Current Status of Extra Dimension (inspired) Models
Transcript of 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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
LHC KK-gluon → tt search
Limit: MKK > 2.2TeV @ 95%CL[ATLAS 1505.07018; CMS 1309.2030]
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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
W ′ cross section
[Agashe, SG, Han, Huang, Soni, 0810.1497]
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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
LHC Data (W ′ → WZ )
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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
VL-fermions direct @ LHC
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
VL-fermions direct @ LHC
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
VL-fermions direct @ LHC
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
VL-fermions direct @ LHC
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
VL-fermions direct @ LHC
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
VL-fermions direct @ LHC
b′ Single Production - II
Single Production : bg → b′Z → bZZ → bjj``
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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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
VL-fermions direct @ LHC
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
VL-fermions direct @ LHC
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
VL-fermions direct @ LHC
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
VL-fermions direct @ LHC
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
VL-fermions direct @ LHC
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
VL-fermions direct @ LHC
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
SM-like VLF - EWPT & Higgs Observables
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
SM-like VLF - EWPT & Higgs Observables
22 + 11 : MVQD
λD = 1, MD = MQ , YQ = (1/6,−1/6) (solid, dashed)
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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
SM-like VLF - EWPT & Higgs Observables
22 + 11 : MVQD
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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
LSS model scan; fine-tuning
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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
LSS model φgg effective coupling (φ = A,H)
L =κφgg
64π2 (1 TeV )φGG
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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
LSS model BRs
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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
Model Independent LHC Limits/Prospects
[SG, Soumya Sadhukhan, Tuhin Subhra Mukherjee: 1504.01074]
5pb
8TeV
1pb
.1pb
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\
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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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Models LHC Probes KK-graviton KK-gluon Z ′ W ′ Vector-like fermions Heavy scalars (2HDM) Flavor aspects
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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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
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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
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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
[Agashe, Davoudiasl, SG, Han, Huang, Perez, Si, Soni - arXiv:0709.0007 [hep-ph]]
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 ′ .
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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
[Agashe, Davoudiasl, SG, Han, Huang, Perez, Si, Soni - arXiv:0709.0007 [hep-ph]]
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
Cross-section (in fb) after cuts:
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
# events above is for
2 TeV : 100 fb−1
3 TeV : 1000 fb−1
nulogo.png
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)
nulogo.png
pp → Z ′ → Z h→ `+`− b b (mh = 120 GeV)
Cross-section (in fb) after cuts:
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
# events above is for
2 TeV : 200 fb−1
3 TeV : 1000 fb−1
nulogo.png
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
# events above is for
2 TeV : 100 fb−1
3 TeV : 300 fb−1
nulogo.png
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
# events above is for
2 TeV : 1000 fb−1
Experimentally clean, but needs a LOT of luminosity
nulogo.png
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
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
0 0.5
1 -1-0.5
0 0.5
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
pTi/pTtot
b-jet Event Jet Cluster (diff)
b Evt 2
dEtadPhi
pTi/pTtot
-1-0.5
0 0.5
1 -1-0.5
0 0.5
1
0 0.05
0.1 0.15
0.2 0.25
0.3 0.35
0.4
pTi/pTtot
t-jet Event Jet Cluster (diff)
t Evt 4
dEtadPhi
pTi/pTtot
-1-0.5
0 0.5
1 -1-0.5
0 0.5
1
0 0.05
0.1 0.15
0.2 0.25
0.3
pTi/pTtot
b-jet Event Jet Cluster (diff)
b Evt 4
dEtadPhi
pTi/pTtot
-1-0.5
0 0.5
1 -1-0.5
0 0.5
1
0 0.05
0.1 0.15
0.2 0.25
0.3 0.35
0.4 0.45
pTi/pTtot
t-jet Event Jet Cluster (diff)
t Evt 3
dEtadPhi
pTi/pTtot
nulogo.png
W ′± → t b → `νb b
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0 50 100 150 200 250
Jet Mass (GeV)
Jet Mass : ConSiz=0.4, VetoFrac=0.25
b-jett-jet
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0 50 100 150 200 250
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)
nulogo.png
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)
nulogo.png
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)
nulogo.png
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
0 0.5 1 1.5 2 2.5/0 0.5 1 1.5 2 2.5|y
W’|
0
0.1
0.2
0.3
0.4
0.5
0.6
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
nulogo.png
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
0 0.5 1 1.5 2 2.5/0 0.5 1 1.5 2 2.5|y
W’|
0
0.1
0.2
0.3
0.4
0.5
0.6
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
nulogo.png
Measuring Chirality (Results)
-1 -0.5 0 0.5 1cos θ
la
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
dσ
/dco
s θla (
pb)
W’R
W’L
-1 -0.5 0 0.5 1cos θ
la
0
50
100
150
dσ
/dco
s θla (
fb) W’
RW’
L
nulogo.png
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
nulogo.png
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)
]
nulogo.png
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