extra dimensions at the lhcqft.web/2010/slides/maru.pdfin this talk, we discuss collider signatures...
TRANSCRIPT
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Extra Dimensionsat the LHC
Nobuhito Maru(Chuo Univ.)
7/23/2010 Workshop@YITP
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このトークの目的(世話人からのリクエスト)
“LHCで新しい物理が発見される前夜の今の時代に
どういう高次元模型があり、どのような将来性があり、どのような特徴があるのか、高次元理論からの実験的予言とはどのようなものがあるのか、
など高次元理論のオーバーヴュー”
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Introduction
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Now LHC is working!!
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One of the guiding principles to go beyond the SM⇒ hierarchy problem
Dynamics: TechnicolorSymmetry: Supersymmetry
The purpose of LHC is to search for NEW PHYSICSas well as Higgs hunting
MW << MP
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One of the guiding principles to go beyond the SM⇒ hierarchy problem
Dynamics: TechnicolorSymmetry: SupersymmetryGeometry: Extra Dimensions
The purpose of LHC is to search for NEW PHYSICSas well as Higgs hunting
MW << MP
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Step 1: Looking for a new particle “X”with coupling to the SM fields
Step 2: Identify the most promising production processes for X (QCD processes are better)
Step 3: Calculate σ(pp→X)Step 4: (1) X is stable
(a) EM charged → X behave like μ(b) Color charged → X hadronized (many BKGs)(c) Weakly charged → X like ν as missing energy
(2) X is unstable ⇒ decay to the SM fields (coloress processes are better)
Compute the branching ratioStep 5: Compute σ(SM background processes)
General strategy of collider physics
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Best wayProduction from color particles
+ Decay to colorless states
g
g
l+
l+l−
l−
Z
Z
X
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In this talk, we discuss collider signatures of various models based on extra dimensions
We introduce basic ideas of each model, and does not discuss the model in detail
Off course, we cannot cover all signatures,so focus on the model independent ones
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Plan
1: Introduction 2: KK Graviton
Large Extra Dimensions Warped Extra Dimension Black Holes
3: Universal Extra Dimensions 4: Gauge-Higgs Unification 5: Higgsless Models 6: Higgs7: Radion 8: Summary
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KK Graviton
“Indirect Collider Signals for Extra Dimensions”J.L. Hewett, PRL82 (1999) 4765
“Quantum Gravity and Extra Dimensions at High-Energy Colliders”G.F. Giudice, R. Rattazzi & J.D. Wells, NPB544 (1999) 3
“Searching for the Kaluza-Klein Graviton in Bulk RS Models”A.L. Fitzpatrick, J. Kaplan, L. Randall & L.T. Wang
JHEP 0709 (2007) 013“Warped Gravitons at the CERN LHC and Beyond”
K. Agashe, H. Davoudiasl, G. Perez & A. Soni, PRD76 (2007) 036006
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Large Extra Dimensions
“The Hierarchy Problem and New Dimensions at a Milimeter”
N. Arkani-Hamed, S. Dimopoulos and G. DvaliPLB429 (1998) 263
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( ) ( ) ( ) ( )
2
4 4 4 42 4 2 4* *
12
2*
1 12 2
12
P
n nn n nn
M
n
Pn
S M d x g M V d x g
MRMπ
+ ++ + +
+
= − − = − −
⇒ =
∫ ∫R R
n = 1n = 2n = 3:
n = 6
# of XD R10^12 m1 mm
10 nm:
10^-11 m
Excluded(No deviations up to 200 μm)
(4+n)-dim gravity compactified on n-dim compact space(SM fields are confined on 3-brane)
Lowering the higher dim. Mp to TeV by large extra dimensionsto solve the hierarchy problem
(n-dim torus)
* 1M TeV= If
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Signatures for KK gravitons
1: Virtual graviton exchangeg
l+
l− ( )22
1nP
T P TM s n R
µνρσµν ρσ=−
∑
( ) ( )42 1
*
,nn
h x y T xd xd y
M
µνµν
+∫
Spin sum of the polarization tensors
Log div. for n=2Power div. for n > 2
Cutoff by the string scale MS λ:O(1) constant
g( )nG
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ADD contributions to the Drell-Yan process@LHC
SM prediction
Hewett (1999)
Ms = 2.5 TeV
Ms = 4.0 TeV
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2: Real graviton emission → Missing energy
Tpp jet E→ +
( )nqg qG→ ( )nqq gG→( )ngg gG→
Dominant process
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Giudice, Rattazzi & Wells (1999)
( ) Tqq Z jet g jet E→ + → + ( )νν
2ˆ ˆ: , :Da s M b all s<
c.o.m. energy in the parton collision
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Giudice, Rattazzi & Wells (1999)
( )T
qq Z jet g
jet E
→ +
→ + ( )νν
2ˆ ˆ: , :Da s M b all s<
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Warped Extra Dimension
“A Large Mass Hierarchy from a Small Extra Dimension”(RS1)
“An Alternative to Compactification”(RS2)L. Randall and R. Sundrum
PRL83 (1999) 3370; PRL83 (1999) 4690
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RS1HiggsSM
Planck TeV
2 2 2kyds e dx dx dyµ νµνη−= +
( )[ ] ( ) ( )
( )
( ) ( ) ( ) ( )
2
†4 2 †
exp 4 exp[2 ]
2†4 †exp[ ]
2 12
1 12 2
1 12 2
P
HiggsMkR kR
kH H kR
R
TeV if kR
S y R d x g g D H D H m H H
y R d x D H D H m He H
µν
µνµ ν
π π η
µ νππ
δ π
δ π→−
−
≈
= − − −
→ − −
∫
∫
O
0 modegraviton
TrancatedAdS5
Lowering the Planck scaleby the warp factor
KK gravitons
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Bulk SM in RS
Higgs
Planck TeV
0 modegraviton
To address the flavor physics, the SM fields except Higgs are in the bulk
Agashe, Delgado, May & Sundrum (2003)
(t, b)L
1st ,2nd generationsbR
tRKK gravitons
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Higgs
Planck TeV
0 modegraviton
tRKK gravitons
1st ,2nd generationsbR
KK gravitons & (right-handed)topare localized on TeV brane⇒ they are strongly coupled
(t, b)L
( ) ( )1gg G tt→ → RS
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All coupling to the KK gravitons can be written as
4XXG XXC d xh T µν
µν∫(XX: a pair of fermions or gauge fields)
( )
( ) ( )
( )( )
( )( )
( )
4
1 2 22† 0
1 24 2
1 1 2 1† 101 5 21 1 2 0
4
1 22
3.831 1 23.831
2 1 211
c
c
XX XXG
ssG
ffG kr
ffG kr
XX T C
ss CM L TeV
dyy J yff i D C
M L TeV J ye
J xtt i D C dyy
M L TeV e
µν
µ ν
νµ ν
π ν
νµ ν νπ ν
φ φ
νψ σ ψ
νψ σ ψ
+
− +
−+− +
∂ ∂ =
+ = −
+=
−
∫
∫
( )( )
( )( )
( )( )
( ) ( )
2
21 2 1
1 2 220
4 2 4
3.833.83
3.831 0.473.83
L
L
ggGc c
y J yJ yJ x
dyy J ygg F F C
kr M L TeV J y kr M L TeV
ν
νµρ ν
ρ π π
−
+
= ≈∫
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Cross section of KK graviton productionFitzpatrick, Kaplan, Randall & Wang (2007)
gg -> G
qq -> q’q’WW -> q’q’G
M4=2.5k
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Branching ratios for KK graviton decay
1G tt→ : dominant modeBackground: t tbar from the SM
KK gluon -> t tbar etc
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1gg G tt→ →
Discovery reachFitzpatrick, Kaplan, Randall & Wang (2007)
5σ
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( ) ( )1 4 ,L Lgg G Z Z l l e µ→ → → =
k/MP = 0.5, 1.0, 1.5, 2.0from bottom to top
Agashe, Davoudiasl, Perez & Soni (2007)
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( ) ( )1 4 ,L Lgg G Z Z l l e µ→ → → =
k/MP = 0.5, 1.0, 1.5, 2.0from bottom to top
Agashe, Davoudiasl, Perez & Soni (2007)
1st KK graviton up to around 2TeV can be seen
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Black Hole
“Black Holes at the Large Hadron Collider”S. Dimopoulos & G. Landsberg
PRL87 161602 (2001)
“High Energy Colliders as Black Hole Factories:The End of Short Distance Physics”
S.B. Giddings & S. ThomasPRD65 056010 (2002)
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Production
( ) ( )( ) ( )2 1
22* *
8 3 212
n
BHBH S
nMM RM M n
σ π
+ Γ +
≈ = +
SR
Two partons with moving in opposite directionsˆ BHs M=
If the impact parameter < RS, a BH with MBH forms
Totalcross section
*M ≈TeV with ⇒ BH production/year!!1 /−30fb y 710(comparable to Z production@LEP)
(Schwarzshildradius)
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Decay
BHs, once produced, evapolate @Hawking temp.
1 1004H
S
nT GeVRπ+
= ≈
BH decay to SM particles with rough equal probability:G, q: 72%, l: 11%, Z, W: 8%, ν, graviton: 6%, H: 2%, γ: 1%
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# of BHs produced @LHC in e or γ decay channelwith 100 fb^-1 of integrated luminosity
The shaded regions -> events for n = 2-7
SM bkg from Z(ee) + jets & γ+ jetsSM bkg from Z(ee) + X
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Universal Extra Dimension
“Bounds on Universal Extra Dimensions”T. Appelquist, H-C. Cheng & B. Dobrescu
PRD64 035002 (2001)
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Universal Extra Dimension (UED) model is just a higher dim. extension of the Standard Model
↓All of the SM fields propagate
in extra dimensions of size 1/R ~ TeV(In ADD & RS, some or all of them are confined to 3-brane)
Motivations for UED (although not a solution of the hierarchy problem…)
1: KK parity
KK parity which is a remnant of KK momentum is conserved even after orbifold (-1)^n
ex. Reflection symmetry w.r.t. the center of line segment for S^1/Z2 orbifold
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☆KK parity relaxes the constraints from EWPT ⇒ 1/R > 300 GeV (5D on S^1/Z2) testable @colliders
Appelquist, Cheng & Dobrescu (2001)
☆KK parity naturally predicts a candidate of dark matter“lightest KK particle (LKP)” like a LSP in SUSY w/ R-parity
∵ 1st KK modes are always produced in pairs
2: # of generations from anomaly cancellation (6D)Dobrescu & Poppitz (2001)
3: Proton stability by Lorentz subgroup (6D)Appelquist, Dobrescu, Ponton & Yee (2001)2
8 2Z T Z⊂
Witten anomaly:
( )( ) ( ) ( )6 2 2 2 0 mod 6 0 mod3gWSU N N n+ −Π = − = =⇒
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Decays & products of 1st KK modes (5D on S^1/Z2)
LKP
Dominant transitionRare transition
(Q,L): SU(2)L doublet(q,l): SU(2)L singlet
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Excludedby CDF
Discovery reach for 5D UED in Q1Q1 -> 4l + missing energy
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Gauge-Higgs Unification
“LHC Signals for Coset Electroweak Gauge Bosonsin Warped/Composite PGB Higgs Models”
K. Agashe, A. Azatov, T. Han, Y. Li, Z-G. Si & L. ZhuPRD81 096002 (2010)
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Mass term is forbidden by the gauge symmetry
Higher dimensionalLorentz invariance
Higher dimensional gauge symmetry
Identified with Higgs in the SM
Gauge-Higgs unification
Higgs potential is generated @1-loop and finite due to the higher dim. gauge symmetry
↓
EW scale is stabilized
Ay ⇔ Aμ
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Gauge symmetry breaking: by an orbifold (ex. S^1/Z2)( ) ( )2 1G H SU U→ ⊇ ×
Parity assignments of gauge sector
( ) ( )( ) ( )
( )( )
0
0
HH Hy
H H Hy y y
A yA y A y
A y A y A yµµ µ ∂ =− = ⇔
− = − =
( ) ( )( ) ( )
( )( )
0
0
G H G H G H
G H G H G Hy y y y
A y A y A y
A y A y A yµ µ µ − = − = ⇔
− = ∂ =
H subgroup
G/H coset :
:
H
G Hy
A
Aµ
SU(2) x U(1)Gauge fields
Higgs
Only even mode has a massless mode
Model independent new fields⇒ SU(2) doublet coset gauge boson partner of Higgs
G HAµ
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( )1C Cpp W t pp W t± ±→ → vs
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( )1C Cpp W t pp W t± ±→ → vs
We focus on the low mass region of
∵our goal is to explore thereach of discover of WC
( )1tM
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Dominant channels of WC production & its decay
( ) ( ) ( )1 1 1Cbg W t bt t→ →
b b
( )1tg
( )1tCW ( )1t
( )( ) ( )( )( ) ( )( )
( )( ) ( )( ) ( )( )( )
( ) ( )( )( ) ( )( )( ) ( )
2 21 1
1 1 1
2
2 21 1
1: 3 2 5
90% 50% 22.5%
2 : 7
2 ,
2 90% 50% 45%
3: 9
, 90% 50% 22.5%
C
C
C
b W l jets
Br W t b Br t bW
bbWtH Z l jets
Br W t b Br t bW Br t tH tZ
btH Z tH Z l jets
Br W t b Br t tH tZ
ν
ν
ν
+ → + → × → ≈ × = → +→ × → × → × → ≈ × × =
→ + → × → ≈ × =
( )
( )1 bW
ttH tZ→
![Page 45: Extra Dimensions at the LHCqft.web/2010/slides/maru.pdfIn this talk, we discuss collider signatures of various models based on extra dimensions We introduce basic ideas of each model,](https://reader033.vdocuments.net/reader033/viewer/2022042205/5ea6fa7267bd6b2b514b0cd1/html5/thumbnails/45.jpg)
14s TeV=
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(3 events)(5 events)(15 events)
14s TeV=
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Higgsless Models
“Collider Phenomenology of the Higgsless Models”A. Birkedal, K. Matchev & M. Perelstein,
PRL94 191803 (2005)
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SU(2) x U(1) -> U(1)em by BCs without a Higgs boson???
Higgsless model???
In extra dimensions, the gauge symmetry can be broken by BCs
⇒ New possibility
Immediate question: How unitarizes W/Z scattering amplitudes
without Higgs???
![Page 49: Extra Dimensions at the LHCqft.web/2010/slides/maru.pdfIn this talk, we discuss collider signatures of various models based on extra dimensions We introduce basic ideas of each model,](https://reader033.vdocuments.net/reader033/viewer/2022042205/5ea6fa7267bd6b2b514b0cd1/html5/thumbnails/49.jpg)
(Warped) Model
Planck TeV
2 2 2kyds e dx dx dyµ νµνη−= +AdS5 on an interval
Csaki, Grojean, Pilo & Terning (2003)
SU(2)L x U(1)B-L↓
U(1)y
SU(2)L x SU(2)R↓
SU(2)D
( )3
5 5
35 5 5
0
0
0
R
R
R
A
g B g A
g B g A
µ
µ µ
µ µ
± =
′ − =
′∂ + =( )5
0
0
La Ra
La Ra
A A
A Aµ µ
µ µ
− =
∂ + =
SU(2)L x SU(2)R x U(1)B-L → U(1)em
![Page 50: Extra Dimensions at the LHCqft.web/2010/slides/maru.pdfIn this talk, we discuss collider signatures of various models based on extra dimensions We introduce basic ideas of each model,](https://reader033.vdocuments.net/reader033/viewer/2022042205/5ea6fa7267bd6b2b514b0cd1/html5/thumbnails/50.jpg)
L L L LW Z W Z± ±→
W W W W WW
Z Z ZZZZ
WW
( ) ( ) ( ) ( )0222
42
4
nn
n
nE E MA E ME
A AM M
+
= + +
A O
![Page 51: Extra Dimensions at the LHCqft.web/2010/slides/maru.pdfIn this talk, we discuss collider signatures of various models based on extra dimensions We introduce basic ideas of each model,](https://reader033.vdocuments.net/reader033/viewer/2022042205/5ea6fa7267bd6b2b514b0cd1/html5/thumbnails/51.jpg)
L L L LW Z W Z± ±→
W W W W WW
W W WWZ Z Z
Z Z Z Z
ZZZ
WW
( )nW( )nW
( ) ( ) ( ) ( )0222
42
4
nn
n
nE E MA E ME
A AM M
+
= + +
A O
![Page 52: Extra Dimensions at the LHCqft.web/2010/slides/maru.pdfIn this talk, we discuss collider signatures of various models based on extra dimensions We introduce basic ideas of each model,](https://reader033.vdocuments.net/reader033/viewer/2022042205/5ea6fa7267bd6b2b514b0cd1/html5/thumbnails/52.jpg)
( )( ) ( )
( )( )
( )( ) ( )( ) ( )( )( )
( )
22 4
42 2 2 2
2
22 222 2
2
0
2
3 0
n
n
WWZZ WWZ WZWn
ZWWZZ WWZ W Z WWZ
W
Z WnWWZW nn
W
g g g E
Mg g M M gM
M Mg M E
M±
±
= + ← =
− + +
− = − ← =
∑
∑
O
O
Necessary conditions for unitarity
This sum rule can be satisfied by only the 1st KK modein a good approximation
( ) ( )1
2
13WWZ Z
WZWWW
g MgM M±
≤
These sum rules are automatically satisfied by higher dimensional gauge invariance
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Check this rule by measuring and ( )1WZWg( )1
WM ±
( )( )
21
13WWZ Z
WZVWW
g MgM M±
≤( )
( ) ( )1
1
0.04
700WZW
W
g
M GeV CDF±
≤
≥
for
( )1 3W W Z l ν± ±→ → +“gold-plated”events
LW ± LW ±
LZLZ
q l±νl+
l−
( )1W ±
q
q′′q′
(Independent of model-building details)
![Page 54: Extra Dimensions at the LHCqft.web/2010/slides/maru.pdfIn this talk, we discuss collider signatures of various models based on extra dimensions We introduce basic ideas of each model,](https://reader033.vdocuments.net/reader033/viewer/2022042205/5ea6fa7267bd6b2b514b0cd1/html5/thumbnails/54.jpg)
Check this rule by measuring and ( )1WZWg( )1
WM ±
( )( )
21
13WWZ Z
WZVWW
g MgM M±
≤( )
( ) ( )1
1
0.04
700WZW
W
g
M GeV CDF±
≤
≥
for
( )1 3W W Z l ν± ±→ → +“gold-plated”events
LW ± LW ±
LZLZ
q l±νl+
l−
( )1W ±
q
q′′q′
(Independent of model-building details)
![Page 55: Extra Dimensions at the LHCqft.web/2010/slides/maru.pdfIn this talk, we discuss collider signatures of various models based on extra dimensions We introduce basic ideas of each model,](https://reader033.vdocuments.net/reader033/viewer/2022042205/5ea6fa7267bd6b2b514b0cd1/html5/thumbnails/55.jpg)
Check this rule by measuring and ( )1WZWg( )1
WM ±
( )( )
21
13WWZ Z
WZVWW
g MgM M±
≤( )
( ) ( )1
1
0.04
700WZW
W
g
M GeV CDF±
≤
≥
for
( )1 3W W Z l ν± ±→ → +“gold-plated”events
LW ± LW ±
LZLZ
q l±νl+
l−
( )1W ±
q
q′′q′
(Independent of model-building details)( )1W production
cross sections @LHC
![Page 56: Extra Dimensions at the LHCqft.web/2010/slides/maru.pdfIn this talk, we discuss collider signatures of various models based on extra dimensions We introduce basic ideas of each model,](https://reader033.vdocuments.net/reader033/viewer/2022042205/5ea6fa7267bd6b2b514b0cd1/html5/thumbnails/56.jpg)
# of events in the 2jet + 3l + ν channel
Discovery reach (10 events)550 GeV (1 TeV) requires 10 (60) fb^-1 for 1-2 year
![Page 57: Extra Dimensions at the LHCqft.web/2010/slides/maru.pdfIn this talk, we discuss collider signatures of various models based on extra dimensions We introduce basic ideas of each model,](https://reader033.vdocuments.net/reader033/viewer/2022042205/5ea6fa7267bd6b2b514b0cd1/html5/thumbnails/57.jpg)
Higgs
“Higgs Production from Gluon Fusion in Warped Extra Dimensions”
A. Azatov, M. Toharia & L. Zhu, arXiv:1006.5939
“Gauge-Higgs Unification at the CERN LHC”N. Maru & N. Okada, PRD77 (2008) 055010
“Kaluza-Klein Effects on Higgs Physics in Universal Extra Dimensions”
F.J. Petriello, JHEP05 (2002) 003
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Discovery Mode
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Discovery Mode
2γ decay is a promising mode for mH < 140GeVand well studied
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g
g
γ
γ
( )nt( )
( )
n
n
t
W
H
gg -> H -> γγ
Model information
,,, t W
t W ny g m
![Page 62: Extra Dimensions at the LHCqft.web/2010/slides/maru.pdfIn this talk, we discuss collider signatures of various models based on extra dimensions We introduce basic ideas of each model,](https://reader033.vdocuments.net/reader033/viewer/2022042205/5ea6fa7267bd6b2b514b0cd1/html5/thumbnails/62.jpg)
GHU (5D SU(3))
mh = 120 GeV14% deviation @m1 = 1 TeV
nt = 1
nt = 3
nt = 5
periodicanti-periodic
← 1st KK mass
SM
Maru & Okada (2007)
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Petriello, JHEP05 (2002) 003
UED (5D)
1/R = 500 GeV
1/R = 750 GeV1/R = 1 TeV
1/R = 1.25 TeV, 1.5 TeV
Additive
SM
![Page 64: Extra Dimensions at the LHCqft.web/2010/slides/maru.pdfIn this talk, we discuss collider signatures of various models based on extra dimensions We introduce basic ideas of each model,](https://reader033.vdocuments.net/reader033/viewer/2022042205/5ea6fa7267bd6b2b514b0cd1/html5/thumbnails/64.jpg)
RS with Bulk Higgs
×: 1/R’ = 5 TeV+: 1/R’ = 2 TeV△: 1/R’ = 1.5 TeV
1, 1RS RSgg h hSM SMgg h h
γγ
γγ
σ σσ σ
→ →
→ →
> <
Azatov, Toharia & Zhu, 1006.5939
mH = 120GeV
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×: 1/R’ = 5 TeV+: 1/R’ = 2 TeV△: 1/R’ = 1.5 TeV
RS with Brane Higgs
Sign cannot be predicted
Azatov, Toharia & Zhu, 1006.5939
mH = 120GeV
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Radion
“Graviscalars from Higher-Dimensional Metrics and Curvature-Higgs Mixing”
G.F. Giudice, R. Rattazzi & J.D. Wells
“Radion Phenomenology on Realistic Warped Space Models”C. Csaki, J. Hubisz & S.J. Lee, PRD76 (2007) 125015
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( ) ( )
( )( ) ( ) ( )( )
222 2
222 2 1
1 2
1 2 1/
ky F
F
ds e F dy
R e dx dx F dz R k z R TeVz
µν
µ νµν
η
η
− +
− −
= − +
′= − + = < < =
Radion is a scalar perturbation of the metric which cannot be gauged away
( )( )
5
25 55
55
12
1 2
MNradion MN
r
S d x gT g
zd x g r x T T gR
µµ
δ= −
= − ′Λ
∫
∫
Radion-Matterinteraction
( ) ( ) ( ) ( )2 221 6, ,
6 rr
r xR z zF z x r x TeVR R R R
= = Λ ≡ ≈ ′ ′ ′Λ
4D canonically normalized radion r(x) Localized on TeV brane
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( ) ( ) ( ), ,L R UV UV IR IR L R Lr r
m mc c r others r t bψ ψ ψ ψ−Λ Λ
( ) ( )2 2
2 22 2
3 32 11 log 1 logW ZW Z
r r r r
M MkR M rW W kR M rZ Zµ µµ µ
′ ′− + + − + Λ Λ Λ Λ
( ) ( )( )( ) ( )
0 01 4
4log 8UV IR
i i ii r
rb F F FkR
µνµν
πα τ τ α κ τπ
− + − + − ′ Λ ∑
Coupling to the SM fermions
Coupling to massive gauge bosons (W, Z)
Coupling to massless gauge bosons (γ, g)
Brane kinetic term Trace anomaly
1-loop effects
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Bulk RS1 RS1Λr = 2 TeV
Branching fraction of the radion
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Branching fraction of Higgs
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Bulk RS1 RS1Λr = 2 TeV
Branching fraction of the radion
Very similar behavior to Higgs boson (Λr ⇔ v), but Br(r -> gg) can be enhanced by comparing to Br(H -> gg)
by a factor “10” due to the radion coupling through the trace anomaly
![Page 72: Extra Dimensions at the LHCqft.web/2010/slides/maru.pdfIn this talk, we discuss collider signatures of various models based on extra dimensions We introduce basic ideas of each model,](https://reader033.vdocuments.net/reader033/viewer/2022042205/5ea6fa7267bd6b2b514b0cd1/html5/thumbnails/72.jpg)
Ratio of gg -> r -> γγ/gg -> H -> γγ
Bulk RS1 RS1
SM
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Summary
Now, “Extra Dimensions” as an alternative to solution to the hierarchy problem
is no longer alternative
KK particles with TeV mass
These give rise to various collider signatures@LHC!!
Let us expect that the news of discovery of extra dimensions
will come soon!!
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Backup
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KK Gluon
“The Bulk RS KK-gluon at the LHC”B. Lillie, L. Randall & L-T. Wang, JHEP09 (2007) 074
“CERN LHC Signals from Warped Extra Dimensions”K. Agashe, A. Belyaev, T. Krupovnicas, G. Perez & J. Virzi
PRD77 (2008) 015003
![Page 76: Extra Dimensions at the LHCqft.web/2010/slides/maru.pdfIn this talk, we discuss collider signatures of various models based on extra dimensions We introduce basic ideas of each model,](https://reader033.vdocuments.net/reader033/viewer/2022042205/5ea6fa7267bd6b2b514b0cd1/html5/thumbnails/76.jpg)
Bulk SM in RS
Higgs
Planck TeV
0 modegraviton
tRKK gluons1st ,2nd generations
bR
KK gluons and (right-handed) topare localized on IR brane
↓KK gluons strongly couple to top
(t, b)L
![Page 77: Extra Dimensions at the LHCqft.web/2010/slides/maru.pdfIn this talk, we discuss collider signatures of various models based on extra dimensions We introduce basic ideas of each model,](https://reader033.vdocuments.net/reader033/viewer/2022042205/5ea6fa7267bd6b2b514b0cd1/html5/thumbnails/77.jpg)
Wave function of 1st KK gluon
( )( )
( )( )1 1
11 1
k k km me J e Y ek k
πφ πφ πφχ φ α
∝ +
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Coupling of 1st KK gluon to zero mode fermion
( )( )
1 3 210.8
ffAc
SM c
gkr
g krπ
π− + O
UVlocalized
IRlocalized
Q3L tR
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Cross section for production of 1st KK gluon
![Page 80: Extra Dimensions at the LHCqft.web/2010/slides/maru.pdfIn this talk, we discuss collider signatures of various models based on extra dimensions We introduce basic ideas of each model,](https://reader033.vdocuments.net/reader033/viewer/2022042205/5ea6fa7267bd6b2b514b0cd1/html5/thumbnails/80.jpg)
Branching ratio of 1st KK gluon
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Invariant mass distribution of ( )1g tt→
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pp → jet + missing energy
Vacavant & Hinchliffe (2001)
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( ) ( ) ( ), ,s
e k s e k s P kµν αβ µναβ=∑
( ) ( )
( )
2 2
2
121 2 26
12
n n
n
P k
k k k km m
k k k k k k k km
µναβ µα νβ µβ να µν αβ
µν µ ν αβ α β
µα ν β νβ µ α µβ ν α να µ β
η η η η η η
η η
η η η η
= + −
+ + +
− + + +
Spin sum of polarization tensors
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Anomaly cancellation
6D Anomaly = One-loop Square diagram
SU(3)C ⇒ ⇒Q ⇔ U, D
Oppositechirality
Gravitational N+ = N-⇒
Q+, U-, D-, L-, E+, N+ & (+ ⇔ -)Q+, U-, D-, L+, E-, N- & (+ ⇔ -)
4 possibilities
Arkani-Hamed, Cheng, Dobrescu & Hall (2000)Dobrescu & Poppitz (2001)
( ) ( )a b c d a b c dTr T T T T Tr T T T T+ −
−∑ ∑
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SU(2)W x U(1)Y sector
SU(2)W x U(1)Y anomalies cannot be canceled by the SM matter, but GS mechanism helps
[SU(2)W]^4, [U(1)Y]^4, [SU(2)W]^2[SU(3)C]^2, [SU(3)C]^2[U(1)Y]^2, [SU(2)W]^2[U(1)Y]^2[SU(2)W]^3 = 0 (identically), [SU(3)C]^3U(1)Y = 0 (per generation)
Global anomaly Π6(G): nontrivial if G= SU(3), SU(2), G2
Π6[SU(3)]: trivial ∵ SU(3)C is vector-like
SU(2)L: N(2+) - N(2-) = 0 mod 6→ ng [N(2+) - N(2-)] = 0 mod 6 ⇒ ng = 0 mod 3
[∵ N(Q)=3, N(L)=1]
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( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( ) ( )
( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( )
3
2 2
4
4 4 4 4
2 2
2 2
1 2 1 2 2 13 (1) 3 06 3 3 6 3 3
1 4 1 2 4 1 13 1 3 336 9 9 36 9 9 2
6 16 3 3 2 1 136 243 951 16 3 3 2 216 54
1 13 2 3 2 3 22 2
32 1 236
SU U A Q A U A D A
SU U C Q C U C D C C
U
SU SU C C C C
SU U C
= + − = − + = = − − = − − = −
× + += + + + + = =
= = =
= ± ( ) ( ) ( )
( ) ( ) ( )( ) ( )( ) ( ) ( )2 2 2 2
1 1 12 2 24 3 6
2 2 3 2 2 2 2 2
C C C
SU SU C C C C
= −
= ± =
or
or
Reducible anomalies
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Discovery significance of gg -> r -> γγ
( )
( )
( ) ( )
( ) ( )
0
03
0 13 3
0 13 3
0
0
2
EMτ
τ
τ τ
τ τ
=
=
=
=
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Discovery significance of gg -> r -> ZZ -> 4l
( )
( )
( ) ( )
( ) ( )
0
03
0 13 3
0 13 3
0
0
2
EMτ
τ
τ τ
τ τ
=
=
=
=
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( )( ) ( )
( )( ) ( )( ) ( )( ) ( )( )( )
( )
2 42
22 24 2 2 22 2 2 222
0
2 3 0
nWWZZ WWZ WZV
n
Z Wn nZWWZZ WWZ W Z WWZ WZV W
nnW W
g g g A
M MMg g M M g g M AM M
±
±
= + ← =
− − + + = − ← =
∑
∑
( )( )( )( ) ( )
22 2
2 22 2 2 04 3
iWWWW WWZ WW WWV
i
iWWWW W WWZ Z WWV i
i
g g g g
g M g M g M
γ= + +
= +
∑
∑
Sum Rules
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×: 1/R’ = 5 TeV+: 1/R’ = 2 TeV△: 1/R’ = 1.5 TeV
Azatov, Toharia & Zhu, 1006.5939
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Angular dependences of gg -> G(V,S) -> t tbar
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Branching fractions
( ) ( )( ) ( )( ) ( )( )( ) ( )( ) ( )
1 1 0 1 1 0
2 31 1 0 1 1 0
1 1 0 1 1 0
1 1 0
1 1 0 1 1 0
1 1 0 1 1 0
0.5
0.65 10 10
0.33 1
0.02
1 6
1 6
B g Q Q B g q q
B Q W Q B q Z q
B Q Z Q B q q
B Q Q
B W L B W L
B Z B Z L L
γ
γ
ν ν
ν ν
± − −
± ± ± ±
±
→ ≈ → ≈
→ ≈ → ≈ −
→ ≈ → ≈
→ ≈
→ = → =
→ = → ≈
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( ) ( )
( )
2 2
1 22 2
2
32
1 1, , ,36 96
3 1 ,16
m S m S
P P
m S
P
d dt m t mqq gG F qG gG Fdt sM s s dt sM s s
d t mgg gG Fdt sM s s
σ α σ α
σ α
→ = → =
→ =
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Total cross section
DifferentialCross section
HawkingTemp.
n=4n=4
n=4
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Ratio of gg -> r -> ZZ-> 4l/gg -> H -> ZZ -> 4l
Bulk RS1 RS1
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Similar type of deviations from the SM are also seen in 1: SUSY model Djouadi, PLB453 (1998) 1012: Little Higgs model Han, Logan, McElrath & Wang, PLB563 (2003) 191
Common feature among GHU, SUSY & LH is that the quadratic divergence in mh^2 is canceled
This can be seen diagrammatically as follows
h h
Start with Higgs self-energy diagramwith a relative minus sign
hhTop Newparticles
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Similar type of deviations from the SM are also seen in 1: SUSY model Djouadi, PLB453 (1998) 1012: Little Higgs model Han, Logan, McElrath & Wang, PLB563 (2003) 191
Common feature among GHU, SUSY & LH is that the quadratic divergence in mh^2 is canceled
This can be seen diagrammatically as follows
<h> h
Replace one of the Higgs by its VEV
h<h>Top Newparticles
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Similar type of deviations from the SM are also seen in 1: SUSY model Djouadi, PLB453 (1998) 1012: Little Higgs model Han, Logan, McElrath & Wang, PLB563 (2003) 191
Common feature among GHU, SUSY & LH is that the quadratic divergence in mh^2 is canceled
This can be seen diagrammatically as follows
<h> h
Attaching 2 gluon lines ⇒ gluon fusion diagram with a relative minus sign
<h> hTop Newparticles
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Bulk RS1 RS1
Branching fraction of the radion
Λr = 2 TeV