"curved extra-dimensions" by nicolas deutschmann (institut de physique nucleaire de lyon,...
DESCRIPTION
Abstract: Universal Extra-Dimension models provide a promising framework for model building as they naturally have rich phenomenological implications, not the least of which is a potential natural dark matter candidate. This candidate takes the form of a Kaluza-Klein excitation of some neutral Standard Model field whose stability is ensured by some isometry of the extra-space. In five dimensions, such a symmetry has to be enforced in an ad-hoc fashion, which is why six-dimensional models have started prompting the interest of model builders. If flat 6D models have been thoroughly surveyed and studied, the realm of curved extra-dimensional models remains mostly uncharted. This talk aims at showing the features of extra dimensional models on a curved background, focusing mostly on positively curved spaces. I will show that the main difficulty for constructing a convincing model revolves around the issue of chiral fermions in the 4D effective theory and how it can be overcome by the addition of a new gauge field which has to be hidden from experimental reach by a symmetry breaking. After going over the phenomenological consequences of a model built using these ingredients, I will briefly review hyperbolic extra-dimensions, for which several problems appearing on positively curved spaces are solved or alleviated.TRANSCRIPT
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CURVEDEXTRA-DIMENSIONS
Nicolas Deutschmann
Work in progress with Giacomo Cacciapaglia and Aldo Deandrea
University of the Witwatersrand, JohannesburgNITheP, July 22th 2014
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Outline
Introduction: Why 2UED is attractive
Survey of Positively Curved Geometries
A UED model with Bulk fermions
Localizing fermions
Conclusion: A negative future ?
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Introduction: Why 2UED isattractive
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Dark Matter!
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Ad hoc parities
Many theoretically satisfying solutions to the short-comings ofthe Standard Model
• Hierarchy: SuSy, RS,Little Higgs
• Neutrinos: See-Saw• Dark Matter: often a
by-product of othermodels with additionalad hoc parity (R-parity,KK-parity...)
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Ad hoc parities
Many theoretically satisfying solutions to the short-comings ofthe Standard Model
• Hierarchy: SuSy, RS,Little Higgs
• Neutrinos: See-Saw• Dark Matter: often a
by-product of othermodels with additionalad hoc parity (R-parity,KK-parity...)
Nicolas Deutschmann Curved Extra-Dimensions 5/25...
5/25
![Page 7: "Curved extra-dimensions" by Nicolas Deutschmann (Institut de Physique Nucleaire de Lyon, France)](https://reader033.vdocuments.net/reader033/viewer/2022052600/5585a37dd8b42a7b1a8b4871/html5/thumbnails/7.jpg)
.
Ad hoc parities
Many theoretically satisfying solutions to the short-comings ofthe Standard Model
• Hierarchy: SuSy, RS,Little Higgs
• Neutrinos: See-Saw
• Dark Matter: often aby-product of othermodels with additionalad hoc parity (R-parity,KK-parity...)
Nicolas Deutschmann Curved Extra-Dimensions 5/25...
5/25
![Page 8: "Curved extra-dimensions" by Nicolas Deutschmann (Institut de Physique Nucleaire de Lyon, France)](https://reader033.vdocuments.net/reader033/viewer/2022052600/5585a37dd8b42a7b1a8b4871/html5/thumbnails/8.jpg)
.
Ad hoc parities
Many theoretically satisfying solutions to the short-comings ofthe Standard Model
• Hierarchy: SuSy, RS,Little Higgs
• Neutrinos: See-Saw• Dark Matter: often a
by-product of othermodels with additionalad hoc parity (R-parity,KK-parity...)
Nicolas Deutschmann Curved Extra-Dimensions 5/25...
5/25
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.
Ad hoc parities
Many theoretically satisfying solutions to the short-comings ofthe Standard Model
• Hierarchy: SuSy, RS,Little Higgs
• Neutrinos: See-Saw• Dark Matter: often a
by-product of othermodels with additionalad hoc parity (R-parity,KK-parity...)
Nicolas Deutschmann Curved Extra-Dimensions 5/25...
5/25
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A potential solution in the UED frame work
Universal Extra-Dimensions: all fields propagate in the bulk
• (4 + n)D space: M4 × Xn a compact space
• The eigenmodes of all fields in Xn create a KK-tower.• Isometries of Xn: Noether theorem imposes selection rules for
decays
A stable excitation of a neutral SM field could be Dark Matter!
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A potential solution in the UED frame work
Universal Extra-Dimensions: all fields propagate in the bulk
• (4 + n)D space: M4 × Xn a compact space• The eigenmodes of all fields in Xn create a KK-tower.
• Isometries of Xn: Noether theorem imposes selection rules fordecays
A stable excitation of a neutral SM field could be Dark Matter!
Nicolas Deutschmann Curved Extra-Dimensions 6/25...
6/25
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.
A potential solution in the UED frame work
Universal Extra-Dimensions: all fields propagate in the bulk
• (4 + n)D space: M4 × Xn a compact space• The eigenmodes of all fields in Xn create a KK-tower.• Isometries of Xn: Noether theorem imposes selection rules for
decays
A stable excitation of a neutral SM field could be Dark Matter!
Nicolas Deutschmann Curved Extra-Dimensions 6/25...
6/25
![Page 13: "Curved extra-dimensions" by Nicolas Deutschmann (Institut de Physique Nucleaire de Lyon, France)](https://reader033.vdocuments.net/reader033/viewer/2022052600/5585a37dd8b42a7b1a8b4871/html5/thumbnails/13.jpg)
.
A potential solution in the UED frame work
Universal Extra-Dimensions: all fields propagate in the bulk
• (4 + n)D space: M4 × Xn a compact space• The eigenmodes of all fields in Xn create a KK-tower.• Isometries of Xn: Noether theorem imposes selection rules for
decays
A stable excitation of a neutral SM field could be Dark Matter!
Nicolas Deutschmann Curved Extra-Dimensions 6/25...
6/25
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Why go to curved (n ≥ 2) UED ?Two limiting factors: Isometries and fermions
1UED
Odd dimensions: no chiralfermions
Classical trick on S1/Z2for a chiral zero-mode
(unique)No symmetry
2UED
Chiral fermions, butconstructed from bothleft- and right-handed
WeylsSimilar tricks for some
R2/GExactly one flat geometry
(Cacciapaglia et al.)
With greater dimensions comes greater freedomNo systematic survey of curved spaces
Nicolas Deutschmann Curved Extra-Dimensions 7/25...
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Why go to curved (n ≥ 2) UED ?Two limiting factors: Isometries and fermions
1UEDOdd dimensions: no chiral
fermions
Classical trick on S1/Z2for a chiral zero-mode
(unique)No symmetry
2UED
Chiral fermions, butconstructed from bothleft- and right-handed
WeylsSimilar tricks for some
R2/GExactly one flat geometry
(Cacciapaglia et al.)
With greater dimensions comes greater freedomNo systematic survey of curved spaces
Nicolas Deutschmann Curved Extra-Dimensions 7/25...
7/25
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.
Why go to curved (n ≥ 2) UED ?Two limiting factors: Isometries and fermions
1UEDOdd dimensions: no chiral
fermionsClassical trick on S1/Z2for a chiral zero-mode
(unique)
No symmetry
2UED
Chiral fermions, butconstructed from bothleft- and right-handed
WeylsSimilar tricks for some
R2/GExactly one flat geometry
(Cacciapaglia et al.)
With greater dimensions comes greater freedomNo systematic survey of curved spaces
Nicolas Deutschmann Curved Extra-Dimensions 7/25...
7/25
![Page 17: "Curved extra-dimensions" by Nicolas Deutschmann (Institut de Physique Nucleaire de Lyon, France)](https://reader033.vdocuments.net/reader033/viewer/2022052600/5585a37dd8b42a7b1a8b4871/html5/thumbnails/17.jpg)
.
Why go to curved (n ≥ 2) UED ?Two limiting factors: Isometries and fermions
1UEDOdd dimensions: no chiral
fermionsClassical trick on S1/Z2for a chiral zero-mode
(unique)No symmetry
2UED
Chiral fermions, butconstructed from bothleft- and right-handed
WeylsSimilar tricks for some
R2/GExactly one flat geometry
(Cacciapaglia et al.)
With greater dimensions comes greater freedomNo systematic survey of curved spaces
Nicolas Deutschmann Curved Extra-Dimensions 7/25...
7/25
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.
Why go to curved (n ≥ 2) UED ?Two limiting factors: Isometries and fermions
1UEDOdd dimensions: no chiral
fermionsClassical trick on S1/Z2for a chiral zero-mode
(unique)No symmetry
2UED
Chiral fermions, butconstructed from bothleft- and right-handed
WeylsSimilar tricks for some
R2/GExactly one flat geometry
(Cacciapaglia et al.)
With greater dimensions comes greater freedom
No systematic survey of curved spaces
Nicolas Deutschmann Curved Extra-Dimensions 7/25...
7/25
![Page 19: "Curved extra-dimensions" by Nicolas Deutschmann (Institut de Physique Nucleaire de Lyon, France)](https://reader033.vdocuments.net/reader033/viewer/2022052600/5585a37dd8b42a7b1a8b4871/html5/thumbnails/19.jpg)
.
Why go to curved (n ≥ 2) UED ?Two limiting factors: Isometries and fermions
1UEDOdd dimensions: no chiral
fermionsClassical trick on S1/Z2for a chiral zero-mode
(unique)No symmetry
2UEDChiral fermions, but
constructed from bothleft- and right-handed
Weyls
Similar tricks for someR2/G
Exactly one flat geometry(Cacciapaglia et al.)
With greater dimensions comes greater freedom
No systematic survey of curved spaces
Nicolas Deutschmann Curved Extra-Dimensions 7/25...
7/25
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.
Why go to curved (n ≥ 2) UED ?Two limiting factors: Isometries and fermions
1UEDOdd dimensions: no chiral
fermionsClassical trick on S1/Z2for a chiral zero-mode
(unique)No symmetry
2UEDChiral fermions, but
constructed from bothleft- and right-handed
WeylsSimilar tricks for some
R2/G
Exactly one flat geometry(Cacciapaglia et al.)
With greater dimensions comes greater freedom
No systematic survey of curved spaces
Nicolas Deutschmann Curved Extra-Dimensions 7/25...
7/25
![Page 21: "Curved extra-dimensions" by Nicolas Deutschmann (Institut de Physique Nucleaire de Lyon, France)](https://reader033.vdocuments.net/reader033/viewer/2022052600/5585a37dd8b42a7b1a8b4871/html5/thumbnails/21.jpg)
.
Why go to curved (n ≥ 2) UED ?Two limiting factors: Isometries and fermions
1UEDOdd dimensions: no chiral
fermionsClassical trick on S1/Z2for a chiral zero-mode
(unique)No symmetry
2UEDChiral fermions, but
constructed from bothleft- and right-handed
WeylsSimilar tricks for some
R2/GExactly one flat geometry
(Cacciapaglia et al.)
With greater dimensions comes greater freedom
No systematic survey of curved spaces
Nicolas Deutschmann Curved Extra-Dimensions 7/25...
7/25
![Page 22: "Curved extra-dimensions" by Nicolas Deutschmann (Institut de Physique Nucleaire de Lyon, France)](https://reader033.vdocuments.net/reader033/viewer/2022052600/5585a37dd8b42a7b1a8b4871/html5/thumbnails/22.jpg)
.
Why go to curved (n ≥ 2) UED ?Two limiting factors: Isometries and fermions
1UEDOdd dimensions: no chiral
fermionsClassical trick on S1/Z2for a chiral zero-mode
(unique)No symmetry
2UEDChiral fermions, but
constructed from bothleft- and right-handed
WeylsSimilar tricks for some
R2/GExactly one flat geometry
(Cacciapaglia et al.)
With greater dimensions comes greater freedomNo systematic survey of curved spaces
Nicolas Deutschmann Curved Extra-Dimensions 7/25...
7/25
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Survey of Positively CurvedGeometries
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Positively curved geometries
.Uniformization theorem..
.All positively curved 2D surfaces can be described as S2/G withG a discrete subgroup of O(3)
First question: Which of these have non-trivial isometries ?Fundamental relation:
S ∈ Isom(S2/G) ⇐⇒ ∀g ∈ G, ∃h ∈ G|S(g(x)) = h(S(x))
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.
Positively curved geometries
.Uniformization theorem..
.All positively curved 2D surfaces can be described as S2/G withG a discrete subgroup of O(3)
First question: Which of these have non-trivial isometries ?
Fundamental relation:
S ∈ Isom(S2/G) ⇐⇒ ∀g ∈ G, ∃h ∈ G|S(g(x)) = h(S(x))
Nicolas Deutschmann Curved Extra-Dimensions 9/25...
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.
Positively curved geometries
.Uniformization theorem..
.All positively curved 2D surfaces can be described as S2/G withG a discrete subgroup of O(3)
First question: Which of these have non-trivial isometries ?Fundamental relation:
S ∈ Isom(S2/G) ⇐⇒ ∀g ∈ G, ∃h ∈ G|S(g(x)) = h(S(x))
Nicolas Deutschmann Curved Extra-Dimensions 9/25...
9/25
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.
Orbifolds with symmetries
(a) S2/Cn (b) S2/Cnh (c) S2/Sn (d) S2/Dn
Next question: Which of this can embed 4D chiral fermions ?
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.
Orbifolds with symmetries
(a) S2/Cn (b) S2/Cnh (c) S2/Sn (d) S2/Dn
Next question: Which of this can embed 4D chiral fermions ?
Nicolas Deutschmann Curved Extra-Dimensions 10/25...
10/25
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.
Orbifolds with symmetries
(a) S2/Cn (b) S2/Cnh (c) S2/Sn (d) S2/Dn
Next question: Which of this can embed 4D chiral fermions ?
Nicolas Deutschmann Curved Extra-Dimensions 10/25...
10/25
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A UED model with Bulkfermions
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11/25
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A gauge field to kill the connection
Method from Randjbar-Daemi, Salam and Strathdee
Add an extra U(1) gauge field X
The connection term in the two Weyl spinors of a chiral 6Dspinors become different:
∇χ = ∂χ + (X + Ω)η ∇η = ∂η + (X − Ω)χ
If X cancels ±Ω one of the chiralities has a zero-mode.
Nicolas Deutschmann Curved Extra-Dimensions 12/25...
12/25
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.
A gauge field to kill the connection
Method from Randjbar-Daemi, Salam and Strathdee
Add an extra U(1) gauge field X
The connection term in the two Weyl spinors of a chiral 6Dspinors become different:
∇χ = ∂χ + (X + Ω)η ∇η = ∂η + (X − Ω)χ
If X cancels ±Ω one of the chiralities has a zero-mode.
Nicolas Deutschmann Curved Extra-Dimensions 12/25...
12/25
![Page 33: "Curved extra-dimensions" by Nicolas Deutschmann (Institut de Physique Nucleaire de Lyon, France)](https://reader033.vdocuments.net/reader033/viewer/2022052600/5585a37dd8b42a7b1a8b4871/html5/thumbnails/33.jpg)
.
A gauge field to kill the connection
Method from Randjbar-Daemi, Salam and Strathdee
Add an extra U(1) gauge field X
The connection term in the two Weyl spinors of a chiral 6Dspinors become different:
∇χ = ∂χ + (X + Ω)η ∇η = ∂η + (X − Ω)χ
If X cancels ±Ω one of the chiralities has a zero-mode.
Nicolas Deutschmann Curved Extra-Dimensions 12/25...
12/25
![Page 34: "Curved extra-dimensions" by Nicolas Deutschmann (Institut de Physique Nucleaire de Lyon, France)](https://reader033.vdocuments.net/reader033/viewer/2022052600/5585a37dd8b42a7b1a8b4871/html5/thumbnails/34.jpg)
.
A gauge field to kill the connection
Method from Randjbar-Daemi, Salam and Strathdee
Add an extra U(1) gauge field X
The connection term in the two Weyl spinors of a chiral 6Dspinors become different:
∇χ = ∂χ + (X + Ω)η ∇η = ∂η + (X − Ω)χ
If X cancels ±Ω one of the chiralities has a zero-mode.
Nicolas Deutschmann Curved Extra-Dimensions 12/25...
12/25
![Page 35: "Curved extra-dimensions" by Nicolas Deutschmann (Institut de Physique Nucleaire de Lyon, France)](https://reader033.vdocuments.net/reader033/viewer/2022052600/5585a37dd8b42a7b1a8b4871/html5/thumbnails/35.jpg)
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Tentative Model
Start by writing the Standard Model Lagrangian in 6D
with thenew gauge field and an additional Higgs field :
L = LSM
− 14
XµνXµν + |DMH|2 + µ2|H|2 − λ
2|H|4
With ⟨X⟩ a magnetic monopole, fixed by GR:
⟨X⟩ = n
2gcos θdϕ =
√2R
κcos θdϕ
How to hide this new gauge boson ?
Nicolas Deutschmann Curved Extra-Dimensions 13/25...
13/25
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.
Tentative Model
Start by writing the Standard Model Lagrangian in 6D with thenew gauge field
and an additional Higgs field :
L = LSM − 14
XµνXµν
+ |DMH|2 + µ2|H|2 − λ
2|H|4
With ⟨X⟩ a magnetic monopole, fixed by GR:
⟨X⟩ = n
2gcos θdϕ =
√2R
κcos θdϕ
How to hide this new gauge boson ?
Nicolas Deutschmann Curved Extra-Dimensions 13/25...
13/25
![Page 37: "Curved extra-dimensions" by Nicolas Deutschmann (Institut de Physique Nucleaire de Lyon, France)](https://reader033.vdocuments.net/reader033/viewer/2022052600/5585a37dd8b42a7b1a8b4871/html5/thumbnails/37.jpg)
.
Tentative Model
Start by writing the Standard Model Lagrangian in 6D with thenew gauge field
and an additional Higgs field :
L = LSM − 14
XµνXµν
+ |DMH|2 + µ2|H|2 − λ
2|H|4
With ⟨X⟩ a magnetic monopole, fixed by GR:
⟨X⟩ = n
2gcos θdϕ =
√2R
κcos θdϕ
How to hide this new gauge boson ?
Nicolas Deutschmann Curved Extra-Dimensions 13/25...
13/25
![Page 38: "Curved extra-dimensions" by Nicolas Deutschmann (Institut de Physique Nucleaire de Lyon, France)](https://reader033.vdocuments.net/reader033/viewer/2022052600/5585a37dd8b42a7b1a8b4871/html5/thumbnails/38.jpg)
.
Tentative Model
Start by writing the Standard Model Lagrangian in 6D with thenew gauge field
and an additional Higgs field :
L = LSM − 14
XµνXµν
+ |DMH|2 + µ2|H|2 − λ
2|H|4
With ⟨X⟩ a magnetic monopole, fixed by GR:
⟨X⟩ = n
2gcos θdϕ =
√2R
κcos θdϕ
How to hide this new gauge boson ?
Nicolas Deutschmann Curved Extra-Dimensions 13/25...
13/25
![Page 39: "Curved extra-dimensions" by Nicolas Deutschmann (Institut de Physique Nucleaire de Lyon, France)](https://reader033.vdocuments.net/reader033/viewer/2022052600/5585a37dd8b42a7b1a8b4871/html5/thumbnails/39.jpg)
.
Tentative Model
Start by writing the Standard Model Lagrangian in 6D with thenew gauge field and an additional Higgs field :
L = LSM − 14
XµνXµν + |DMH|2 + µ2|H|2 − λ
2|H|4
With ⟨X⟩ a magnetic monopole, fixed by GR:
⟨X⟩ = n
2gcos θdϕ =
√2R
κcos θdϕ
How to hide this new gauge boson ?
Nicolas Deutschmann Curved Extra-Dimensions 13/25...
13/25
![Page 40: "Curved extra-dimensions" by Nicolas Deutschmann (Institut de Physique Nucleaire de Lyon, France)](https://reader033.vdocuments.net/reader033/viewer/2022052600/5585a37dd8b42a7b1a8b4871/html5/thumbnails/40.jpg)
.
Higgs Mechanism in a Monopole Background
Need to find the minimum
|DMH|2 − µ2|H|2 + λ
2|H|4
A priori θ-dependent :
Numerical Solution
.Method..
.Minimization usingFourier coefficients
1 2 3 4 5
0.001
0.01
0.1
1
1 2 3 4 5
Mode
Αi
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.
Higgs Mechanism in a Monopole Background
Need to find the minimum
|DMH|2 − µ2|H|2 + λ
2|H|4
A priori θ-dependent : Numerical Solution
.Method..
.Minimization usingFourier coefficients
1 2 3 4 5
0.001
0.01
0.1
1
1 2 3 4 5
Mode
Αi
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.
Higgs Mechanism in a Monopole Background
Need to find the minimum
|DMH|2 − µ2|H|2 + λ
2|H|4
A priori θ-dependent : Numerical Solution
.Method..
.Minimization usingFourier coefficients
1 2 3 4 5
0.001
0.01
0.1
1
1 2 3 4 5
Mode
Αi
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.
Higgs Mechanism in a Monopole Background
Need to find the minimum
|DMH|2 − µ2|H|2 + λ
2|H|4
A priori θ-dependent : Numerical Solution
.Method..
.Minimization usingFourier coefficients
1 2 3 4 5
0.001
0.01
0.1
1
1 2 3 4 5
Mode
Αi
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.
Effects of the symmetry breaking• Higgs:
O(1/R)• X: g/R ∼ 10 keV
Too weak coupling for collider physics.Compatible with short-range gravity tests
1 10 100 100010-2
10-1
100
101
102
103
104
105
106
107
108
109
1010
Excludedbyexperiment
Lamoreaux
U.Colorado
Stanford2
Stanford1
U.Washington2
gauged
B#
Yukawamessengers
dilaton
KKgravitons
strange
modulus
gluon
modulus
heavyq
moduli
Stanford3
α
λ (µm)
U.Washington1
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.
Effects of the symmetry breaking• Higgs: O(1/R)
• X: g/R ∼ 10 keV
Too weak coupling for collider physics.Compatible with short-range gravity tests
1 10 100 100010-2
10-1
100
101
102
103
104
105
106
107
108
109
1010
Excludedbyexperiment
Lamoreaux
U.Colorado
Stanford2
Stanford1
U.Washington2
gauged
B#
Yukawamessengers
dilaton
KKgravitons
strange
modulus
gluon
modulus
heavyq
moduli
Stanford3
α
λ (µm)
U.Washington1
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.
Effects of the symmetry breaking• Higgs: O(1/R)• X: g/R ∼ 10 keV
Too weak coupling for collider physics.Compatible with short-range gravity tests
1 10 100 100010-2
10-1
100
101
102
103
104
105
106
107
108
109
1010
Excludedbyexperiment
Lamoreaux
U.Colorado
Stanford2
Stanford1
U.Washington2
gauged
B#
Yukawamessengers
dilaton
KKgravitons
strange
modulus
gluon
modulus
heavyq
moduli
Stanford3
α
λ (µm)
U.Washington1
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.
Effects of the symmetry breaking• Higgs: O(1/R)• X: g/R ∼ 10 keV
Too weak coupling for collider physics.Compatible with short-range gravity tests
1 10 100 100010-2
10-1
100
101
102
103
104
105
106
107
108
109
1010
Excludedbyexperiment
Lamoreaux
U.Colorado
Stanford2
Stanford1
U.Washington2
gauged
B#
Yukawamessengers
dilaton
KKgravitons
strange
modulus
gluon
modulus
heavyq
moduli
Stanford3
α
λ (µm)
U.Washington1
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.
Effects of the symmetry breaking• Higgs: O(1/R)• X: g/R ∼ 10 keV
Too weak coupling for collider physics.Compatible with short-range gravity tests
1 10 100 100010-2
10-1
100
101
102
103
104
105
106
107
108
109
1010
Excludedbyexperiment
Lamoreaux
U.Colorado
Stanford2
Stanford1
U.Washington2
gauged
B#
Yukawamessengers
dilaton
KKgravitons
strange
modulus
gluon
modulus
heavyq
moduli
Stanford3
α
λ (µm)
U.Washington1
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.
Spectrum of the model
SM Gauge scalar X vector Extra-Higgs
0
1
2
3
4
5
6
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.
Some Experimental Remarks.X boson properties..
.
• Interacts too weakly for colliders• Can decay into neutrinos
(Γ ≃ 10−11 eV)• Not a good DM candidate
.Tier-2 Excitations..
.
• As for Tier-1: Gluon• If Isom(S2/G) = Z2: Single production• Need less √
s
• Striking jj resonance easier to look for• Sets a limit around 1.5 − 2 TeV
• Constraints can be escaped if S2/G hasa continuous symmetry
.Extra-Higgs..
.No direct SM interaction so not expected atcollidersDecay mostly into X pairs
.Tier-1 Excitations..
.
• Need to be pair-produced• Gluon most likely (massless zero-mode &
QCD)• Signature: jj + ET
• Loop calculation needed to raisedegeneracy with γ
• Open question: prompt decay to LKK ?
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.
Some Experimental Remarks.X boson properties..
.
• Interacts too weakly for colliders• Can decay into neutrinos
(Γ ≃ 10−11 eV)• Not a good DM candidate
.Tier-2 Excitations..
.
• As for Tier-1: Gluon• If Isom(S2/G) = Z2: Single production• Need less √
s
• Striking jj resonance easier to look for• Sets a limit around 1.5 − 2 TeV
• Constraints can be escaped if S2/G hasa continuous symmetry
.Extra-Higgs..
.No direct SM interaction so not expected atcollidersDecay mostly into X pairs
.Tier-1 Excitations..
.
• Need to be pair-produced• Gluon most likely (massless zero-mode &
QCD)• Signature: jj + ET
• Loop calculation needed to raisedegeneracy with γ
• Open question: prompt decay to LKK ?
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.
Some Experimental Remarks.X boson properties..
.
• Interacts too weakly for colliders• Can decay into neutrinos
(Γ ≃ 10−11 eV)• Not a good DM candidate
.Tier-2 Excitations..
.
• As for Tier-1: Gluon• If Isom(S2/G) = Z2: Single production• Need less √
s
• Striking jj resonance easier to look for• Sets a limit around 1.5 − 2 TeV
• Constraints can be escaped if S2/G hasa continuous symmetry
.Extra-Higgs..
.No direct SM interaction so not expected atcollidersDecay mostly into X pairs
.Tier-1 Excitations..
.
• Need to be pair-produced• Gluon most likely (massless zero-mode &
QCD)• Signature: jj + ET
• Loop calculation needed to raisedegeneracy with γ
• Open question: prompt decay to LKK ?
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.
Some Experimental Remarks.X boson properties..
.
• Interacts too weakly for colliders• Can decay into neutrinos
(Γ ≃ 10−11 eV)• Not a good DM candidate
.Tier-2 Excitations..
.
• As for Tier-1: Gluon• If Isom(S2/G) = Z2: Single production• Need less √
s
• Striking jj resonance easier to look for• Sets a limit around 1.5 − 2 TeV
• Constraints can be escaped if S2/G hasa continuous symmetry
.Extra-Higgs..
.No direct SM interaction so not expected atcollidersDecay mostly into X pairs
.Tier-1 Excitations..
.
• Need to be pair-produced• Gluon most likely (massless zero-mode &
QCD)• Signature: jj + ET
• Loop calculation needed to raisedegeneracy with γ
• Open question: prompt decay to LKK ?
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.
Some Experimental Remarks.X boson properties..
.
• Interacts too weakly for colliders• Can decay into neutrinos
(Γ ≃ 10−11 eV)• Not a good DM candidate
.Tier-2 Excitations..
.
• As for Tier-1: Gluon• If Isom(S2/G) = Z2: Single production• Need less √
s
• Striking jj resonance easier to look for• Sets a limit around 1.5 − 2 TeV• Constraints can be escaped if S2/G has
a continuous symmetry
.Extra-Higgs..
.No direct SM interaction so not expected atcollidersDecay mostly into X pairs
.Tier-1 Excitations..
.
• Need to be pair-produced• Gluon most likely (massless zero-mode &
QCD)• Signature: jj + ET
• Loop calculation needed to raisedegeneracy with γ
• Open question: prompt decay to LKK ?
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.
Summing up the model
Spherical Extra-Dimensions are hard to construct.• Chiral fermions do not come easily• Need to add two extra-fields: X and H ′
• Unsatisfying because X and H ′ are rather untestable They are ugly
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.
Localizing fermions
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.
Branes, fat branes and all that
Bottom-upAll but one symmetricorbifolds have singularpoints• QFT argument:
localized counter-terms• GR argument: branes
Top-Bottom ∃ explicitexamples of localization:• RS (not relevant)• Georgi mechanism on
S1/Z2
Nice for later if the modelis phenomenologicallyrelevant.
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.
What the model looks like
l=0
l=2
l=3
m=0m=-2 m=2
l=1
• Specific orbifoldchoice: S2/S4
• 6D QCD+EW• 4D Standard model
fermion content withgauge couplings to the4D gauge vectors
• first tier: unstablescalars (loop-level)
• second tier: unstablevectors, stable scalars(DM)
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.
What the model looks like
l=0
l=2
l=3
m=0m=-2 m=2
l=1
• Specific orbifoldchoice: S2/S4
• 6D QCD+EW
• 4D Standard modelfermion content withgauge couplings to the4D gauge vectors
• first tier: unstablescalars (loop-level)
• second tier: unstablevectors, stable scalars(DM)
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.
What the model looks like
l=0
l=2
l=3
m=0m=-2 m=2
l=1
• Specific orbifoldchoice: S2/S4
• 6D QCD+EW• 4D Standard model
fermion content withgauge couplings to the4D gauge vectors
• first tier: unstablescalars (loop-level)
• second tier: unstablevectors, stable scalars(DM)
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.
What the model looks like
l=0
l=2
l=3
m=0m=-2 m=2
l=1
• Specific orbifoldchoice: S2/S4
• 6D QCD+EW• 4D Standard model
fermion content withgauge couplings to the4D gauge vectors
• first tier: unstablescalars (loop-level)
• second tier: unstablevectors, stable scalars(DM)
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.
What the model looks like
l=0
l=2
l=3
m=0m=-2 m=2
l=1
• Specific orbifoldchoice: S2/S4
• 6D QCD+EW• 4D Standard model
fermion content withgauge couplings to the4D gauge vectors
• first tier: unstablescalars (loop-level)
• second tier: unstablevectors, stable scalars(DM)
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.
Phenomenology
Two competing constraints: LHC v.s. Dark Matter.LHC constraints..
.
• Tier-1 excitations couple at loop level:
sub-dominant a priori
• Tier-2 excitations provide resonances:
R ≥ 1.5 TeV
.Dark matter..
.
Likely DM candidate: scalar Tier-2 photon:
WIMPZILLA!
• Direct detection:
hard because loop-suppressed
• Relic density:
needs loop calculations
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.
Phenomenology
Two competing constraints: LHC v.s. Dark Matter.LHC constraints..
.
• Tier-1 excitations couple at loop level: sub-dominant a priori• Tier-2 excitations provide resonances:
R ≥ 1.5 TeV
.Dark matter..
.
Likely DM candidate: scalar Tier-2 photon:
WIMPZILLA!
• Direct detection:
hard because loop-suppressed
• Relic density:
needs loop calculations
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.
Phenomenology
Two competing constraints: LHC v.s. Dark Matter.LHC constraints..
.
• Tier-1 excitations couple at loop level: sub-dominant a priori• Tier-2 excitations provide resonances: R ≥ 1.5 TeV
.Dark matter..
.
Likely DM candidate: scalar Tier-2 photon:
WIMPZILLA!
• Direct detection:
hard because loop-suppressed
• Relic density:
needs loop calculations
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.
Phenomenology
Two competing constraints: LHC v.s. Dark Matter.LHC constraints..
.
• Tier-1 excitations couple at loop level: sub-dominant a priori• Tier-2 excitations provide resonances: R ≥ 1.5 TeV
.Dark matter..
.
Likely DM candidate: scalar Tier-2 photon: WIMPZILLA!• Direct detection:
hard because loop-suppressed
• Relic density:
needs loop calculations
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.
Phenomenology
Two competing constraints: LHC v.s. Dark Matter.LHC constraints..
.
• Tier-1 excitations couple at loop level: sub-dominant a priori• Tier-2 excitations provide resonances: R ≥ 1.5 TeV
.Dark matter..
.
Likely DM candidate: scalar Tier-2 photon: WIMPZILLA!• Direct detection: hard because loop-suppressed• Relic density:
needs loop calculations
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.
Phenomenology
Two competing constraints: LHC v.s. Dark Matter.LHC constraints..
.
• Tier-1 excitations couple at loop level: sub-dominant a priori• Tier-2 excitations provide resonances: R ≥ 1.5 TeV
.Dark matter..
.
Likely DM candidate: scalar Tier-2 photon: WIMPZILLA!• Direct detection: hard because loop-suppressed• Relic density: needs loop calculations
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.
Conclusion: A negative future ?
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.
A Brighter Horizon: Hyperbolic Extra-Dimensions
• Fermions behave much more nicely: there is a massless mode
• Much more freedom: arbitrary high volumes for a givencurvature radius
• Mass gap protected by curvature radius• Can pull down Mpl while keeping MKK high enough• Many features attractive for cosmology (flatness, uniformity,
inflation, ...)• Topological constraints (genus↔ V/Rn) make the curvature
radius the only thing to stabilize• Quantum corrections could play a significant role as Mpl goes
down
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.
A Brighter Horizon: Hyperbolic Extra-Dimensions
• Fermions behave much more nicely: there is a massless mode• Much more freedom: arbitrary high volumes for a given
curvature radius
• Mass gap protected by curvature radius• Can pull down Mpl while keeping MKK high enough• Many features attractive for cosmology (flatness, uniformity,
inflation, ...)• Topological constraints (genus↔ V/Rn) make the curvature
radius the only thing to stabilize• Quantum corrections could play a significant role as Mpl goes
down
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.
A Brighter Horizon: Hyperbolic Extra-Dimensions
• Fermions behave much more nicely: there is a massless mode• Much more freedom: arbitrary high volumes for a given
curvature radius• Mass gap protected by curvature radius
• Can pull down Mpl while keeping MKK high enough• Many features attractive for cosmology (flatness, uniformity,
inflation, ...)• Topological constraints (genus↔ V/Rn) make the curvature
radius the only thing to stabilize• Quantum corrections could play a significant role as Mpl goes
down
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24/25
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.
A Brighter Horizon: Hyperbolic Extra-Dimensions
• Fermions behave much more nicely: there is a massless mode• Much more freedom: arbitrary high volumes for a given
curvature radius• Mass gap protected by curvature radius• Can pull down Mpl while keeping MKK high enough
• Many features attractive for cosmology (flatness, uniformity,inflation, ...)
• Topological constraints (genus↔ V/Rn) make the curvatureradius the only thing to stabilize
• Quantum corrections could play a significant role as Mpl goesdown
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.
A Brighter Horizon: Hyperbolic Extra-Dimensions
• Fermions behave much more nicely: there is a massless mode• Much more freedom: arbitrary high volumes for a given
curvature radius• Mass gap protected by curvature radius• Can pull down Mpl while keeping MKK high enough• Many features attractive for cosmology (flatness, uniformity,
inflation, ...)
• Topological constraints (genus↔ V/Rn) make the curvatureradius the only thing to stabilize
• Quantum corrections could play a significant role as Mpl goesdown
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![Page 75: "Curved extra-dimensions" by Nicolas Deutschmann (Institut de Physique Nucleaire de Lyon, France)](https://reader033.vdocuments.net/reader033/viewer/2022052600/5585a37dd8b42a7b1a8b4871/html5/thumbnails/75.jpg)
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A Brighter Horizon: Hyperbolic Extra-Dimensions
• Fermions behave much more nicely: there is a massless mode• Much more freedom: arbitrary high volumes for a given
curvature radius• Mass gap protected by curvature radius• Can pull down Mpl while keeping MKK high enough• Many features attractive for cosmology (flatness, uniformity,
inflation, ...)• Topological constraints (genus↔ V/Rn) make the curvature
radius the only thing to stabilize
• Quantum corrections could play a significant role as Mpl goesdown
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![Page 76: "Curved extra-dimensions" by Nicolas Deutschmann (Institut de Physique Nucleaire de Lyon, France)](https://reader033.vdocuments.net/reader033/viewer/2022052600/5585a37dd8b42a7b1a8b4871/html5/thumbnails/76.jpg)
.
A Brighter Horizon: Hyperbolic Extra-Dimensions
• Fermions behave much more nicely: there is a massless mode• Much more freedom: arbitrary high volumes for a given
curvature radius• Mass gap protected by curvature radius• Can pull down Mpl while keeping MKK high enough• Many features attractive for cosmology (flatness, uniformity,
inflation, ...)• Topological constraints (genus↔ V/Rn) make the curvature
radius the only thing to stabilize• Quantum corrections could play a significant role as Mpl goes
down
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24/25
![Page 77: "Curved extra-dimensions" by Nicolas Deutschmann (Institut de Physique Nucleaire de Lyon, France)](https://reader033.vdocuments.net/reader033/viewer/2022052600/5585a37dd8b42a7b1a8b4871/html5/thumbnails/77.jpg)
.
Thank you for your attention
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