flavor physics from warped extra dimensionsweb.ics.purdue.edu/~markru/chang.pdf · a short tour...
TRANSCRIPT
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Flavor Physics from Warped Extra Dimensions
Talk at Purdue University
Chang, Sanghyeon
Yonsei University
November 14, 2007
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Table of Contents
Introduction
Extra Dimensions
Bulk Standard Model
Fermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
What is Extra Dimension?Hierarchy ProblemSupersymmetry
What is Extra Dimension?
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
What is Extra Dimension?Hierarchy ProblemSupersymmetry
For us, a rope is 1-D, but for ant, it is 2-D space.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
What is Extra Dimension?Hierarchy ProblemSupersymmetry
Hierarchy Problem
I Why Gravity is so weak?
Weak Scale (MW ) = 1000 GeV
Planck Scale (Mpl) = 1019 GeV
I Weak scale : Standard Model
I Above Planck Scale : Quantum Gravity
I Between two scales : GUT, Supersymmetry, Superstring etc.
There is no experimental clue on the intermediate scale.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
What is Extra Dimension?Hierarchy ProblemSupersymmetry
Hierarchy Problem
I Why Gravity is so weak?
Weak Scale (MW ) = 1000 GeV
Planck Scale (Mpl) = 1019 GeV
I Weak scale : Standard Model
I Above Planck Scale : Quantum Gravity
I Between two scales : GUT, Supersymmetry, Superstring etc.
There is no experimental clue on the intermediate scale.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
What is Extra Dimension?Hierarchy ProblemSupersymmetry
Hierarchy Problem
I Why Gravity is so weak?
Weak Scale (MW ) = 1000 GeV
Planck Scale (Mpl) = 1019 GeV
I Weak scale : Standard Model
I Above Planck Scale : Quantum Gravity
I Between two scales : GUT, Supersymmetry, Superstring etc.
There is no experimental clue on the intermediate scale.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
What is Extra Dimension?Hierarchy ProblemSupersymmetry
That’s not what they wanted to prove.
Loading..
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
llaw2.aviMedia File (video/avi)
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
What is Extra Dimension?Hierarchy ProblemSupersymmetry
The Problem of Higgs Mass
In Standard Model(SM),
Higgs mass correction is quadratic divergent to cutoff scale.
M2Higgs −→ M2Higgs + cΛ2cut
We need an upper bound of Λcut to be around 1 TeV.
In SM, Mpl is a natural cut-off.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
What is Extra Dimension?Hierarchy ProblemSupersymmetry
The Problem of Higgs Mass
In Standard Model(SM),
Higgs mass correction is quadratic divergent to cutoff scale.
M2Higgs −→ M2Higgs + cΛ2cut
We need an upper bound of Λcut to be around 1 TeV.
In SM, Mpl is a natural cut-off.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
What is Extra Dimension?Hierarchy ProblemSupersymmetry
Supersymmetry(SUSY)
To solve Hierarchy problem, SUSY was introduced.
SUSY is a symmetry between boson and fermion.
Each particle in SM has a superpartner
with the same quantum number but different spin.
Each loop-correction by scalar loop is cancelled by higgsino loop.
(soft) SUSY breaking generates natural cut-off at ∼TeV.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
What is Extra Dimension?Hierarchy ProblemSupersymmetry
Supersymmetry(SUSY)
To solve Hierarchy problem, SUSY was introduced.
SUSY is a symmetry between boson and fermion.
Each particle in SM has a superpartner
with the same quantum number but different spin.
Each loop-correction by scalar loop is cancelled by higgsino loop.
(soft) SUSY breaking generates natural cut-off at ∼TeV.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
What is Extra Dimension?Hierarchy ProblemSupersymmetry
Supersymmetry(SUSY)
To solve Hierarchy problem, SUSY was introduced.
SUSY is a symmetry between boson and fermion.
Each particle in SM has a superpartner
with the same quantum number but different spin.
Each loop-correction by scalar loop is cancelled by higgsino loop.
(soft) SUSY breaking generates natural cut-off at ∼TeV.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
What is Extra Dimension?Hierarchy ProblemSupersymmetry
Not exactly replacing SUSY, but a simple idea was brought by
Arkani-Hamed, Dimopoulos and Dvali PLB 429 (1998).
ADD suggest that the hierarchy problem can be solved by
existence of extra spatial dimensions.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
What is Extra Dimension?Hierarchy ProblemSupersymmetry
Not exactly replacing SUSY, but a simple idea was brought by
Arkani-Hamed, Dimopoulos and Dvali PLB 429 (1998).
ADD suggest that the hierarchy problem can be solved by
existence of extra spatial dimensions.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
The FLATLAND
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
Flat Extra dimensions
If our Universe has a thickness R,
we will find extra dimensions in a small scale r < R.
Let the number of extra dimensions n.
Then the gravity become stronger in small range.
G1
r, (r > R)
G(4+n)1
rn+1, (r < R)
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
Flat Extra dimensions
If our Universe has a thickness R,
we will find extra dimensions in a small scale r < R.
Let the number of extra dimensions n.
Then the gravity become stronger in small range.
G1
r, (r > R)
G(4+n)1
rn+1, (r < R)
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
Flat Extra dimensions
If our Universe has a thickness R,
we will find extra dimensions in a small scale r < R.
Let the number of extra dimensions n.
Then the gravity become stronger in small range.
G1
r, (r > R)
G(4+n)1
rn+1, (r < R)
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
V
Gravity
ElectroMagnetic
R r
The 4D gravity can be weakened by extra-dimensions.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
A short tour into the Extra dimensions
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
How to compactify extra-dimensions is not yet understood.
It is hard to comprehend due to its “large” size.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
How to compactify extra-dimensions is not yet understood.
It is hard to comprehend due to its “large” size.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
We are here
Gravity is confined here
Our (3 + 1)D universe
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
We are here
Gravity
Gravity is confined here
Flat extra dimension S1 (Arkani-Hamed et.al.)
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
We are hereGravity is localized
Gravity is confined here
RS1 Warped extra dimension S1/Z2
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
All SM filed should be confined on the 3+1D brane except gravity
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
This can be related with the string theory with brane solutions
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
As you know, string need to be compactified.
Loading..
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
aang2c.aviMedia File (video/avi)
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
The object of this model is to solve the hierarchy problem.
To explicit, to keep the Higgs mass 1-loop contribution TeV
which should be the QG scale.
In short,QG scale = TeV
Existence of massive Kaluza-Kelin(KK) graviton is cosmologically
dangerous.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
The object of this model is to solve the hierarchy problem.
To explicit, to keep the Higgs mass 1-loop contribution TeV
which should be the QG scale.
In short,QG scale = TeV
Existence of massive Kaluza-Kelin(KK) graviton is cosmologically
dangerous.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
The object of this model is to solve the hierarchy problem.
To explicit, to keep the Higgs mass 1-loop contribution TeV
which should be the QG scale.
In short,QG scale = TeV
Existence of massive Kaluza-Kelin(KK) graviton is cosmologically
dangerous.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
Randall-Sundrum model (RS1)
Loading..
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
aang1.aviMedia File (video/avi)
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
Randall-Sundrum model (RS1)Randall and Sundrum PRL (1999)
RS1 is model with one warped extra-dimension.
ds2 = e−2σ(y)(dt2 − dx2)− dy2,
σ(y) = k |y | is the warp factork ∼ Mpl is the curvature of warped space.
The 5th direction y is bounded and the bulk is AdS5
All SM fields are confined on TeV brane (IR boundary)
Gravity resides in the bulk.
TeV scale KK gravitons.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
Randall-Sundrum model (RS1)Randall and Sundrum PRL (1999)
RS1 is model with one warped extra-dimension.
ds2 = e−2σ(y)(dt2 − dx2)− dy2,
σ(y) = k |y | is the warp factork ∼ Mpl is the curvature of warped space.
The 5th direction y is bounded and the bulk is AdS5
All SM fields are confined on TeV brane (IR boundary)
Gravity resides in the bulk.
TeV scale KK gravitons.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
Randall-Sundrum model (RS1)Randall and Sundrum PRL (1999)
RS1 is model with one warped extra-dimension.
ds2 = e−2σ(y)(dt2 − dx2)− dy2,
σ(y) = k |y | is the warp factork ∼ Mpl is the curvature of warped space.
The 5th direction y is bounded and the bulk is AdS5
All SM fields are confined on TeV brane (IR boundary)
Gravity resides in the bulk.
TeV scale KK gravitons.Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
Where do we live in RS1?
UV(IR) brane is actually a UV(IR) cut-off (boundary).
There is no reason for SM to be confined.
If the energy level is close to TeV,
SM fields behave more tamed in the bulk.
But, how can we develop bulk SM?
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
Where do we live in RS1?
UV(IR) brane is actually a UV(IR) cut-off (boundary).
There is no reason for SM to be confined.
If the energy level is close to TeV,
SM fields behave more tamed in the bulk.
But, how can we develop bulk SM?
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
Where do we live in RS1?
UV(IR) brane is actually a UV(IR) cut-off (boundary).
There is no reason for SM to be confined.
If the energy level is close to TeV,
SM fields behave more tamed in the bulk.
But, how can we develop bulk SM?
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
Where do we live in RS1?
UV(IR) brane is actually a UV(IR) cut-off (boundary).
There is no reason for SM to be confined.
If the energy level is close to TeV,
SM fields behave more tamed in the bulk.
But, how can we develop bulk SM?
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
The conformal coordinate of z ≡ eσ/k is useful.
ds25 =1
(kz)2
(dt2 − d~x 2 − dz2) .
y is confined in 0 ≤ y ≤ L
z is also bounded in 1/k ≤ z ≤ 1/T .T ≡ e−kLk ≡ � k.
With kL ≈ 35, the warp factor � ≡ e−kL reduces T at TeV scalefrom k at Planck scale:
With this scaling the gauge hierarchy problem is answered.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
The conformal coordinate of z ≡ eσ/k is useful.
ds25 =1
(kz)2
(dt2 − d~x 2 − dz2) .
y is confined in 0 ≤ y ≤ L
z is also bounded in 1/k ≤ z ≤ 1/T .T ≡ e−kLk ≡ � k.
With kL ≈ 35, the warp factor � ≡ e−kL reduces T at TeV scalefrom k at Planck scale:
With this scaling the gauge hierarchy problem is answered.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
AAD ModelStructure of flat extra-dimensionRandall-Sundrum modelRS1 modelWhere do we live in RS1 space?
The conformal coordinate of z ≡ eσ/k is useful.
ds25 =1
(kz)2
(dt2 − d~x 2 − dz2) .
y is confined in 0 ≤ y ≤ L
z is also bounded in 1/k ≤ z ≤ 1/T .T ≡ e−kLk ≡ � k.
With kL ≈ 35, the warp factor � ≡ e−kL reduces T at TeV scalefrom k at Planck scale:
With this scaling the gauge hierarchy problem is answered.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Bulk fields in RS1
I Bulk scalar field was introduced at early stage of RS model.
Goldberger and Wise, (1999).
I Then Bulk gauge field was introduced by
Davoudiasl,Hewett and Rizzo, (1999).
I And bulk fermion was followed soon after.
SC, Hisano, Nakano, Okada and Yamaguchi, (1999),
Grossman and Neubert (1999).
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Bulk fields in RS1
I Bulk scalar field was introduced at early stage of RS model.
Goldberger and Wise, (1999).
I Then Bulk gauge field was introduced by
Davoudiasl,Hewett and Rizzo, (1999).
I And bulk fermion was followed soon after.
SC, Hisano, Nakano, Okada and Yamaguchi, (1999),
Grossman and Neubert (1999).
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Bulk fields in RS1
I Bulk scalar field was introduced at early stage of RS model.
Goldberger and Wise, (1999).
I Then Bulk gauge field was introduced by
Davoudiasl,Hewett and Rizzo, (1999).
I And bulk fermion was followed soon after.
SC, Hisano, Nakano, Okada and Yamaguchi, (1999),
Grossman and Neubert (1999).
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Bulk gauge bosons
The action for a 5D U(1) gauge field
Sgauge =∫
d4xdz√
G[−14gMPgNQFMNFPQ + 12M2gMNAMAN] ,
where FMN = ∂MAN − ∂NAM .
The general mass term M2(z),
M2(z) = aUV2k δ(z − zUV) + aIR2k δ(z − zIR) + b2k2,
the dimensionless b and aUV(aIR) are bulk mass and localized mass
on the UV (IR) brane.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Bulk gauge bosons
The action for a 5D U(1) gauge field
Sgauge =∫
d4xdz√
G[−14gMPgNQFMNFPQ + 12M2gMNAMAN] ,
where FMN = ∂MAN − ∂NAM .
The general mass term M2(z),
M2(z) = aUV2k δ(z − zUV) + aIR2k δ(z − zIR) + b2k2,
the dimensionless b and aUV(aIR) are bulk mass and localized mass
on the UV (IR) brane.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
The KK expansion of the dimension 3/2 field AM(x , z) is
Aν(x , z) =√
k∑
n A(n)ν (x)f
(n)A (z)
With the equation of motion for mode function
−z∂z(
1z ∂z f
(n)A (z)
)+ M
2(z)k2z2
f(n)A (z) = m
(n)A
2f
(n)A (z),
The mode function can be obtained
f(n)A (z) =
z
N(n)A
[Jν(m
(n)A z) + β
(n)A Yν(m
(n)A z)
],
where ν =√
1 + b2, b = 0 if the gauge symmetry is conserved in
the bulk.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
The KK expansion of the dimension 3/2 field AM(x , z) is
Aν(x , z) =√
k∑
n A(n)ν (x)f
(n)A (z)
With the equation of motion for mode function
−z∂z(
1z ∂z f
(n)A (z)
)+ M
2(z)k2z2
f(n)A (z) = m
(n)A
2f
(n)A (z),
The mode function can be obtained
f(n)A (z) =
z
N(n)A
[Jν(m
(n)A z) + β
(n)A Yν(m
(n)A z)
],
where ν =√
1 + b2, b = 0 if the gauge symmetry is conserved in
the bulk.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
The KK expansion of the dimension 3/2 field AM(x , z) is
Aν(x , z) =√
k∑
n A(n)ν (x)f
(n)A (z)
With the equation of motion for mode function
−z∂z(
1z ∂z f
(n)A (z)
)+ M
2(z)k2z2
f(n)A (z) = m
(n)A
2f
(n)A (z),
The mode function can be obtained
f(n)A (z) =
z
N(n)A
[Jν(m
(n)A z) + β
(n)A Yν(m
(n)A z)
],
where ν =√
1 + b2, b = 0 if the gauge symmetry is conserved in
the bulk.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Fermions in RS1 Bulk
Sfermion =∫
d4xdy[Ψ̂eσ iγµ∂µΨ̂− 12 Ψ̂γ5∂y Ψ̂ + 12 (∂y Ψ̂)γ5Ψ̂ + mDΨ̂Ψ̂
]
Bulk Lagrangian should respect the Z2 parity
γ5Ψ(x ,−y) = ±Ψ(x , y)
The bulk fermion can be divided into two chiral components,
Ψ̂ = Ψ̂L + Ψ̂R
which can be expanded to KK modes
Ψ̂(x , y)L(R) =√
k∑n
ψ(n)L(R)(x)f
(n)L(R)(y).
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Fermions in RS1 Bulk
Sfermion =∫
d4xdy[Ψ̂eσ iγµ∂µΨ̂− 12 Ψ̂γ5∂y Ψ̂ + 12 (∂y Ψ̂)γ5Ψ̂ + mDΨ̂Ψ̂
]Bulk Lagrangian should respect the Z2 parity
γ5Ψ(x ,−y) = ±Ψ(x , y)
The bulk fermion can be divided into two chiral components,
Ψ̂ = Ψ̂L + Ψ̂R
which can be expanded to KK modes
Ψ̂(x , y)L(R) =√
k∑n
ψ(n)L(R)(x)f
(n)L(R)(y).
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Fermions in RS1 Bulk
Sfermion =∫
d4xdy[Ψ̂eσ iγµ∂µΨ̂− 12 Ψ̂γ5∂y Ψ̂ + 12 (∂y Ψ̂)γ5Ψ̂ + mDΨ̂Ψ̂
]Bulk Lagrangian should respect the Z2 parity
γ5Ψ(x ,−y) = ±Ψ(x , y)
The bulk fermion can be divided into two chiral components,
Ψ̂ = Ψ̂L + Ψ̂R
which can be expanded to KK modes
Ψ̂(x , y)L(R) =√
k∑n
ψ(n)L(R)(x)f
(n)L(R)(y).
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Fermions in RS1 Bulk
Sfermion =∫
d4xdy[Ψ̂eσ iγµ∂µΨ̂− 12 Ψ̂γ5∂y Ψ̂ + 12 (∂y Ψ̂)γ5Ψ̂ + mDΨ̂Ψ̂
]Bulk Lagrangian should respect the Z2 parity
γ5Ψ(x ,−y) = ±Ψ(x , y)
The bulk fermion can be divided into two chiral components,
Ψ̂ = Ψ̂L + Ψ̂R
which can be expanded to KK modes
Ψ̂(x , y)L(R) =√
k∑n
ψ(n)L(R)(x)f
(n)L(R)(y).
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
We are hereGravity is localized
Gravity is confined here
SM fields
Parity of RS1 Warped extra dimension S1/Z2Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
We are hereGravity is localized
Parity of RS1 Warped extra dimension S1/Z2
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
I The 5-th D parity should be conserved.
I Bulk fermion with odd parity cannot have a zero mode.
I The zero mode is chiral (thus massless).
I Chiral fermion is automatically localized on IR boundary.
I All bulk gauge boson have (massless) zero mode.
I (Massless) SM fields can be induced from bulk fields (except
the Higgs).
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Will KK fields survive experimental bounds?
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Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Experimental signals
Energy scale is warped down at IR boundary (y = y0).
Mple−ky0 ∼ TeV
The QG scale is about TeV.
Bulk field generates KK modes with about TeV scale mass gap.
Quark KK mode contribution to MW /MZ conflicts with
experimental data
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Experimental signals
Energy scale is warped down at IR boundary (y = y0).
Mple−ky0 ∼ TeV
The QG scale is about TeV.
Bulk field generates KK modes with about TeV scale mass gap.
Quark KK mode contribution to MW /MZ conflicts with
experimental data
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Experimental signals
Energy scale is warped down at IR boundary (y = y0).
Mple−ky0 ∼ TeV
The QG scale is about TeV.
Bulk field generates KK modes with about TeV scale mass gap.
Quark KK mode contribution to MW /MZ conflicts with
experimental data
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Custodial isospin
In 2003, Agashe et.al. suggested that if there is
SU(2)L×SU(2)R ×U(1)B−L gauge symmetry on S1/Z2×Z′2.
There exist Ads5/CFT conformal dual global SU(2) custodial
isospin.
Which protect MW /MZ ratio from KK mode contributions.
Agashe, Delgado, May and Sundrum, (2003)
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Custodial isospin
In 2003, Agashe et.al. suggested that if there is
SU(2)L×SU(2)R ×U(1)B−L gauge symmetry on S1/Z2×Z′2.
There exist Ads5/CFT conformal dual global SU(2) custodial
isospin.
Which protect MW /MZ ratio from KK mode contributions.
Agashe, Delgado, May and Sundrum, (2003)
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Other than custodial isospin,
this model has another important feature in it.
Two independent parities on each boundary (UV,IR).
(±,±) and (±,∓)
For bulk fermions, this gives symmetry
γ5Ψ(x ,−y) = ±Ψ(x , y) , γ5Ψ(x , L− y) = ±Ψ(x , L + y)
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Other than custodial isospin,
this model has another important feature in it.
Two independent parities on each boundary (UV,IR).
(±,±) and (±,∓)
For bulk fermions, this gives symmetry
γ5Ψ(x ,−y) = ±Ψ(x , y) , γ5Ψ(x , L− y) = ±Ψ(x , L + y)
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Other than custodial isospin,
this model has another important feature in it.
Two independent parities on each boundary (UV,IR).
(±,±) and (±,∓)
For bulk fermions, this gives symmetry
γ5Ψ(x ,−y) = ±Ψ(x , y) , γ5Ψ(x , L− y) = ±Ψ(x , L + y)
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
We are here
Gravity is localized
Parities of Agashe et.al. Warped extra dimension S1/Z2 × Z′2Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
We are here
Gravity is localized
Parities of Agashe et.al. Warped extra dimension S1/Z2 × Z′2Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Gauge boson KK mode mass on S1/Z2 × Z′2
246810m(n)A =T
(++)(+�) (�+) (��)aIR!1aUV!1
aIR;UV!1Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Only (++) parity bulk field can have zero mode.
The gauge symmetry in 4D is broken for all other parities.
Thus WR fields are massive without bulk mass term.
The (+−) field contains a very light KK mode.
If the boundary mass term turns on and start to increase,
each mode mass transform to the other parity
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Only (++) parity bulk field can have zero mode.
The gauge symmetry in 4D is broken for all other parities.
Thus WR fields are massive without bulk mass term.
The (+−) field contains a very light KK mode.
If the boundary mass term turns on and start to increase,
each mode mass transform to the other parity
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
The boundary mass modifies the KK modes masses
(++)
(−+)
(−−)
(+−)
aUV →∞
aIR →∞
aIR →∞
aUV →∞
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
KK mass of bulk gauge boson
m(1)A(++) ≈ 2.45 T , m
(2)A(++) ≈ 5.57 T , m
(3)A(++) ≈ 8.70 T ,
m(1)A(+−) ≈ 0.24 T , m
(2)A(+−) ≈ 3.88 T , m
(3)A(+−) ≈ 7.06 T ,
m(1)A(−+) ≈ 2.40 T , m
(2)A(−+) ≈ 5.52 T , m
(3)A(−+) ≈ 8.65 T ,
m(1)A(−−) ≈ 3.83 T , m
(2)A(−−) ≈ 7.02 T , m
(3)A(−−) ≈ 10.17 T .
If T ∼ TeV, m(1)A(+−) can be about 100 GeV. (Without Higgs)
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
KK mass of bulk gauge boson
m(1)A(++) ≈ 2.45 T , m
(2)A(++) ≈ 5.57 T , m
(3)A(++) ≈ 8.70 T ,
m(1)A(+−) ≈ 0.24 T , m
(2)A(+−) ≈ 3.88 T , m
(3)A(+−) ≈ 7.06 T ,
m(1)A(−+) ≈ 2.40 T , m
(2)A(−+) ≈ 5.52 T , m
(3)A(−+) ≈ 8.65 T ,
m(1)A(−−) ≈ 3.83 T , m
(2)A(−−) ≈ 7.02 T , m
(3)A(−−) ≈ 10.17 T .
If T ∼ TeV, m(1)A(+−) can be about 100 GeV.
(Without Higgs)
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
KK mass of bulk gauge boson
m(1)A(++) ≈ 2.45 T , m
(2)A(++) ≈ 5.57 T , m
(3)A(++) ≈ 8.70 T ,
m(1)A(+−) ≈ 0.24 T , m
(2)A(+−) ≈ 3.88 T , m
(3)A(+−) ≈ 7.06 T ,
m(1)A(−+) ≈ 2.40 T , m
(2)A(−+) ≈ 5.52 T , m
(3)A(−+) ≈ 8.65 T ,
m(1)A(−−) ≈ 3.83 T , m
(2)A(−−) ≈ 7.02 T , m
(3)A(−−) ≈ 10.17 T .
If T ∼ TeV, m(1)A(+−) can be about 100 GeV. (Without Higgs)
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Bulk fermion can have four different Z2 × Z′2 parity sets,Ψ̂i (x , y) =
√k∑
n[ψ(n)iL (x)f
(n)iL (y) + ψ
(n)iR (x)f
(n)iR (y)]
i = 1, 2 represent the parallel conditions (±±)fiL has (±±) parity and fiR has (∓∓),
i = 3, 4 represent the crossed conditions, where (±∓)fiL has (±∓) parity and fiR has (∓±).
f(n)iL (z) =
√z
N(n)i
[Jci + 12
(m(n)i z) + β
(n)i Yci + 12
(m(n)i z)
],
f(n)iR (z) =
√z
N(n)i
[Jci− 12
(m(n)i z) + β
(n)i Yci− 12
(m(n)i z)
].
ci is the bulk fermion mass.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Bulk fermion can have four different Z2 × Z′2 parity sets,Ψ̂i (x , y) =
√k∑
n[ψ(n)iL (x)f
(n)iL (y) + ψ
(n)iR (x)f
(n)iR (y)]
i = 1, 2 represent the parallel conditions (±±)fiL has (±±) parity and fiR has (∓∓),
i = 3, 4 represent the crossed conditions, where (±∓)fiL has (±∓) parity and fiR has (∓±).
f(n)iL (z) =
√z
N(n)i
[Jci + 12
(m(n)i z) + β
(n)i Yci + 12
(m(n)i z)
],
f(n)iR (z) =
√z
N(n)i
[Jci− 12
(m(n)i z) + β
(n)i Yci− 12
(m(n)i z)
].
ci is the bulk fermion mass.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Bulk fermion can have four different Z2 × Z′2 parity sets,Ψ̂i (x , y) =
√k∑
n[ψ(n)iL (x)f
(n)iL (y) + ψ
(n)iR (x)f
(n)iR (y)]
i = 1, 2 represent the parallel conditions (±±)fiL has (±±) parity and fiR has (∓∓),
i = 3, 4 represent the crossed conditions, where (±∓)fiL has (±∓) parity and fiR has (∓±).
f(n)iL (z) =
√z
N(n)i
[Jci + 12
(m(n)i z) + β
(n)i Yci + 12
(m(n)i z)
],
f(n)iR (z) =
√z
N(n)i
[Jci− 12
(m(n)i z) + β
(n)i Yci− 12
(m(n)i z)
].
ci is the bulk fermion mass.Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
m(0)1;2m(1)1m(2)1m(3)1
m(1)2m(2)2m(3)2
massinunitofT
0.80.60.40.20-0.2-0.4-0.6-0.8
1086420 m(1)3m(2)3m
(3)3m(1)4m(2)4m
(3)4KKmassinunitofT
0.80.60.40.20-0.2-0.4-0.6-0.8
1086420Figure: KK mass spectra of bulk fermion without Higgs in unit of T
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Only (++) parity bulk mode function can be a zero mode.
The gauge field with other parity is massive in 4D.
(+−) parity mode has a light gauge boson without Higgs.
The fermions with other than (++) parity become massive in 4D.
(+−) and (−+) mode can have very light KK modes.
Higgs should be confined on IR boundary
Bulk Higgs scalar brings back hierarchy problem again.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Only (++) parity bulk mode function can be a zero mode.
The gauge field with other parity is massive in 4D.
(+−) parity mode has a light gauge boson without Higgs.
The fermions with other than (++) parity become massive in 4D.
(+−) and (−+) mode can have very light KK modes.
Higgs should be confined on IR boundary
Bulk Higgs scalar brings back hierarchy problem again.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Higgsless Standard Model
If the VEV of Higgs become very large, SM fields
((++) mode) simulate the (+−) KK modes without Higgs field.
Since (+−) has light gauge boson, and can have light fermionsThere is a possible Higgsless SM (Higgsless gauge symmetry
breaking).
Unfortunately, due to the parity conservation,
one of the fermion doublet component should have zero mass.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Higgsless Standard Model
If the VEV of Higgs become very large, SM fields
((++) mode) simulate the (+−) KK modes without Higgs field.
Since (+−) has light gauge boson, and can have light fermionsThere is a possible Higgsless SM (Higgsless gauge symmetry
breaking).
Unfortunately, due to the parity conservation,
one of the fermion doublet component should have zero mass.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Fields in RS1 BulkExperimental signalsBulk SM with Custodial isospinBulk SM KK modeHiggsless model
Higgsless Standard Model
If the VEV of Higgs become very large, SM fields
((++) mode) simulate the (+−) KK modes without Higgs field.
Since (+−) has light gauge boson, and can have light fermionsThere is a possible Higgsless SM (Higgsless gauge symmetry
breaking).
Unfortunately, due to the parity conservation,
one of the fermion doublet component should have zero mass.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
Basic assumptions
1. All mass hierarchy are generated from bulk mass structure:
All 5D SM parameters are considered O(1).
2. There should not be a order changing cancellation during the
matrix algebra between mixing and mass matrices.
With this two simple assumptions, we construct a bulk SM in
warped RS1.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
Basic assumptions
1. All mass hierarchy are generated from bulk mass structure:
All 5D SM parameters are considered O(1).
2. There should not be a order changing cancellation during the
matrix algebra between mixing and mass matrices.
With this two simple assumptions, we construct a bulk SM in
warped RS1.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
Basic assumptions
1. All mass hierarchy are generated from bulk mass structure:
All 5D SM parameters are considered O(1).
2. There should not be a order changing cancellation during the
matrix algebra between mixing and mass matrices.
With this two simple assumptions, we construct a bulk SM in
warped RS1.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
Universal Yukawa coupling
The SM fermion mass and mixing is decided by
both bulk fermion masses and Yukawa coupling with Higgs.
We assume “(almost) universal Yukawa coupling”.
There is no hierarchy within Yukawa coupling matrix.
yf '
1 1 1
1 1 1
1 1 1
.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
Universal Yukawa coupling
The SM fermion mass and mixing is decided by
both bulk fermion masses and Yukawa coupling with Higgs.
We assume “(almost) universal Yukawa coupling”.
There is no hierarchy within Yukawa coupling matrix.
yf '
1 1 1
1 1 1
1 1 1
.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
The fermions mass matrix is generated from,
Mij/vW ' FL(ci )× FR(cj),
where
FL(ci ) = �ci−1/2
√2ci−1
1−�2ci−1 , FR(ci ) = �−ci−1/2
√2ci +1
�−2ci−1−1 ,
ci is mass of bulk fermion fi .
Left-handed and right handed SM fermion comes from different
bulk fermions.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
The fermions mass matrix is generated from,
Mij/vW ' FL(ci )× FR(cj),
where
FL(ci ) = �ci−1/2
√2ci−1
1−�2ci−1 , FR(ci ) = �−ci−1/2
√2ci +1
�−2ci−1−1 ,
ci is mass of bulk fermion fi .
Left-handed and right handed SM fermion comes from different
bulk fermions.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
The fermions mass matrix is generated from,
Mij/vW ' FL(ci )× FR(cj),
where
FL(ci ) = �ci−1/2
√2ci−1
1−�2ci−1 , FR(ci ) = �−ci−1/2
√2ci +1
�−2ci−1−1 ,
ci is mass of bulk fermion fi .
Left-handed and right handed SM fermion comes from different
bulk fermions.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
FL(c) as a function of bulk mass c .
0
2
4
6
8
–0.4 –0.2 0 0.2 0.4 0.6 0.8
FL(c)
FL(0.5)
c
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
If we increase (−)ci , FL(R)(ci ) decrease slowly until (−)ci = 1/2.
For (−)ci > 1/2, it decrease fast in power of �(−)ci .
Without a large hierarchy in bulk fermion mass ci ,
All SM fermion masses can be generated.
If (−)ci < 0, the 1st KK mode can be very light. m(1) � TeV.
Model with larger symmetry might contains light neutral
and stable KK mode, i.e. WIMPS.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
If we increase (−)ci , FL(R)(ci ) decrease slowly until (−)ci = 1/2.
For (−)ci > 1/2, it decrease fast in power of �(−)ci .
Without a large hierarchy in bulk fermion mass ci ,
All SM fermion masses can be generated.
If (−)ci < 0, the 1st KK mode can be very light. m(1) � TeV.
Model with larger symmetry might contains light neutral
and stable KK mode, i.e. WIMPS.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
WIMPS are ...
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
Bulk fermions
Qi contains left handed quark
Ui ,Di contains right handed quark
Li contains lepton doublet
Ei contains lepton singlet
Ni contains right handed neutrino
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
Quark mass and mixing
(Ma)ij ' vW FL(cQi )FR(cAj),
where a = u, d and A = U,D.
UTqLMqUqR = Mdiagq for q = u, d .
The CKM matrix is defined as K = UTuLUdL.
K '
1 λ λ3
λ 1 λ2
λ3 λ2 1
,For simplified Wolfenstein parameterization and λ ' 0.22.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
Quark mass and mixing
(Ma)ij ' vW FL(cQi )FR(cAj),
where a = u, d and A = U,D.
UTqLMqUqR = Mdiagq for q = u, d .
The CKM matrix is defined as K = UTuLUdL.
K '
1 λ λ3
λ 1 λ2
λ3 λ2 1
,For simplified Wolfenstein parameterization and λ ' 0.22.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
We also assume that there is no order changing cancellation
in matrix diagonalization or other algebras.
i.e. 1 is a approximation of a number between√λ and 1/
√λ.
Thus the order λ in matrix will not change after the algebra.
This simple assumption leads to a unique bulk mass structure for
SM fermions.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
We also assume that there is no order changing cancellation
in matrix diagonalization or other algebras.
i.e. 1 is a approximation of a number between√λ and 1/
√λ.
Thus the order λ in matrix will not change after the algebra.
This simple assumption leads to a unique bulk mass structure for
SM fermions.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
Since uL and dL has almost the same matrix form
UuL ' UdL '
1 λ λ3
λ 1 λ2
λ3 λ2 1
.
Write the quark masses with λ
Mdiagu = diag(mu,mc ,mt) ' vW diag(λ8, λ3.5, 1),Mdiagd = diag(md ,ms ,mb) ' vW diag(λ7, λ5, λ2.5).
With known masses of SM fermions,
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
Since uL and dL has almost the same matrix form
UuL ' UdL '
1 λ λ3
λ 1 λ2
λ3 λ2 1
.
Write the quark masses with λ
Mdiagu = diag(mu,mc ,mt) ' vW diag(λ8, λ3.5, 1),Mdiagd = diag(md ,ms ,mb) ' vW diag(λ7, λ5, λ2.5).
With known masses of SM fermions,
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
Since uL and dL has almost the same matrix form
UuL ' UdL '
1 λ λ3
λ 1 λ2
λ3 λ2 1
.
Write the quark masses with λ
Mdiagu = diag(mu,mc ,mt) ' vW diag(λ8, λ3.5, 1),Mdiagd = diag(md ,ms ,mb) ' vW diag(λ7, λ5, λ2.5).
With known masses of SM fermions,
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
Following hierarchical relations are obtained:
FL(cQ1) : FL(cQ2) : FL(cQ3) ' λ3 : λ2 : 1,FR(cA1) : FR(cA2) : FR(cA3) ' λ3 : λ2 : 1,FR(cD1)
2 + FR(cD2)2 + FR(cD2)
2 'λ5[FR(cU1)
2 + FR(cU2)2 + FR(cu2)
2].
The SM quark mixing matrices can be approximated as
(UqL)ij(i≤j) ≈FL(cQi )
FL(cQj ), (UqR)ij(i≤j) ≈
FR(cAi )
FR(cAj ),
where A = U,D.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
From various experimental constraints, (e.g. Z → bb̄)
The bulk quark masses which satisfy all SM parameters can be
determined for T ∼ TeV.(SC, Kim, Yamaguchi)
cQ1 ' 0.61, cQ2 ' 0.56, cQ3 ' 0.3± 0.03.
cU1 ' −0.70, cU2 ' −0.52, 0
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
From various experimental constraints, (e.g. Z → bb̄)
The bulk quark masses which satisfy all SM parameters can be
determined for T ∼ TeV.(SC, Kim, Yamaguchi)
cQ1 ' 0.61, cQ2 ' 0.56, cQ3 ' 0.3± 0.03.
cU1 ' −0.70, cU2 ' −0.52, 0
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
Lepton mass matrix
UMNS = U†eUν ,
where
M†νMν = Uν(Mdiagν )2U
†ν , M
†eMe = Ue(M
diage )2U
†e .
MNS matrix can be approximated as
|UMNS| ∼
1 1 λm
1 1 1
1 1 1
where the experimental constraint on Ue3 gives m > 1.3.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
Universal lepton mass matrices are
(Mν)ij ' vW FL(cLi )FR(cNj),(Me)ij ' vW FL(cLi )FR(cEj).
Individual neutrino masses are not yet measured.
But from the neutrino oscillation
∆m2sol = m22 −m21 ' 7.5× 10−5 eV2,
∆m2atm = |m23 −m22| ' 2.5× 10−3 eV2.
Neutrino mass can be either Normal Hierarchy(NH) ( m1 ' 0 )Or Inverse Hierarchy(IH) (m3 = 0)
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
Universal lepton mass matrices are
(Mν)ij ' vW FL(cLi )FR(cNj),(Me)ij ' vW FL(cLi )FR(cEj).
Individual neutrino masses are not yet measured.
But from the neutrino oscillation
∆m2sol = m22 −m21 ' 7.5× 10−5 eV2,
∆m2atm = |m23 −m22| ' 2.5× 10−3 eV2.
Neutrino mass can be either Normal Hierarchy(NH) ( m1 ' 0 )Or Inverse Hierarchy(IH) (m3 = 0)
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
Universal lepton mass matrices are
(Mν)ij ' vW FL(cLi )FR(cNj),(Me)ij ' vW FL(cLi )FR(cEj).
Individual neutrino masses are not yet measured.
But from the neutrino oscillation
∆m2sol = m22 −m21 ' 7.5× 10−5 eV2,
∆m2atm = |m23 −m22| ' 2.5× 10−3 eV2.
Neutrino mass can be either Normal Hierarchy(NH) ( m1 ' 0 )Or Inverse Hierarchy(IH) (m3 = 0)
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
Assumption of no order changing cancellation in matrix product
allows only NH for neutrino mass.
MTν Mν ∝
λ2n λn λn
λn 1 1
λn 1 1
(NH).Also we parameterize lepton masses
Mdiagν = diag(m1,m2,m3) = vW diag(< λ20.5, λ20.5, λ19),
Mdiage = diag(me ,mµ,mτ ) = vW diag(λ8.5, λ5, λ3).
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
Assumption of no order changing cancellation in matrix product
allows only NH for neutrino mass.
MTν Mν ∝
λ2n λn λn
λn 1 1
λn 1 1
(NH).Also we parameterize lepton masses
Mdiagν = diag(m1,m2,m3) = vW diag(< λ20.5, λ20.5, λ19),
Mdiage = diag(me ,mµ,mτ ) = vW diag(λ8.5, λ5, λ3).
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
Maximal mixing between 2 and 3 flavors suggests the mixing
Uf '
1 λaf λn
λbf 1 1
λcf 1 1
,with f = e, ν.
To have a desired mass hierarchy,
1.5 + aν & n, 2 + ae & n.
Unlike quark mass, lepton mass has some ambiguity.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
Maximal mixing between 2 and 3 flavors suggests the mixing
Uf '
1 λaf λn
λbf 1 1
λcf 1 1
,with f = e, ν.
To have a desired mass hierarchy,
1.5 + aν & n, 2 + ae & n.
Unlike quark mass, lepton mass has some ambiguity.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
With MNS matrix UMNS = UTe Uν
λaν ∼ λbν + λcν ∼ 1, λbe + λce . λm, λn . λm.
The allowed values of n and m in a narrow range
1.3 . m . n . 1.5.
Thus, as a representative value, we expect
Ue3 ' λm ' 0.10− 0.14,
which is almost marginal to experimental bound.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
With MNS matrix UMNS = UTe Uν
λaν ∼ λbν + λcν ∼ 1, λbe + λce . λm, λn . λm.
The allowed values of n and m in a narrow range
1.3 . m . n . 1.5.
Thus, as a representative value, we expect
Ue3 ' λm ' 0.10− 0.14,
which is almost marginal to experimental bound.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
With MNS matrix UMNS = UTe Uν
λaν ∼ λbν + λcν ∼ 1, λbe + λce . λm, λn . λm.
The allowed values of n and m in a narrow range
1.3 . m . n . 1.5.
Thus, as a representative value, we expect
Ue3 ' λm ' 0.10− 0.14,
which is almost marginal to experimental bound.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
Lepton flavor violation
If we focus the KK mass within detectable range 2− 3 TeV,The Lepton flavor violation(LFV) processes gives a strong bound.
Γ(τ → 3e)Γ(µ→ eνµν̄e) ' (K
(1)L11K
(1)L12)
2
(mZ
M(1)A
)4
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
The K(1)Lij factor represents li -lj -A
(1) vertex,
K(n)Lij =
∑3k=1
(UeL)ik
ĝ (n)(cLk )(U†eL
)kj,
where effective coupling of KK gauge mode is,
ĝ(n)L (cfi ) =
√kL∫
dzk[f
(0)L (z , cfi )
]2f
(n)A (z) ≡ ĝ (n)(cfi ).
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
ĝ (n)(c) saturates around -0.2 if c > 0.55.
–0.5
0
0.5
1
1.5
2
2.5
0.2 0.3 0.4 0.5 0.6
ĝ(c)
c
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
if KK gauge boson is experimentally testable, i.e. M(1)A ' 2-3 TeV,
we can specify its mixing matrix
UeL '
1 δ δ
< δ2 1 1
δ 1 1
,where δ = λm ' 0.1,
and bulk lepton masses (SC, Kim, Song)
cL1 ' 0.59, cL2 ' 0.5, cL3 ' 0.5,
cE1 ' −0.74, cE2 ' −0.65, cE3 ' −0.55.
cN2 ' −1.2, cN3 ' −1.1.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Basic assumptionsQuark mass and mixingLepton mass and mixingBound from Lepton flavor violation
if KK gauge boson is experimentally testable, i.e. M(1)A ' 2-3 TeV,
we can specify its mixing matrix
UeL '
1 δ δ
< δ2 1 1
δ 1 1
,where δ = λm ' 0.1, and bulk lepton masses (SC, Kim, Song)
cL1 ' 0.59, cL2 ' 0.5, cL3 ' 0.5,
cE1 ' −0.74, cE2 ' −0.65, cE3 ' −0.55.
cN2 ' −1.2, cN3 ' −1.1.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Experimental signal of flavor violation?B mixingresults
Is there experimental application of this model?
Theoretical or Experimental?
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Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Experimental signal of flavor violation?B mixingresults
B0q − B̄0q mixing data
The current experimental results are well measured
∆Mexpd = (0.507± 0.004) ps−1 ,∆Mexps =
[17.33+0.42−0.21(stat)± 0.07(syst)
]ps−1 .
There is no tree level contribution to B0q − B̄0q in SM.
Can be a good test for the RS bulk SM.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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Flavor physics in warped extra-dimension
Experimental signal of flavor violation?B mixingresults
B0q − B̄0q mixing at tree level by bulk gluon
q̄
b
b̄
q
G(n)
The KK gluon contribution to B0q − B̄0q is tree level while SMcontribution is from box diagram.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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Experimental signal of flavor violation?B mixingresults
For the B0q − B̄0q transition amplitude Mqbb̄ defined by
〈B0q |H∆B=2eff |B̄0q〉 = 2MBqMqbb̄,
where
∆Mq = 2 |Mqbb̄|.
“mixing-induced” CP violation by phase
φq = arg(Mq
bb̄
).
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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B0q − B̄0q mixing from the SM box diagrams and the RS KK gluons:
Mqbb̄
= Mq,SMbb̄
(1 +
Mq,RSbb̄
Mq,SMbb̄
).
We parameterize the new physics effect by
rqeiσq =
Mq,RSbb̄
Mq,SMbb̄
,
where rq ≥ 0 and σq is real.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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Experimental signal of flavor violation?B mixingresults
The rq and σq are constrained by the experimental result for ∆Mq
and the theoretical calculation of the ∆MSMq ,
of which the ratio is defined by ρq:
ρq ≡∣∣∣∣ ∆Mq∆MSMq
∣∣∣∣ =∣∣∣∣∣M
q,SM
bb̄+ Mq,RS
bb̄
Mq,SMbb̄
∣∣∣∣∣ = √1 + 2rq cosσq + r2q .
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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φd can be divided into the SM phase and that from New Physics
(NP) contributions.
φq = φSMq + φ
NPq = φ
SMq + arg(1 + rqe
iσq ).
φNPq is determined by rq and σq.
sinφNPq =rq sinσq√
1 + 2rq cosσq + r2q
,
cosφNPq =1 + rq cosσq√
1 + 2rq cosσq + r2q
.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Experimental signal of flavor violation?B mixingresults
SM amplitude is
Mq,SMbb̄
=G2Fm
2W
12π2MBq η̂
B B̂Bq f2Bq
(V ∗tqVtb)2S0(xt) ,
where xt = m2top/m
2W , and S0 is an “Inami–Lim” function .
CKM components are
|V ∗tdVtb| = (8.6±1.3)×10−3 , |V ∗tsVtb| = (41.3±0.7)×10−3.
Short-distance QCD correction η̂B = 0.552
B̂Bd,s f2Bd,s
is determined from lattice simulation by JLQCD
collaboration.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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Flavor physics in warped extra-dimension
Experimental signal of flavor violation?B mixingresults
New physics effect becomes
rqeiσq ≡ M
q,RS
bb̄
Mq,SMbb̄
=16π2
NC
8g2sg4S0(xt)
m2Wκ233κ
2q3
∑n=1
(ĝ (n)(cQ3)
m(n)A
)2.
O(1) ambiguity and phases in mixings are absorbed in√λ < κij <
1√λ
.
(UqL)ij = κijVCKMij ,
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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Experimental signal of flavor violation?B mixingresults
φd associated with B0d − B̄0d is well measured,
(sinφd)ccs̄ = sin(2β + φNPd ) = 0.687± 0.032,
where φSMd = 2β.
φNPd is estimated by (Ball and Fleischer, 2006)
φNPd∣∣incl
= −(10.1± 4.6)◦, φNPd∣∣excl
= −(2.5± 8.0)◦.
New Physics parameters are constrained by the CP phases.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Experimental signal of flavor violation?B mixingresults
1
2
3
4
5
6
7
8
9
10
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
MKK
[TeV]
c=0.32, κ =1/ 22
ρd
(JLQCD)
φd
incl
π π π π π π π π π π
σd
Figure: Allowed parameter space of (σd , MKK ). Red lines satisfy the
observed ρd and blue lines for φNPd |incl, with 1σ uncertainty.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
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Flavor physics in warped extra-dimension
Experimental signal of flavor violation?B mixingresults
1
2
3
4
5
6
7
8
9
10
0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 2
MKK
[TeV]
σs
c=0.32, κ =1/ 22
π π π π π π π π π π
ρs
(JLQCD)
0
Figure: Allowed parameter space of (σs , MKK ) from the observed ∆Ms .
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Experimental signal of flavor violation?B mixingresults
Results
For the choice of optimistic parameters for bulk SM,
cQ3 = 0.32, κ = 1/√
2
B0d − B̄0d bounds allow KK mode mass as low as 3 TeV.
Bs mixing gives a weaker bound than Bd mixng.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Experimental signal of flavor violation?B mixingresults
Summary
1 SM field can be resides on S1/Z2 × Z′2 bulk space.
2 Fermion bulk masses Can be estimate from SM parameters.
3 In universal Yukawa coupling model, Ue3 ∼ 0.1 in the neutrinomixing matrix.
4 B0d − B̄0d constrains 1st KK mode M(1)A >∼ 3 TeV.
The last one is rather disappointing, since it will be impossible to
detect for LC and will be hard for LHC.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Experimental signal of flavor violation?B mixingresults
Summary
1 SM field can be resides on S1/Z2 × Z′2 bulk space.2 Fermion bulk masses Can be estimate from SM parameters.
3 In universal Yukawa coupling model, Ue3 ∼ 0.1 in the neutrinomixing matrix.
4 B0d − B̄0d constrains 1st KK mode M(1)A >∼ 3 TeV.
The last one is rather disappointing, since it will be impossible to
detect for LC and will be hard for LHC.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Experimental signal of flavor violation?B mixingresults
Summary
1 SM field can be resides on S1/Z2 × Z′2 bulk space.2 Fermion bulk masses Can be estimate from SM parameters.
3 In universal Yukawa coupling model, Ue3 ∼ 0.1 in the neutrinomixing matrix.
4 B0d − B̄0d constrains 1st KK mode M(1)A >∼ 3 TeV.
The last one is rather disappointing, since it will be impossible to
detect for LC and will be hard for LHC.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Experimental signal of flavor violation?B mixingresults
Summary
1 SM field can be resides on S1/Z2 × Z′2 bulk space.2 Fermion bulk masses Can be estimate from SM parameters.
3 In universal Yukawa coupling model, Ue3 ∼ 0.1 in the neutrinomixing matrix.
4 B0d − B̄0d constrains 1st KK mode M(1)A >∼ 3 TeV.
The last one is rather disappointing, since it will be impossible to
detect for LC and will be hard for LHC.
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
-
IntroductionExtra Dimensions
Bulk Standard ModelFermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension
Experimental signal of flavor violation?B mixingresults
Credit for the movie files
I NBC TV series Law & Order
Episode : Big Bang
I WB TV series Angel
Episode : Supersymmetry
Chang, Sanghyeon Flavor Physics from Warped Extra Dimensions
Introduction
Extra Dimensions
Bulk Standard Model
Fermion mass and mixing in Bulk SM
Flavor physics in warped extra-dimension