1 =

„ −σa∗/2 « , Qa

2 =

„ 0 σa/2 « , Y1 = diag(−3, −3, 2, 2, 2)/10, Y2 = diag(2, 2, 2, −3, −3)/10

= ⇒ In the g1, g′

1 → 0 limit, h becomes an (exactly massless) NG boson. (The potential

for h generated only from those diagram which involves both g1 and g2.) = ⇒ No m2

h generated at 1-loop.

. .

h h g1 g1 h h g2

1

h h h h φ g2

2

g2

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 q3 = (u3, d3) to an SU(3)1 triplet χ = (d3, −u3, U) by introducing an EW singlet U.

• 2. Couple this to Σ(≡ e2iπa ˆ

TaΣ) and another EW singlet uc′ 3 in an SU(3)1 invariant way,

• 3. Add a mass term for U by introducing another EW singlet U c.

Lt =λfǫijkχiΣj4Σk5uc′

3 + λ′fUU c + H.c.

(i, j, k = 1, . . . , 3) =i √ 2λq3huc′

3 + fU(λuc′ 3 + λ′U c) + H.c.

• 4. After integrating out U, we are left with the top Yukawa coupling,

Lt = √ 2λλ′ √ |λ|2 + |λ′|2q3huc

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

• nly from the diagrams which involve both λ2 and (λ′f)2. =

⇒ m2

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− → tBH. (BH: neutral and stable. Observed as ETmiss at the LHC.)

. . . .

q ¯ q T− T− t BH BH ¯ t g g T− T− T− t BH BH ¯ t

We simulate this process using CompHEP + Herwig + AcerDET, taking sample parameters favored by EW precision measurements and the WMAP observations. (MT− = 600, . . . , 900 GeV, MBH = 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)

0.001 0.01 0.1 1 10 500 750 1000 1250 1500 σ(pp→T−T –

−X) (pb)

mT− (GeV)

• cf. Main Background (BG): pp → ttX (∼ 400pb)

How to reduce the BG?

• Hemisphere Analysis
• Look at diff. in Meff vs ETmiss 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.

Seminar at Univ. of Toyama. June 29, 2007 Daisuke Nomura

BG Reduction 1: Hemisphere Analysis — Our Results

Our Results: (Plot of the inv. mass of (j1, j2, j3) in each hemisphere, where j1 and j2 are those jets which maximize M(j1, j2), and j3 is the jet which minimizes M(j1, j2, j3).)

100 200 300 400 500 m1(jjj) (GeV) 100 500 m2(jjj) (GeV) 200 300 400 100 500 m2(jjj) (GeV) 200 300 400 200 300 100 200 300 400 500 m1(jjj) (GeV) 100 60 80 40 20

Background Signal

Since we imposed ETmiss > 400 GeV, BG events can originate only from leptonic decays

• f the top quark. In such cases, at least one of the three jets is a “fake” (not a decay product
• f the top, but just a QCD radiation).

Seminar at Univ. of Toyama. June 29, 2007 Daisuke Nomura

BG Reduction 2: Meff vs ETmiss distributions

• Def. of Effective Mass: Meff ≡ ∑

ℓ,γ,j |

pT| + ETmiss Configuration which maximizes the effective mass: Signal: BG:

jets jets t

• t

−

(T T production) (t t production) − −

T T − B B

H H

jets jets −

For these configurations, Meff = 4ET,BH, 2ET,jets ETmiss = 2ET,BH, = ⇒ Different Meff vs ETmiss distribution expected, in particular at high Meff region.

Seminar at Univ. of Toyama. June 29, 2007 Daisuke Nomura

BG Reduction 2: Meff vs ETmiss distributions — Our Results

Meff vs ETmiss distributions for signal and BG (for mT− = 800 GeV):

Tmiss

E (GeV) 200 400 600 800 M (GeV)

eff

600 1000 1400 1800 M (GeV)

eff

600 1000 1400 1800

Signal

Tmiss

E (GeV) 200 400 600 800 20 40 60 80 100 100 200 300

Signal Background

Difference in the Meff vs ETmiss distributions seen, in particular at high Meff region, as expected. = ⇒ If we impose a cut on Meff, e.g. 1500 GeV < Meff, we can effectively reduce the BG.

Seminar at Univ. of Toyama. June 29, 2007 Daisuke Nomura

Effects of Cuts

For our sample points, ... mT− M min

eff

Ecut

Tmiss

Signal/BG Signal/BG Signal/BG (GeV) (GeV) (GeV) (with top cut) (0-lepton with top cut) 600 1000 400 3336/1304 1053/313 842/106 700 1200 450 1284/582 332/114 263/54 800 1300 500 874/417 249/57 208/28 900 1500 550 397/203 105/16 93/7 (top mass cut: m(jjj) < 200 GeV) In the region ETmiss ∼ 0.5Meff, the signal dominates over the BG after imposing the cuts.

Seminar at Univ. of Toyama. June 29, 2007 Daisuke Nomura

Results

After imposing the BG reductions discussed earlier, the ETmiss distributions at high Meff interval are

Tmiss

E (GeV)

Tmiss

E (GeV)

Tmiss

E (GeV)

Tmiss

E (GeV) 100 200 300 400 500 40 80 120 160 120 40 80 20 10 30 50 100 150 250 200 300 500 700 300 500 700 20 40 60 80 300 500 700 900 20 10 30 40 50 300 500 700 900 5 10 15 20

Tmiss

E (GeV)

Tmiss

E (GeV)

Tmiss

E (GeV)

Tmiss

E (GeV) 300 500 700 300 500 700 300 500 700 900 500 300 700 900 No isolated lepton No isolated lepton No isolated lepton No isolated lepton m = 600 GeV

T−

m = 700 GeV

T−

m = 800 GeV

T−

m = 900 GeV

T−

m = 600 GeV

T−

m = 700 GeV

T−

m = 800 GeV

T−

m = 900 GeV

T−

Red: Signal, Blue: BG, Green: Signal + BG The signal seen as a bump structure!

Seminar at Univ. of Toyama. June 29, 2007 Daisuke Nomura

Summary

In the Little Higgs model with T-parity, we studied the pair production signatures of the T-odd partner of the top-quark at the LHC. To separate signal from BG, we used the hemisphere analysis, which turned out to be useful. The Meff vs ETmiss plane is also useful to separate the signal and BG. The signal can be

• bserved as a bump structure in the ETmiss distribution for relatively high Meff intervals.

For our sample parameters up to MT− ≤ 900 GeV, we can discover the T− particle.