current status of extra dimension (inspired) models

Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects

Current Status ofExtra Dimension (inspired) Models

Shrihari Gopalakrishna

Institute of Mathematical Sciences (IMSc)Chennai, India

Workshop on High Energy Physics Phenomenology XIV

IIT Kanpur

Dec 2015

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Motivation

SM hierarchy problem: MEW � MPl

SM flavor problem: me � mt

Explained by new dynamics?

Extra dimensions (Warped (AdS), Flat)SupersymmetryStrong dynamicsLittle Higgs

AdS/CFT correspondence [Maldacena 97]

5-D gravity theory in AdS ←→DUAL

4-D conformal field theory

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Warped Model

SM in background 5D warped AdS space [Randall, Sundrum 99]

ds2 = e−2k|y|(ηµνdxµdxν) + dy 2

Z2 orbifold fixed points:

Planck (UV) Brane

TeV (IR) Brane

R : radius of Ex. Dim.k : AdS curvature scale (k . Mpl )

πR0

y

y=0

y=πR

UV

IR

Hierarchy prob soln:

IR localized Higgs : MEW ∼ ke−kπR : Choose kπR ∼ 34

CFT dual is a composite Higgs model

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AdS/CFT Correspondence

AdS/CFT Correspondence [Maldacena, 1997]

A classical supergravity theory in AdS5 × S5 at weak coupling is dual to a4D large-N CFT at strong coupling

The CFT is at the boundary of AdS [Witten 1998; Gubser, Klebanov, Polyakov 1998]

ZCFT [φ0] = e−ΓAdS [φ0]

L ⊃∫

d4x OCFT (x)φ0(x)

Eg: 〈O(x1)O(x2)〉 = δ2ZCFT [φ0]δφ0(x1)δ(x2)

with ZCFT given by the RHS

ΓAdS [φ] supergravity eff. actionφ(y , x) is a solution of the EOM (δΓ = 0)for given bndry value φ0(x) = φ(y = y0, x)

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4D ↔ 5D descriptions

[Arkani-Hamed, Porrati, Randall, 2000; Rattazzi, Zaffaroni, 2001]

Dual of Randall-Sundrum model RS1 (SM on IR Brane)

Planck brane =⇒ UV Cutoff; Dynamical gravity in the 4D CFTTeV (IR) brane =⇒ IR Cutoff; Conformal invariance broken belowa TeV

All SM fields are composites of the CFT

Dual of Warped Models with Bulk SM

UV localized fields are elementaryIR localized fields (Higgs) are composite

4D dual is Composite Higgs model [Georgi, Kaplan 1984]

Shares many features with Walking Extended Technicolor

Partial Compositeness

AdS dual is weakly coupled and hence calculable!

KK states are dual to composite resonances

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AdS ↔ Minimal Composite Higgs Model [SO(5)/SO(4)]

[Agashe, Contino, Pomarol, 2004]

AdS/CFT Corrsp : G global symm of CFT ↔ AdS gauge symm

Bulk gauge group : SO(5)⊗ U(1)X AM = (Aµ, A5)

Impose boundary condition (BC) to keep/break a symm:

(UV , IR) = (±,±) : + is Neumann, − is DirichletDirichlet BC (−) breaks a symmetry on that boundaryA−+(x , y) BC: A|y=0 = 0 ; ∂y A |y=πR = 0

Minimal Composite Higgs Model (MCHM) dual is[SO(5)⊗ U(1)X ]/[SO(4)⊗ U(1)X ] Aa

µ(−−), Aa5(++)

TL,T 3R + X Aµ(++), A5(−−)

T±R,T 3

R − X Aµ(−+), A5(+−)

Aa5(++) dual of PNGB πa = {φ1,2,3, H}! [Contino, Nomura, Pomarol 2003]

Gauge symmetry forbids tree-level massMass at loop-level from gauge and top loops [Hosotani 1983]

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KK tower

Kaluza-Klein (KK) tower

Kaluza-Klein (KK) decomposition

5D (compact) field ↔ Infinite tower of 4D fields

Look for this tower

at the LHCin Precision-EW obs, Flavor Changing NC, CC

SM

1st KK

2nd KK

Example LHC:b

q′

q

t

ℓ+

W+(1) b

W+ν

Look for heavy Kaluza-Klein (KK) states : KK h(1)µν , g

(1)µ , W

(1)µ , Z

(1)µ , b

(1)α , ...

LEP precision electroweak constraints⇒ W(1)µ , Z

(1)µ & 2 TeV

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Constraints

Precision EW Constraints

W,Z, γPrecision Electroweak Constraints (S, T, Zbb)

Bulk gauge symm - SU(2)L × U(1) (SM ψ, H on TeV Brane)

T parameter ∼ ( vMKK

)2(kπR) [Csaki, Erlich, Terning 02]

S parameter also (kπR) enhanced

AdS bulk gauge symm SU(2)R ⇔ CFT Custodial Symm[Agashe, Delgado, May, Sundrum 03]

T parameter - ProtectedS parameter - 1

kπRfor light bulk fermions

Problem: Zbb shifted

3rd gen quarks (2,2) [Agashe, Contino, DaRold, Pomarol 06]

Zbb coupling - ProtectedPrecision EW constraints ⇒ MKK & 2− 3 TeV

[Carena, Ponton, Santiago, Wagner 06,07] [Bouchart, Moreau-08] [Djouadi, Moreau, Richard 06]

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AdS model structure

Bulk Gauge Group

[Agashe, Delgado, May, Sundrum 03]

Bulk gauge group : SU(3)QCD ⊗ SU(2)L ⊗ SU(2)R ⊗ U(1)X

8 gluons

3 neutral EW (W 3L ,W

3R ,X )

2 charged EW (W±L ,W±R )

Gauge Symmetry breaking:By Boundary Condition (BC): A−+(x, y) BC: A|y=0 = 0 ; ∂y A |y=πR = 0

SU(2)R × U(1)X → U(1)Y

By VEV of TeV brane Higgs Higgs Σ = (2, 2)

SU(2)L × U(1)Y → U(1)EM

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AdS model structure

Fermion reps (Model II)

[Agashe, Contino, DaRold, Pomarol 06]

Custodial protection for ZbLbL coupling

Impose custodial SU(2)L+R ⊗ PLR invariance

Fermions:

QL = (2, 2)=

(tL χbL T

)tR : (1, 1) OR (1, 3)⊕ (3, 1)=

χ′RtRb′R

⊕ χ′′R

t′′Rb′′R

; bR : (1, 1) OR (1, 3)⊕ (3, 1)

ZbLbL coupling protected! Note: WtLbL, ZtLtL not protected, so expect shifts

New “exotic” fermions ζL, TL, χ′R , b′R , ...

No zero-mode. (−,+) BC =⇒ Mψ′ < MA′ [Agashe, Servant 04]

Promising LHC signatures

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AdS model structure

4-D couplings

ξ ≡√kπR ≈ 5

Compare to SM couplings:

ξ enhanced: tRtRA′, hhA′, φφA′ (Equivalence Theorem ⇒ φ↔ AL)

1/ξ suppressed: ψlight ψlight A′++ Note: ψlight ψlight A

′−+ = 0

SM strength: tLtLA′

Effective coupling (Eg: Z ′):

L4D ⊃ ψL,Rγµ[

eQIA1 µ + gZ

(T 3

L − s2W TQ

)IZ1 µ + gZ′

(T 3

R − s′2TY

)IZX 1 µ

]ψL,R

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KK states (heavy resonances) at the LHC

h(1)µν (KK Graviton) gg → h(1) → tt

L = 300 fb−1 LHC reach is about 2 TeV [Agashe, Davoudiasl, Perez, Soni 07][Fitzpatrick, Kaplan, Randall, Wang 07]

g(1)µ (KK Gluon) qq → g (1) → tt

L = 100 fb−1 LHC reach is 4 TeV [Agashe, Belyaev, Krupovnickas,Perez,Virzi 06][Lillie, Randall, Wang, 07] [Lillie, Shu, Tait 07]

Z(1)µ , W

(1)±µ

(ZKK ≡ Z ′ , W±KK ≡W ′) qq → Z ′,W ′ → XX

[Agashe, Davoudiasl, SG, Han, Huang, Perez, Si, Soni 07, 08]

ψ(1) (KK Fermion) [Agashe, Servant 04][Dennis et al 07][Contino, Servant 08][SG, Moreau, Singh, 10][SG, Mandal, Mitra, Moreau, Tibrewala 11, 14]

Radion [Csaki et al, 2001, 2007] [Gunion et al, 2004]

Extended Higgs sector [T. Mukherjee, S. Sadhukhan, SG: In progress]

Review: [Davoudiasl, SG, Ponton, Santiago, New J.Phys.12:075011,2010. arXiv:0908.1968 [hep-ph]]

ATLAS Exotics searches

CMS Exotics searches

CMS Exotica Physics Group Summary – Moriond, 2015

stopped gluino (cloud)stopped stop (cloud)HSCP gluino (cloud)

HSCP stop (cloud)q=2/3e HSCP

q=3e HSCPchargino, ctau>100ns, AMSB

neutralino, ctau=25cm, ECAL time

0 1 2 3 4

RS1(γγ), k=0.1RS1(ee,μμ), k=0.1

RS1(jj), k=0.1RS1(WW→4j), k=0.1

0 1 2 3 4

coloron(jj) x2coloron(4j) x2

gluino(3j) x2gluino(jjb) x2

0 1 2 3 4

RS Gravitons

Multijet Resonances

Long-Lived Particles

SSM Z'(ττ)SSM Z'(jj)

SSM Z'(bb)SSM Z'(ee)+Z'(µµ)

SSM W'(jj)SSM W'(lv)

SSM W'(WZ→lvll)SSM W'(WZ→4j)

0 1 2 3 4

Heavy Gauge Bosons

CMS Preliminary

j+MET, vector DM=100 GeV, Λj+MET, axial-vector DM=100 GeV, Λ

j+MET, scalar DM=100 GeV, Λγ+MET, vector DM=100 GeV, Λ

γ+MET, axial-vector DM=100 GeV, Λl+MET, ξ=+1, SI/SD DM=100 GeV, Λl+MET, ξ=-1, SI/SD DM=100 GeV, Λl+MET, ξ=0, SI/SD DM=100 GeV, Λ

0 1 2 3 4

Dark Matter

LQ1(ej) x2LQ1(ej)+LQ1(νj)

LQ2(μj) x2LQ2(μj)+LQ2(νj)

LQ3(νb) x2LQ3(τb) x2LQ3(τt) x2LQ3(vt) x2

Single LQ1 (λ=1)Single LQ2 (λ=1)

0 1 2 3 4

Leptoquarks

e* (M=Λ)μ* (M=Λ)

q* (qg)q* (qγ)

b*0 1 2 3 4

Excited Fermions dijets, Λ+ LL/RR

dijets, Λ- LL/RRdimuons, Λ+ LLIMdimuons, Λ- LLIM

dielectrons, Λ+ LLIMdielectrons, Λ- LLIM

single e, Λ HnCMsingle μ, Λ HnCMinclusive jets, Λ+inclusive jets, Λ-

0 1 2 3 4 5 6 7 8 9 101112131415161718192021

ADD (γ+MET), nED=4, MDADD (j+MET), nED=4, MDADD (ee,μμ), nED=4, MS

ADD (γγ), nED=4, MSADD (jj), nED=4, MS

QBH, nED=4, MD=4 TeVNR BH, nED=4, MD=4 TeV

QBH (jj), nED=4, MD=4 TeVJet Extinction Scale

String Scale (jj)

0 1 2 3 4 5 6 7 8 9

Large Extra Dimensions

Compositeness

TeV

TeV

TeV

TeV

TeV

TeV

TeV

TeV

TeV

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KK-graviton[Agashe et al, 07] [Fitzpatrick et al, 07]

mn = xnke−kπr xn = 3.83, 7.02, ...

L ⊃ −C ffG

ΛTαβh

(n)αβ Λ = MPe

−kπr

SM in Bulk (flavor)

light fermion couplings highlysuppressedgauge field couplings 1

kπrsuppressedDecays dominantly tot, h, VLong

gg → h(1) → ZZ → 4`

1.5 2 2.5 3 3.5 4 4.5 5m1GHTeVL

0.001

0.01

0.1

1

10

100

Σ@HggLRS,Hqq�LSM->ZZDHfbL Η<2 cut

various kMp

; SM dashed[Agashe, Davoudiasl, Perez, Soni, 2007]

[ATLAS 1503.04677]

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KK-gluon[Agashe et al, 06] [Lillie et al, 07]

mn = xnke−kπr xn ≈ 2.45, 5.57, ... Width Γ ≈ M

6

g (1)tt : parity violating couplings!

LHC: qq → g(1) → tt

invariant mass / GeVtt

2000 2500 3000 3500 4000

-1# e

ve

nts

/ 2

00

Ge

V /

100

fb

0

10

20

30

40

50

60 mass distributiontt

total reconstructed

total partonic

W+jets background

SM prediction

/ GeVtt

m1800 2000 2200 2400 2600 2800 3000 3200 3400 3600

-+

N+

N

--N

+N

2

-1

-0.5

0

0.5

1

LRP

total reconstructed

total partonic

SM prediction

PLR = 2 N+−N−N++N−

N+ forward going ` wrt kt

LHC reach: About 4 TeV with 100 fb−1

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KK-gluon[Agashe et al, 06] [Lillie et al, 07]

mn = xnke−kπr xn ≈ 2.45, 5.57, ... Width Γ ≈ M

6

g (1)tt : parity violating couplings!

LHC: qq → g(1) → tt

invariant mass / GeVtt

2000 2500 3000 3500 4000

-1# e

ven

ts / 2

00 G

eV

/ 1

00 f

b

0

10

20

30

40

50

60 mass distributiontt

total reconstructed

total partonic

W+jets background

SM prediction

/ GeVtt

m1800 2000 2200 2400 2600 2800 3000 3200 3400 3600

-+

N+

N

--N

+N

2

-1

-0.5

0

0.5

1

LRP

total reconstructed

total partonic

SM prediction

PLR = 2 N+−N−N++N−

N+ forward going ` wrt kt

LHC reach: About 4 TeV with 100 fb−1

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LHC KK-gluon → tt search

Limit: MKK > 2.2TeV @ 95%CL[ATLAS 1505.07018; CMS 1309.2030]

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Z ′ production at the LHC

[Agashe, Davoudiasl, SG, Han, Huang, Perez, Si, Soni - arXiv:0709.0007 [hep-ph]]

Z ′

q

q

Z ′W−

W+

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Z ′ channels summary

[Agashe, Davoudiasl, SG, Han, Huang, Perez, Si, Soni: 0709.0007]

pp → Z ′ →W+W− (L2 TeV ; L3 TeV ) in fb−1

Fully leptonic : W → `ν ; W → `ν L : (100; 1000) fb−1

Semi leptonic : W → `ν ; W → (j j) L : (100; 1000) fb−1

pp → Z ′ → Z h

Z → `+`− ; h→ b b L : (200; 1000) fb−1

pp → Z ′ → `+`− L : (1000; −) fb−1

BR`` ∼ 10−3 Tiny!

pp → Z ′ → t t , b b

KK gluon “pollution” [Djouadi, Moreau, Singh 07]

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W ′ cross section

[Agashe, SG, Han, Huang, Soni, 0810.1497]

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W ′± channels summary

[Agashe, SG, Han, Huang, Soni, 0810.1497]

W ′± → t b: (L2 TeV ; L3 TeV ) in fb−1

Leptonic L : (100; 1000) fb−1

W ′± → Z W :Fully leptonic L : (100; 1000) fb−1

Semi leptonic L : (300; −) fb−1

W ′± →W h: L : (100; 300) fb−1

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LHC Data (W ′ → WZ )

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Vector-like fermions Decoupling

Independent source of mass M (not given by m = λv)

Can make M arbitrarily large

without hitting Landau pole in Yukawa coupling (4th Gen)

M could be related to EW scale (or not)

Eg: ExtraDim Th M = MKK ∼ TeV , SUSY solutions to µproblem

Decoupling behavior : S ,T , U, h→ γγ, gg → h, ...

For instance hγγ, ggh couplings

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Warped vectorlike fermions

SM fermions : (+,+) BC → zero-mode

“Exotic” fermions : (−,+) BC → No zero-mode

1st KK vectorlike fermion

Typical ctR , ctL : (−,+) top-partners “light”

c : Fermion bulk mass parameter

[Choi, Kim, 2002] [Agashe, Delgado, May, Sundrum, 03][Agashe, Perez, Soni, 04] [Agashe, Servant 04]

Look for it at the LHC

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

0.10

1.00

0.50

0.20

2.00

0.30

0.15

1.50

0.70

cMΨ

MKK

[Contino, da Rold, Pomarol, ’06]

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VL-fermions direct @ LHC

t ′, b′, χ5/3 Vectorlike fermions at the LHC

Model independent analysis,motivated by Warped extra dimensions

[SG, T.Mandal, S.Mitra, R.Tibrewala, arXiv:1107.4306, PRD84 (2011) 055001][SG, T.Mandal, S.Mitra, G.Moreau : arXiv:1306.2656, JHEP 1408 (2014) 079]

See Also (a partial list!): [Dennis et al, ‘07] [Carena et al, ‘07] [Contino, Servant, ‘08][Atre et al, ’08, ‘09, ‘11] [Aguilar-Saavedra, ‘09] [Mrazek, Wulzer, ‘09] [Han et al. ’10]

[SG, Moreau, Singh, ‘10] [Bini et al. ’12][Buchkremer et al. ’13][Delaunay et al. ’14][Flacke et al. ’14] [Backovic et al. ’14]

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Decay Modes of t ′, b′, χ

EWSB induced mixing =⇒ Tree-level NC Couplings

as usual will have t′LbLW± and b′LtLW

± CC couplings

also, from Yukawa coupling 〈Σ〉 = v =⇒ t ↔ t′, b ↔ b′ mixing

L ⊃(

b b′)γµ(

gZ 00 g′Z

)(bb′

)L,R

Zµ +(

bL b′L) ( mb 0

mb Mb′

)(bRb′R

)+ h.c.

Diagonalize to go to mass basis

v → v(1 + h/v) leads to b′bh couplinggZ 6= g ′Z leads to b′bZ couplingSimilarly t′tZ , t′th couplings also, in addition to t′bW

VL Tree-level Decays

b′ → tW , b′ → bZ , b′ → bht ′ → bW , t ′ → tZ , t ′ → thχ→ tW

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b′ Single & Double Resonant channels

*

... followed by b2 → bZ

Both b2 on-shell : Double Resonant (DR) channel

Only one b2 on-shell : Single Resonant (SR) channel

|M(bZ )−Mb2 | ≥ αcutMb2 ; αcut = 0.05

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b′ Double Resonant

Pair Production : pp → b′b′ → bZbZ → bjj b``

400 600 800 1000 1200 1400

1

10

100

1000

104

Mb2HGeVL

ΣHfbL

400 600 800 1000 1200 1400

0.1

1

10

100

1000

Mb2HGeVL

LHfb-1M

Cuts:

Rapidity: −2.5 < yb,j,Z < 2.5,Transverse momentum: pT b,j,Z > 25 GeV,Invariant mass cuts:MZ − 10 GeV < Mjj < MZ + 10 GeV,0.95Mb2

< M(bZ) < 1.05Mb2.

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b′ Single Resonant - I

Single Resonant : bg → b′bZ → bZbZ → bbJJ``

Model Independent LHC-14 reach

Mb2 = 1250 GeV

1000

750

500

0.05 0.10 0.150

200

400

600

800

1000

Κb2 L b1 L Z

LDHfb-1L

Brown dots : DT Model Green dots : TT Model

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b′ Single Production - II

Single Production : bg → b′Z → bZZ → bjj``

æ

æ

ææ

æ æ

400 600 800 1000 1200 1400 1600

0.0

0.2

0.4

0.6

0.8

1.0

Mb2HGeVL

Κb2bZ

Σ = 0.1 fb

1

10

100

1000

æ

æ

ææ

æ

500 1000 1500

0.0

0.2

0.4

0.6

0.8

1.0

Mb2HGeVL

Κb2bZ

L = 3000 fb-1

100

10

1

Cuts:

Rapidity: −2.5 < yb,j,Z < 2.5,Transverse momentum: pT b,j,Z > 0.1Mb2

,

Invariant mass cuts:MZ − 10 GeV < Mjj < MZ + 10 GeV,0.95Mb2

< M(bZ) OR (bjj) < 1.05Mb2.

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χ Phenomenology at the LHC

[SG, T.Mandal, S.Mitra, G.Moreau : arXiv:1306.2656]

[Contino, Servant ’08][Mrazek, Wulzer ’10][Cacciapaglia et al. ’12]

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χ Double and Single Resonant channels

pp → χtW → tWtW → tWt`ν

X Mχ σtot σSR cuts S BG L(GeV) (fb) (fb) (fb) (fb) (fb−1)

X1 500 2406 261.5 Basic 977.5 3.257 -Disc. 146.1 0.115 0.826

X2 750 235.5 29.31 Basic 99.99 3.257 -Disc. 42.74 0.115 2.824

X3 1000 39.19 5.198 Basic 17.92 3.257 -Disc. 11.36 0.115 10.63

X4 1250 8.576 1.231 Basic 4.305 3.257 -Disc. 3.226 0.115 37.42

X5 1500 2.188 0.364 Basic 1.235 3.257 -Disc. 1.010 0.115 119.5

X6 1750 0.613 0.121 Basic 0.393 3.257 -Disc. 0.339 0.115 355.8

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χ Single Resonant Channel

MΧ1 = 1500 GeV

1250

1000

750

500

0.02 0.04 0.06 0.08 0.10 0.120

200

400

600

800

1000

Κx1 R t1 RW

LDHfb-1L

Blue Dots - ST Model Green Dots - TT Model

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t ′ Phenomenology at the LHC

[SG, Tanumoy Mandal, Subhadip Mitra, Gregory Moreau : arXiv:1306.2656]

See also: [Harigaya et al., ‘12] [Giridhar, Mukhopadhyaya, 2012] [Azatov et al., ‘12][Berger, Hubisz, Perelstein, ‘12] [Cacciapaglia et al., ’10, ‘12] [Aguilar-Saavedra et al. ’05]

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t ′ Double and Single Resonant channels

pp → t2th→ thth→ tbbtbb → 6 b 4 j (4 b-tags)

T Mt2σtot σSR cuts S BG L

(GeV) (fb) (fb) (fb) (fb) (fb−1)T1 500 1207 223.0 Basic 237.4 102.7 -

Disc. 52.38 0.389 6.379T2 750 115.2 18.30 Basic 22.67 102.7 -

Disc. 13.25 0.389 25.22T3 1000 18.38 2.715 Basic 3.088 102.7 -

Disc. 2.421 0.389 138.0T4 1250 3.821 0.590 Basic 0.477 102.7 -

Disc. 0.415 0.389 1889.2

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t ′ Single Resonant channel

Mt2 = 1250 GeV

1000

750

500

0.0 0.5 1.0 1.5 2.0 2.50

200

400

600

800

1000

Κt2 L t1 R h

LDHfb-1L

Blue Dots - ST Model Green Dots - TT Model

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SM-like VLF - EWPT & Higgs Observables

VL fermions in EWPT and Higgs Observables

Survey of vector-like fermion extensions of the Standard Model and their

phenomenological implications

[S.Ellis, R.Godbole, SG, J.Wells; 1404.4398 [hep-ph], JHEP 1409 (2014) 130]

Precision electroweak observables (S ,T ,U)

Modifications to hgg , hγγ couplings:

σ(gg → h)

λf

f

Γ(h→ γγ)

λf

f W

W

We compute ratiosΓh→gg

SM,

Γh→γγSM

using leading-order expressionsQCD corrections to ratios small: [Furlan ’11] [Gori, Low ’13]

µVBFγγ ≈

Γγγ

ΓSMγγ

; µgghZZ ≈

Γgg

ΓSMgg

; µgghγγ ≈

Γgg

ΓSMgg

Γγγ

ΓSMγγ

;µgghγγ

µgghZZ

≈Γγγ

ΓSMγγ

≈ µVBFγγ

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SM-like vectorlike fermions

Simple VL extensions of SM (No mixing to SM fermions)

11 : SU(2) singlet VL pair

22 : SU(2) doublet VL pair

22 + 11 : MVSM

22 + 11 + 11 : Vector-like extension of the SM (VSM)

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22 + 11 : MVQD

λD = 1, MD = MQ , YQ = (1/6,−1/6) (solid, dashed)

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22 + 11 : MVQD

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Heavy 2HDM Scalars (in SU(6)/Sp(6) Little-Higgs)

[SG, Soumya Sadhukhan, Tuhin S. Mukherjee: on-going]

Low, Skiba, Smith (LSS) Model (2002) : SU(6)/Sp(6)

Σ = exp{ iπaX a

f} 〈Σ〉 ; 〈Σ〉 =

(0 −11 0

)6×6

;

2HDM: VLSS = m21|φ1|2+m2

2|φ2|2+(b2φT1 ·φ2+h.c.)+λ′5|φT

1 ·φ2|2

Take “Alignment limit”

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LSS model scan; fine-tuning

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LSS model φgg effective coupling (φ = A,H)

L =κφgg

64π2 (1 TeV )φGG

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LSS model BRs

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Model Independent LHC Limits/Prospects

[SG, Soumya Sadhukhan, Tuhin Subhra Mukherjee: 1504.01074]

5pb

8TeV

1pb

.1pb

0 10 20 30 40

0.0

0.2

0.4

0.6

0.8

1.0

ΚAgg

BRHA®ttL

2pb

.5pb

8TeV

.005pb

0 5 10 15 20

0.0

0.2

0.4

0.6

0.8

1.0

ΚAgg

BRHA®ΤΤL

\

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Flavor structure

[Agashe, Perez, Soni, 04]

L ⊃ Ψi iΓµDµΨi + Mij Ψi Ψj + y 5Dij HΨi Ψj + h.c.

Basis choice: Mij diagonal ≡ Mi

All flavor violation from y 5Dij

KK decompose and go to mass basis

=⇒ g Ψi(n)W

(k)µ Ψj

(m) off-diagonal in flavor

(due to non-degenerate f i i.e. M i )

5D fermion Ψ is vector-like

Mij is independent of 〈H〉 = vBut zero-mode made chiral (SM)

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Example FCNC processes

K 0K 0 mixing:

Tree-level FCNC vertex g(1)d s ∝ V d†L

( [g(1)d d

]0

0[g(1)s s

] ) V dL

b → sγ :

No tree-level contribution to helicity flip dipole operatorSo 1-loop with g (1) b s OR φ b s(1)

b → s `+`− , b → s s s, K → πνν :

Tree level FCNC vertex Z s d , Z b s

Bound : mKK & few TeV [Agashe et al][Buras et al][Neubert et al][Csaki et al]

Relaxed with flavor alignment : MFV, NMFV, flavor symmetries, ...[Fitzpatrick et al][Agashe et al]

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Example LHC flavor changing processes

Tree-level FCNC t → c h [Agashe, Contino 09]

BR(t → c h) ∼ 10−4

Tree-level FCNC BR(t → c Z) ∼ 10−5[Agashe, Perez, Soni 06]

Loop FCNC t → c γ

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Conclusions

In Warped models or Composite-Higgs models: SM + Heavy states

Spin-2 (hµν), Vectors (g (1),Z ′,W ′), Fermions (b′, t′, χ),Scalars (2HDM?)

LHC direct and indirect probes

Precision electroweak constraints imply MKK & 2TeV

Now LHC has entered the game!

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BACKUP SLIDES

BACKUP SLIDES

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Explaining SM mass hierarchy

Bulk Fermions explain SM mass hierarchy [Gherghetta, Pomarol 00][Grossman, Neubert 00]

S(5) ⊃∫

d4x dy{

cψ k Ψ(x, y) Ψ(x, y)}

Fermion bulk mass (cψ parameter) controls f ψ(y) localization

h

q

χ Rt

3

RS-GIM keeps FCNC under control

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Kaluza-Klein (KK) expansion

[See for example: Gherghetta, Pomarol, 2000]

S5 = −∫

d4x

∫dy√−g

[1

4g25

F 2MN + |∂Mφ|

2 + iΨγM DM Ψ + m2φ|φ|

2 + imΨΨΨ

]

EOM: [e2σ

ηµν∂µ∂ν + esσ

∂5(e−sσ∂5)− M2

Φ

]Φ(xµ, y) = 0

Kaluza-Klein expansion

Φ(xµ, y) =1

√2πR

∞∑n=0

Φ(n)(xµ)fn(y)

Orthonormality relation:

1

2πR

∫ πR

−πRdy e(2−s)σ fn(y)fm(y) = δnm

EOM implies [−esσ

∂5(e−sσ∂5) + M2

Φ

]fn = e2σm2

nfn

Solution is

fn(y) =esσ/2

Nn

[Jα(

mn

keσ) + bα(mn) Yα(

mn

keσ)

]Φ(n) →KK tower with mass mn. Equivalent 4D theory

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Bulk EW Gauge Sector

Bulk EW Gauge group : SU(2)L × SU(2)R × U(1)X

Three neutral gauge bosons: (W 3L ,W

3R ,X )

Two charged gauge bosons: (W±L ,W±R )

Symmetry Breaking:

By Boundary Condition (BC):ZX (−,+) means ZX |y=0 = 0 ; ∂yZX |y=πR = 0

SU(2)R × U(1)X → U(1)Y : (W 3L ,W

3R ,X )→ (W 3

L ,B,ZX )A→ (+,+) ; Z → (+,+) ; ZX → (−,+)

ZX ≡ 1√g 2

x +g 2R

(gRW3R − gXX )→ (−,+) ; W±R → (−,+)

B ≡ 1√g 2

x +g 2R

(gXW3R + gRX )→ (+,+) ; W±L → (+,+)

By VEV of TeV brane Higgs

SU(2)L × U(1)Y → U(1)EM : (W 3L ,B,ZX )→ (A,Z ,ZX )

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Gauge KK States

Gauge Boson

“Zero” modes: A(0),Z (0) ; W(0)L

First KK modes: A(1),Z (1),Z(1)X → Z ′ ; W

(1)L , W

(1)R

EWSB mixes : Z (0) ↔ Z (1) ; Z (0) ↔ Z(1)X ; Z (1) ↔ Z

(1)X

W(0)L ↔W

(1)L ; W

(0)L ↔W

(1)R ; W

(1)L ↔W

(1)R

Mass eigenstates :

“Zero” modes: A,Z ; W±

First KK modes: A1, Z1, ZX1 → Z ′ ; WL1,WR1 →W ′±

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Explaining Flavor in a Warped extra dimension

Bulk fermions explain standard model (SM) Mass hierarchy puzzle

Fermion profiles controlled by bulk mass (cL,R )

L(5)Yuk ⊃

√|g |{

cLk ψLψL + cR k ψRψR +(λ5 ψRψLH + h.c.

)}ΨL(x, y) =

e(2−c)σ

√2πRN0

Ψ(0)L

(x) + . . . N20 =

e2πkR(1/2−c) − 1

2πkR(1/2− c)

h

q

χ Rt

3

rescaled u(y)→

FCNC under control

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4-D KK couplings

f

f

0

1

h

q

χ Rt

3

Integrate S(5) over y → equivalent 4D theory

S(4) =∫

d4x∑

m2nφ

(n)φ(n) + g(nml)4D ψ(n)ψ(m)A(l) + λ

(nm)4D ψ

(n)L ψ

(m)R H

φ(n) →KK tower with mass mn ; Denote φ(1) ≡ φ′; m1 ≡ mKK ∼TeV

Compute overlap integral over y to get 4D couplings

Yukawas: λ(00)4D = λ5D

∫dy f

ψL0 f

ψR0 f H

Gauge couplings: g(001)4D = g5D

∫dy f ψ0 f ψ0 f A

1

nulogo.png

Fermion reps (Model I)

[Agashe, Delgado, May, Sundrum 03]

Complete SU(2)R multiplet

QL ≡ (2, 1)1/6 = (tL, bL)QtR ≡ (1, 2)1/6 = (tR , b

′R )

QbR ≡ (1, 2)1/6 = (t′R , bR )

“Project-out”b′, t ′ zero-modes by (−,+) B.C.

b ↔ b′ mixing

Zbb coupling shifted!

So severe constraints (LEP)

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KK Graviton

[Agashe et al, 07] [Fitzpatrick et al, 07]

mn = xnke−kπr xn = 3.83, 7.02, ...

L ⊃ −C ffG

Λ Tαβh(n)αβ Λ = MPe

−kπr

SM on IR brane

CDF & D0 bounds : m1 > 300− 900 GeV for kMp

=0.01-0.1

ATLAS & CMS reach : 3.5 TeV with 100fb-1

SM in Bulk (flavor)

light fermion couplingshighly suppressedgauge field couplings

1kπr suppressedDecays dominantly tot, h, VLong

gg → h(1) → ZZ → 4`

1.5 2 2.5 3 3.5 4 4.5 5m1GHTeVL

0.001

0.01

0.1

1

10

100

Σ@HggLRS,Hqq�LSM->ZZDHfbL Η<2 cut

various kMp

; SM dashed[Agashe, Davoudiasl, Perez, Soni, 2007]

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Z ′ Overlap Integrals

Define: ξ ≡√kπR = 5.83

Z ′ overlap with Higgs → ξZ ′ overlap with fermions:

Q3L tR other fermions

I+ −1.13ξ + 0.2ξ ≈ 1 −1.13

ξ + 0.7ξ ≈ 3.9 −1.13ξ ≈ −0.2

I− 0.2ξ ≈ 1.2 0.7ξ ≈ 4.1 0

Compared to SMZ ′ couplings to h enhanced (also VL - Equivalence Theorem!)Z ′ couplings to tR enhancedZ ′couplings to χ suppressed

ψL,Rγµ[eQIA1 µ + gZ

(T 3

L − s2WTQ

)IZ1 µ +

gZ ′(T 3

R − s ′2TY

)IZX 1 µ

]ψL,R

nulogo.png

EWSB induced Z ′W+W− coupling

Z (1)V (0)V (0) is zero by orthogonality ...... but induced after EWSB

Using Goldstone equivalence:

φ−

φ+

Z ′

In Unitary Gauge:

Z ′ Z(1)

W (1)+

W+ W+W+

W− W−W−

W (1)−Z(1)ZZ(1)

W+

W−

=

Even though ξ · ( vMKK

)2 suppressed ...

... can be overcome by ( MKK

mZ)2 (from long. pol. vectors)

Hence important to keep

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Z ′decays


Z ′ W−W+

Z ′ h

Z

Z ′ t, b, `+

t, b, `−

Γ(A1 →WLWL) =e2κ2

192π

M5Z ′

m4W

; κ ∝√

kπrc

(mW

MW±1

)2

,

Γ(Z1, ZX 1 →WLWL) =g2

Lc2Wκ2

192π

M5Z ′

m4W

; κ ∝√

kπrc

(mZ

(MZ1 ,MZX 1)

)2

,

Γ(Z1, ZX 1 → ZLh) =g2

Zκ2

192πMZ ′ ; κ ∝

√kπrc ,

Γ(Z ′ → f f ) =(e2, g2

Z )

12π

(κ2

V + κ2A

)MZ ′ .

nulogo.png

Widths & BR’s (For MZ ′ = 2TeV)

A1 Z1 ZX 1

Γ(GeV) BR Γ(GeV) BR Γ(GeV) BRtt 55.8 0.54 18.3 0.16 55.6 0.41bb 0.9 8.7× 10−3 0.12 10−3 28.5 0.21uu 0.28 2.7× 10−3 0.2 1.7× 10−3 0.05 4× 10−4

dd 0.07 6.7× 10−4 0.25 2.2× 10−3 0.07 5.2× 10−4

`+`− 0.21 2× 10−3 0.06 5× 10−4 0.02 1.2× 10−4

W+L W−L 45.5 0.44 0.88 7.7× 10−3 50.2 0.37ZLh - - 94 0.82 2.7 0.02

Total 103.3 114.6 135.6

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Total Widths

MZ ′ = 2TeV A1 Z1 ZX 1

Γ (GeV) 103.3 114.6 135.6

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Z ′decays


Z ′ W−W+

Z ′ h

Z

Z ′ t, b, `+

t, b, `−

MZ′ = 2TeV A1 Z1 ZX 1

Γ (GeV) 103.3 114.6 135.6

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Z ′ Branching Ratios

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pp → Z ′ → W+W− → ` ν j j

Meff ≡ pTjj + pT` + /pT MTWW ≡ 2√p2

Tjj+ m2

W

1e-04

0.001

0.01

0.1

1000 1500 2000 2500 3000 3500 4000

Diff

c.s

. [fb

/GeV

]

MWW, MTWW (GeV)

MWW and MTWW

2TeV Z’ MTWW2TeV Z’ MWW

SM MWW

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pp → Z ′ → W+W− → ` ν j j (Boosted W → (jj))

0

1

2

3

4

5

6

7

8

9

10

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

∆θjj

jj opening angle

2TeV Z’

0

0.005

0.01

0.015

0.02

0.025

0 50 100 150 200

Mjet (GeV)

Jet-mass

Z’ no SmrSM no Smr

Z’ w/ SmrSM w/ Smr

j j Collimation implies forming mW nontrivial : use jet-massIn our study: Jet-mass after Parton shower in Pythia

[Thanks to Frank Paige for discussions]

To account for (HCal) expt. uncert.Smearing by δE = 80%/

√E ; δη, δφ = 0.05

Tracker + ECal (2 cores?) have better resolutions [F. Paige; M. Strassler]

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pp → Z ′ → W+W− → ` ν ` ν

2 ν’s ⇒ cannot reconstruct event

1e-09

1e-08

1e-07

1e-06

1e-05

1e-04

0.001

0 500 1000 1500 2000 2500 3000

Diff

c. s

. [pb

/GeV

]

Mll

Di-lepton invariant mass

2TeV Z’3TeV Z’SM WW

SM τ τ

1e-09

1e-08

1e-07

1e-06

1e-05

1e-04

0.001

0 1000 2000 3000 4000 5000D

iff c

. s. [

pb/G

eV]

MT

Transverse mass

2TeV Z’3TeV Z’SM WW

SM τ τ

Meff ≡ pT`1+ pT`2

+ /pT MTWW ≡ 2√p2

T``+ M2

``

L needed: 100 fb−1 (2 TeV) ; 1000 fb−1 (3 TeV)

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pp → Z ′ → W+W− → ` ν ` ν

Cross-section (in fb) after cuts:

2 TeV Basic cuts |η`| < 2 Meff > 1 TeV MT >1.75 TeV # Evts S/B S/√

B

Signal 0.48 0.44 0.31 0.26 26 0.9 4.9WW 82 52 0.4 0.26 26ττ 7.7 5.6 0.045 0.026 2.6

3 TeV Basic cuts |η`| < 2 1.5 < Meff < 2.75 2.5 < MT < 5 # Evts S/B S/√

B

Signal 0.05 0.05 0.03 0.025 25WW 82 52 0.08 0.04 40 0.6 3.8ττ 7.7 5.6 0.015 0.003 3

# events above is for

2 TeV : 100 fb−1

3 TeV : 1000 fb−1

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pp → Z ′ → W+W− → ` ν j j


MZ ′ = 2 TeV pT η`,j Meff MTWWMjet # Evts S/B S/

√B

Signal 4.5 2.40 2.37 1.6 1.25 125 0.39 6.9W+1j 1.5× 105 3.1× 104 223.6 10.5 3.15 315WW 1.2× 103 226 2.9 0.13 0.1 10

MZ ′ = 3 TeV

Signal 0.37 0.24 0.24 0.12 - 120 0.17 4.6W+1j 1.5× 105 3.1× 104 88.5 0.68 - 680WW 1.2× 103 226 1.3 0.01 - 10


2 TeV : 100 fb−1

3 TeV : 1000 fb−1

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pp → Z ′ → Z h→ `+`− b b (mh = 120 GeV)

1e-08

1e-07

1e-06

1e-05

1e-04

0.001

1000 1500 2000 2500 3000 3500 4000

Diff

c.s

. [pb

/GeV

]

MZh (GeV)

Z h invariant mass

2TeV Z’3TeV Z’SM Z b

SM Z b B

1e-10

1e-09

1e-08

1e-07

1e-06

1e-05

1e-04

0.001

0.01

500 1000 1500 2000 2500

Diff

c.s

. [pb

/GeV

]

pTZ (GeV)

Z pT

2TeV Z’3TeV Z’SM Z b

SM Z b B

How well can we tag high pT b’s ?For εb = 0.4, expect Rj ≈20 – 50; Rc = 5

Two b’s close : ∆Rbb ∼ 0.16

L needed: 200 fb−1 (2 TeV) ; 1000 fb−1 (3 TeV)

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pp → Z ′ → Z h→ `+`− b b (mh = 120 GeV)


MZ ′ = 2 TeV Basic pT , η cos θZh Minv b-tag # Evts S/B S/√

B

Z ′ → hZ → bb `` 0.81 0.73 0.43 0.34 0.14 27 1.1 5.3SM Z + b 157 1.6 0.9 0.04 0.016 3

SM Z + bb 13.5 0.15 0.05 0.01 0.004 0.8SM Z + ql 2720 48 22.4 1.5 0.08 15SM Z + g 505.4 11.2 5.8 0.5 0.025 5SM Z + c 184 1.9 1.1 0.05 0.01 2

MZ ′ = 3 TeV

Z ′ → hZ → bb `` 0.81 0.12 0.05 0.04 0.016 16 2 5.7SM Z + b 157 0.002 0.001 3× 10−4 1.2× 10−4 0.12

SM Z + bb 13.5 0.018 0.014 0.002 0.001 1SM Z + ql 2720 1.1 0.7 0.1 0.005 5SM Z + g 505.4 0.3 0.2 0.03 0.0015 1.5SM Z + c 183.5 0.03 0.02 0.002 4× 10−4 0.4


2 TeV : 200 fb−1

3 TeV : 1000 fb−1

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pp → Z ′ → Z h : Z → j j ; h→ W+W− → j j ` ν(mh = 150 GeV)

1e-10

1e-09

1e-08

1e-07

1e-06

1e-05

1e-04

1000 1500 2000 2500 3000 3500 4000

Diff

c.s

. [pb

/GeV

]

Minv , MT (GeV)

Minv and MT

2TeV Z’ Minv2TeV Z’ MT

3TeV Z’ Minv3TeV Z’ MT

MTZh ≡√

p2TZ

+ m2Z +

√p2

Th+ m2

h

MZ′ = 2 TeV mh = 150 GeV Basic pT , η cos θ MT Mjet # Evts S/B S/√

B

Z ′ → hZ → ` /ET (jj) (jj) 2.4 1.6 0.88 0.7 0.54 54 2.5 11.5

SM W j j 3× 104 35.5 12.7 0.62 0.19 19SM W Z j 184 0.45 0.15 0.02 0.02 2SM W W j 712 0.54 0.2 0.02 0.01 1

MZ′ = 3 TeV mh = 150 GeV

Z ′ → hZ → ` /ET (jj) (jj) 0.26 0.2 0.14 0.06 − 18 1.2 4.7

SM W j j 3× 104 4.1 0.05 − 15


2 TeV : 100 fb−1

3 TeV : 300 fb−1

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pp → Z ′ → `+`−

MZ′ = 2 TeV Basic pT` M`` # Evts S/B S/√

B

Signal 0.1 0.09 0.06 60 0.3 4.2

SM `` 3× 104 5.4 0.2 200SM WW 295 0.03 0.002 2


2 TeV : 1000 fb−1

Experimentally clean, but needs a LOT of luminosity

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pp → Z ′ → tt

1e-08

1e-07

1e-06

1e-05

1e-04

0.001

0.01

0.1

1

10

500 1000 1500 2000 2500

Diff

c.s

. [pb

/GeV

]

pTt (GeV)

Top pT

2TeV Z’3TeV Z’

SM tt

1e-07

1e-06

1e-05

1e-04

0.001

0.01

0.1

1

1000 1500 2000 2500 3000 3500 4000 4500 5000

Diff

c.s

. [pb

/GeV

]

Mtt (GeV)

t t invariant mass

2TeV Z’3TeV Z’

SM tt

MZ′ = 2 TeV Basic pT > 800 1900 < Mtt < 2100

Signal 17 7.2 5.6

SM tt 1.9× 105 31.1 19.1

MZ′ = 3 TeV Basic pT > 1250 2850 < Mtt < 310

Signal 1.7 0.56 0.45

SM tt 1.9× 105 4.1 1.1

nulogo.png

Little RS (LRS) (Z ′ → `+`−)

Vary kπR : (kπR)LRS < (kπR)RS = 35 [Davoudiasl, Perez, Soni 08]

MEW ∼ k e−kπR ; RS: k . Mpl ; LRS: k � Mpl

RS as a theory of flavor! (give-up solution to hierarchy problem)

pp → Z ′LRS → `+`− [Davoudiasl, SG, Soni 09; arXiv:0908.1131]

10 15 20 25 30 35

0.050

0.020

0.010

0.005

kΠr

BR

��

{{

MZ’

=

2TeV

10 15 20 25 30 35

1.00

0.50

5.00

0.10

0.05

kΠr

Σ{{

HfbL

MZ’ = 2

TeV, ,s

= 14 TeV

,s

= 10 TeV

Bkgnd, 14TeV

Bkgnd, ,s=10TeV

1000 2000 3000 4000 5000

0.1

1

10

100

1000

104

MZ’

L5

HfbL-

1

kΠr =

35

kΠr =

21

kΠr =

7

,s=10TeV

1000 2000 3000 4000 5000

0.1

1

10

100

1000

104

MZ’

L5

HfbL-

1

kΠr=35

kΠr=21

kΠr=7

,s=14TeV

nulogo.png

Little RS (LRS) (Z ′ → `+`−)

Vary kπR : (kπR)LRS < (kπR)RS = 35 [Davoudiasl, Perez, Soni 08]

MEW ∼ k e−kπR ; RS: k . Mpl ; LRS: k � Mpl

RS as a theory of flavor! (give-up solution to hierarchy problem)

pp → Z ′LRS → `+`− [Davoudiasl, SG, Soni 09; arXiv:0908.1131]

10 15 20 25 30 35

0.050

0.020

0.010

0.005

kΠr

BR

��

{{

MZ’

=

2TeV

10 15 20 25 30 35

1.00

0.50

5.00

0.10

0.05

kΠrΣ{{

HfbL

MZ’ = 2

TeV, ,s

= 14 TeV

,s

= 10 TeV

Bkgnd, 14TeV

Bkgnd, ,s=10TeV

1000 2000 3000 4000 5000

0.1

1

10

100

1000

104

MZ’

L5

HfbL-

1

kΠr =

35

kΠr =

21

kΠr =

7

,s=10TeV

1000 2000 3000 4000 5000

0.1

1

10

100

1000

104

MZ’

L5

HfbL-

1

kΠr=35

kΠr=21

kΠr=7

,s=14TeV

nulogo.png

W ′±width

100

200

300

400

500

600

700

800

900

1000

1100

1000 1500 2000 2500 3000 3500 4000 4500 5000

Wid

th [

GeV

]

MW’ [GeV]

W’+ → X X

W~

L1

+ (i)W~

R1

+ (i)W~

L1

+ (ii)W~

R1

+ (ii)

nulogo.png

W ′± width and BR

100

200

300

400

500

600

700

800

900

1000

1100

1000 1500 2000 2500 3000 3500 4000 4500 5000

Wid

th [

GeV

]

MW’ [GeV]

W’+ → X X

W~

L1

+ (i)W~

R1

+ (i)W~

L1

+ (ii)W~

R1

+ (ii)

0.0001

0.001

0.01

0.1

1

1000 1500 2000 2500 3000 3500 4000 4500 5000MW’ [GeV]

BR(W~

L1

+ → X X)

tL b-

W+ hTL b

-

χL t-L

Z W+

u d-

νe e+

0.0001

0.001

0.01

0.1

1

1000 1500 2000 2500 3000 3500 4000 4500 5000MW’ [GeV]

BR(W~

R1

+ → X X)

TL b-

χL t-L

Z W+

tL b-

W+ h

u d-

νe e+

nulogo.png

W ′±BR

0.0001

0.001

0.01

0.1

1

1000 1500 2000 2500 3000 3500 4000 4500 5000MW’ [GeV]

BR(W~

L1

+ → X X)

tL b-

W+ hTL b

-

χL t-L

Z W+

u d-

νe e+

0.0001

0.001

0.01

0.1

1

1000 1500 2000 2500 3000 3500 4000 4500 5000MW’ [GeV]

BR(W~

R1

+ → X X)

TL b-

χL t-L

Z W+

tL b-

W+ h

u d-

νe e+

nulogo.png

W ′± → t b → `νb b

Signal c.s. ∼ 1fbBkgnd is single top + QCD W b b .... AND ...tt : hadronically decaying top can fake a b

-1-0.5

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W ′± → t b → `νb b

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Jet Mass (GeV)

Jet Mass : ConSiz=0.4, VetoFrac=0.25

b-jett-jet

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Jet Mass (GeV)

Jet Mass : ConSiz=1.0, VetoFrac=0.2 : 2 TeV

b-jett-jet

Jet-mass cut: cone size 1.0 and 0 < jM < 75 ⇒0.4% of top fakes bL needed: 100 fb−1 (2 TeV)

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W ′± → Z W and W h

W ′± → Z W :

Fully leptonic → L : 100 fb−1 (2 TeV) ; 1000 fb−1 (3 TeV)

Semi leptonic →L : 300 fb−1 (2 TeV) (SM W /Z + 1j large)

W ′± →W h:

mh ≈ 120 : h→ b b

What is b-tagging eff?

mh ≈ 150 : h→W W

Use W jet-mass to reject light jet

L needed: 100 fb−1(2TeV) ; 300 fb−1 (3TeV)

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Measuring Chirality in (pp) ud → W ′+ → t b → `+νbbA Model Independent Study [SG, Han, Lewis, Si, Zhou, 2010: arXiv:1008.3508]

L ⊃ ψu (gLPL + gR PR )ψd W ′Can we measure gud

L,R , g tbL,R ?

Yes, encoded in top polarization!

1 Need to fix u direction:

Statistical only: On avg u carries higher momentum fraction than d

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W’|

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dσ

/d |y

W’|

(p

b)

W’R

W’L

CorrectDirection

Total

Total

CorrectDirection

∴ direction of yW ′ > 0.8 is u direction2 θ` distribution analyzes top polarization

Analyze in top rest frame

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Measuring Chirality (Results)

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la

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/dco

s θla (

pb)

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dσ

/dco

s θla (

fb) W’

RW’

L

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FCNC couplings

hµν(0)ψ(0)ψ(0) : diagonal{A(0), g(0)

}ψ(0)ψ(0) : diagonal (unbroken gauge symmetry){

Z(0),Zx(0)

}ψ(0)ψ(0) : almost diagonal (non-diagonal due to EWSB effect)

hψ(0)ψ(0) : diagonal (only source of mass is 〈h〉 = v)

hµν(1)ψ(0)ψ(0) : off-diagonal{A(1), g(1)

}ψ(0)ψ(0) : off-diagonal{

Z(1),Zx(1)

}ψ(0)ψ(0) : off-diagonal

(i=1,2 almost diagonal)

hµν(0)ψ(0)ψ(1) : 0{A(0), g(0)

}ψ(0)ψ(1) : 0 (unbroken gauge symmetry){

Z(0),Zx(0)

}ψ(0)ψ(1) : off-diagonal (EWSB effect)

hψ(0)ψ(1) : off-diagonal (since Mψ is extra source of mass)

ψ(0) ↔ ψ(1) mixing due to EWSB

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FCCC couplings

W±L(0)ψi(0)ψ

j(0) : g V ij

CKM

{W±L(1),W

±R(1)

}ψ(0)ψ(0) : g V100 [fW (1) fψfψ]

[...] suppressed for i = 1, 2; (Not suppr for bL, tL, tR )

W±L(0)ψ(0)ψ(1) : g V001

[fW (1) fψfψ(1)

]

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Radion

[Csaki et al, 2001, 2007] [Gunion et al, 2004]

Fluctuations of size of extra dimension → scalar d.o.f

L ⊃ rΛT

µµ

SM on IR brane

L ⊃ −r

Λr

(2M2

W W +µW−

µ+ M2

Z ZµZµ)

SM in bulk

L ⊃ −1

2Λr

[1

(kπR)+ ε

]rW−µνW +µν −

1

4Λr

[1

(kπR)+ ε

]rZµνZµν −

1

4Λr

[1

(kπR)+ ε

]rFµνFµν

−2M2

W

Λr

[1−

1

2M2

W R′2(kπR)−ε

2

]rW +µW−

µ −M2

Z

Λr

[1−

1

2M2

Z R′2(kπR)−ε

2

]rZµZµ

Curvature-scalar mixing

L ⊃ ξRH†H leads to r ↔ h mixing

current status of extra dimension (inspired) models

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