Introduction to the
“Beyond the Standard Model” session
JJC 2014
Dec. 11th 2014
Samuel Calvet
Outline
Why do we need “Beyond the Standard Model” (BSM) theories ?
BSM theories on the market : their predictions/particles
SuperSYmetry, Extra-dimensions, compositness, ...
2
Why do we need BSM theories ?
2 reasons (among others) that drive searches at LHC ?
3
Dark matter
Astrophysical observations in contradiction w/ the theories
Rotation of galaxies needs
“extra mass”
Cluster of galaxies:
–
Same velocity issue
–
Gravitational lensing
–
Bullet cluster
–
….
Observed
Prediction
4
Dark matter
Astrophysical observations in contradiction w/ the theories
Rotation of galaxies needs
“extra mass”
Cluster of galaxies:
–
Same velocity issue
–
Gravitational lensing
–
Bullet cluster
–
….
Observed
Prediction
→ Need of neutral
particles weakly interacting
(dark matter)
5
Naturalness
Higgs mass modified by quantum corrections
H
Λ: scale of new physic
H
t
H
If:
Λ is large (up to Planck scale to include the gravity ?)
No ultra precise cancellation of terms (→ fine tuning)
→ Large mh
6
Naturalness
Higgs mass modified by quantum corrections
H
Λ: scale of new physic
H
t
H
If:
Λ is large (up to Planck scale to include the gravity ?)
No ultra precise cancellation of terms (→ fine tuning)
→ Large mh
Observation : mh~125GeV → light !
Not natural !
7
Solving naturalness issue
Main ideas to solve the naturalness issue:
No ultra precise cancellation of terms (→ fine tuning)
Λ can be large (up to Planck scale to include the gravity ?)
New symmetry
–
Each correction balanced by another (new) one
–
Protects mH
H
t
→ supersymmetry
8
Solving naturalness issue
Main ideas to solve the naturalness issue:
No ultra precise cancellation of terms (→ fine tuning)
Λ can be large (up to Planck scale to include the gravity ?)
New symmetry
New spatial dimensions
–
Bring the Planck scale to lower value
→Λ is small
9
Solving naturalness issue
Main ideas to solve the naturalness issue:
No ultra precise cancellation of terms (→ fine tuning)
Λ can be large (up to Planck scale to include the gravity ?)
New symmetry
New spatial dimensions
Higgs boson is not the SM one
–
Higgs is a composite particle at scale Λ
→ naturalness issue disappears
10
Solving naturalness issue
Main ideas to solve the naturalness issue:
No ultra precise cancellation of terms (→ fine tuning)
Λ can be large (up to Planck scale to include the gravity ?)
New symmetry
New spatial dimensions
Have to appear at the TeV scale
to be efficient
Higgs boson is not the SM one
11
Supersymmetry
12
Supersymmetry
Add new symmetry: fermion ↔ boson
( )( )( )
uL
cL
tL
g
dL
sL
bL

uR
cR
tR
W±
dR
sR
bR
Z
S=1
( )( )( )

e
L




L
L
h
eL
L
L
H
eR
R
R
A
S=1/2
( )( )( )
↔
~
uL
~
dL
c~L
s~
~t
L
~
b
~
u
R
~
dR
c~R
s~
~t
R
~
bR
L
R
L
( )( )( )
H±
S=0
~
 eL
~
e
~

L
~
L
L
~

L
~
L
~
eR
~R
~

R
S=0
g~
~
~±
W
~
Z
S=1/2
~
h
~
H
~
A
~±
H
S=1/2
Extended Higgs sector
13
Supersymmetry
Add new symmetry: fermion ↔ boson
( )( )( )
→ cancellation of radiative corrections
uL
cL
tL
g
dL
sL
bL

uR
cR
tR
W±
dR
sR
bR
Z
S=1
( )( )( )

e
L




L
L
h
eL
L
L
H
eR
R
R
A
S=1/2
( )( )( )
↔
~
uL
~
dL
c~L
s~
~t
L
~
b
~
u
R
~
dR
c~R
s~
~t
R
~
bR
L
R
L
( )( )( )
H±
S=0
~
 eL
~
e
~

L
~
L
L
~

L
~
L
~
eR
~R
~

R
S=0
g~
~
~±
W
~
Z
S=1/2
~
h
~
H
~
A
~±
H
S=1/2
Extended Higgs sector
14
Supersymmetry
Add new symmetry: fermion ↔ boson
( )( )( )
→ cancellation of radiative corrections
uL
cL
tL
g
dL
sL
bL

uR
cR
tR
W±
dR
sR
bR
Z
S=1
( )( )( )

e
L




L
L
h
eL
L
L
H
eR
R
R
A
S=1/2
H±
S=0
( )( )( )
↔
~
uL
~
dL
c~L
s~
~t
L
~
b
~
u
R
~
dR
c~R
s~
~t
R
~
bR
L
R
t~2
L
( )( )( )
~
 eL
~
e
~

L
~
L
L
~

L
~
L
~
eR
~R
~

R
S=0
“heavy”
“light”
~t
1
g~
~
~±
W
~
Z
S=1/2
~
h
~
H
~
A
~±
H
S=1/2
Add a pinch of mixing
15
Supersymmetry
Add new symmetry: fermion ↔ boson
( )( )( )
→ cancellation of radiative corrections
uL
cL
tL
g
dL
sL
bL

uR
cR
tR
W±
dR
sR
bR
Z
S=1
( )( )( )

e
L




L
L
h
eL
L
L
H
eR
R
R
A
S=1/2
H±
S=0
( )( )( )
↔
~
uL
~
dL
c~L
s~
~t
L
~
b
t~2
~
u
R
~
dR
c~R
s~
~t
R
~
bR
~t
1
L
R
L
( )( )( )
~
 eL
~
e
~

L
~
L
L
~

L
~
L
~
eR
~R
~

R
S=0
g~
~
~±
W
~
Z
S=1/2
~
h
~
H
~
A
~±
H
S=1/2
Add a pinch of mixing
16
Supersymmetry
Add new symmetry: fermion ↔ boson
( )( )( )
→ cancellation of radiative corrections
uL
cL
tL
g
dL
sL
bL

uR
cR
tR
W±
dR
sR
bR
Z
S=1
( )( )( )

e
L




L
L
h
eL
L
L
H
eR
R
R
A
S=1/2
H±
S=0
( )( )( )
↔
~
uL
~
dL
c~L
s~
~t
L
~
b
~
u
R
~
dR
c~R
s~
~t
R
~
bR
L
R
L
( )( )( )
~
 eL
~
e
~

L
~
L
L
~

L
~
L
~
eR
~R
~

R
S=0
t~2
~t
1
g~
~
~±
W
~
Z
S=1/2
~
h
~
H
~
A
~±
H
χ~±1
χ~±2
χ~01
χ~02
χ~03
χ~04
S=1/2 S=1/2
Add a pinch of mixing
17
Supersymmetry: R-parity
R=(-1)L+3B+2J
L/B: leptonic/baryoni number, J:spin
+1 for SM particles
-1 for SuSy particles
R-parity:
Assumed prefect or weakly violated (to preserve proton lifetime)
SuSy particle produced by pair
SM, R=1
SuSy, R=-1
SM
SM, R=1
R=1
SuSy, R=-1
18
Supersymmetry: R-parity
R=(-1)L+3B+2J
L/B: leptonic/baryoni number, J:spin
+1 for SM particles
-1 for SuSy particles
R-parity:
Assumed prefect or weakly violated (to preserve proton lifetime)
SuSy particle produced by pair
Lightest SuSy particle (LSP) is stable → Dark matter candidate
SM, R=1
SuSy, R=-1
SM
SM, R=1
SuSy, R=-1
R=1
SuSy, R=-1
SuSy, R=-1
SM, R=1
19
Breaking SuSy
Super-partners not yet observed → heavier than SM partners
SuSy has to be broken
By an unknown mechanism
Introduces many free parameters
→ Phenomenological assumptions to express results
(mSUGRA, MSSM, nMSSM, pMSSM, …)
or
→ Simplified models:
●
●
branching ratio=100%
decouple other sparticles
20
A rich phenomenology
A simple example
2 b + missing energy
21
A rich phenomenology
A more complex one
t
~
t
~
t
t
22
A rich phenomenology
A more complex one
t
~
t
~
t
t
23
A rich phenomenology
A more complex one
t
~
t
~
t
t
24
A rich phenomenology
A more complex one
t
~
t
~
t
t
25
Extra-dimensions
Nice ref: M. Besancon, Moriond EW 2010
Models & signatures of extra dimensions at the LHC
26
Kaluza–Klein excitations
Add a space-dimension (y)
y
Flat (ie factorisable): ds2=gμνdxμdxν
μ,ν=0, 1, 2, 3, ... D
Our 4-d world
27
Kaluza–Klein excitations
Compactification
Add a space-dimension (y)
y
y
Flat (ie factorisable): ds2=gμνdxμdxν
μ,ν=0, 1, 2, 3, ... D
Our 4-d world
R
Our 4-d world
28
Kaluza–Klein excitations
Compactification
Add a space-dimension (y)
y
y
Flat (ie factorisable): ds2=gμνdxμdxν
μ,ν=0, 1, 2, 3, ... D
Our 4-d world
R
Our 4-d world
Fourier mode expansion
Φ(x,y)=ΣkΦ(k)(x)eiky/R
Assume some fields can propagate along y
Kaluza–Klein (KK) excitations
mk2=m02+k2/R2
Momentum in new dimensions ↔ mass 4-D (Kaluza–Klein resonance)
29
Kaluza–Klein excitations
Compactification
Add a space-dimension (y)
y
y
Flat (ie factorisable): ds2=gμνdxμdxν
Our 4-d world
μ,ν=0, 1, 2, 3, ... D
R
Our 4-d world
y
Fourier mode expansion
Wrapped: ds =a(y) (gμνdx dx ) + dy
2
μ
ν
Φ(x,y)=ΣkΦ(k)(x)eiky/R
2
μ,ν=0, 1, 2, 3
Our 4-d world
Assume some fields can propagate along y
Kaluza–Klein (KK) excitations
mk2=m02+k2/R2
Momentum in new dimensions ↔ mass 4-D (Kaluza–Klein resonance)
30
Adding extradimensions...
A lot of room to play...
ADD
TeV-1
mUED
RS1
Bulk RS
Topology
Flat
Flat
Flat
Wrapped
Wrapped
N extradim
≥2
≥1
≥1
1
1
Propagating fields
Graviton
Vector boson (V)
V, fermions
Graviton
Everything apart Higgs
...
31
ADD (Arkani-Hamed, Dimopoulos and Dvali)
n compactified flat extra-dimensions
Only grativity propagates in the bulk
Dilution of the gravity
Planck mass in 4+nD
R
Our 4-d world
Planck mass in 4D
If MPl=1TeV (to address the hierarchy problem):
n=1 → R=1010km
n=2 → R=1mm
n=3 → R=1nm
Large R, but gravity not yet probed at these scales !
...
32
ADD signatures at colliders
“Large” R → states close to each other (Δm~eV) → continuum
s-channel
q
q
KK graviton in final states
→ detected
→ Missing Energy
Gamma+MET
33
TeV-1 / mUED
5D flat bulk
R
No gravity included
Our 4-d world
TeV-1:
R=O(TeV-1)
gauge bosons in the bulk → Z', W', gKK
1st, 2nd 3rd, … modes well separated
Minimal Universal Extra-Dimensions
All the SM fields in the bulk
Assume momentum conservation in the bulk
→ KK-parity
Similar effect than R-parity (pair production of 1st mode, dark matter candidate)
34
Randal–Sundrum (RS)
y
Wrapped compacted 5D
ds2=e-2kRθ (gμνdxμdxν) + Rdθ2
(θ∈[0,π], k~MPl)
Wrap factor
Our 4-d world
Wrap generates vev~O(TeV) on a brane
from Planck scale on another brane
→ Fix hierarchy problem
Graviton near Planck brane
GKK near TeV brane
35
Randal–Sundrum (RS)
Minimal RS (RS1): Only gravity propagates in bulk
Well separated (Δm~TeV) KK gravitons
Democratic couplings
A Oliveira arXiv:1404.0102
36
Randal–Sundrum (RS)
Minimal RS (RS1): Only gravity propagates in bulk
Well separated (Δm~TeV) KK gravitons
Democratic couplings
Bulk RS:
Higgs localized on/near TeV brane
Other fields in bulk
→ KK resonances
1st and 2nd generations : Planck brane
3rd generation: TeV brane
A Oliveira arXiv:1404.0102
→ ~large Yukawa
Prediction of Vector-like quark
(see next slides)
37
Compositness
38
Compositness
Assume new Strong sector (QCD-like) at TeV-scale
SO(5) → SO(4) + 4 Goldstone bosons (=Higgs doublet)
→ Higgs boson is composite (like pion in QCD)
Consequences:
Fix naturalness issue
Lagrangian modified as:
Stolen to A. Pomarol
(SM: a=b=c=1)
39
Compositness: consequence
SM without Higgs
No unitarity at high energy
SM with Higgs: unitarity recovered
Figures stolen to A. Pomarol
40
Compositness: consequence
If the Higgs is (partially) composite:
→ Need extra states:
Figures stolen to A. Pomarol
Also predicts Vector-Like Quarks (VLQ)
41
Vector-Like Quark (VLQ)
Predicted by many theories
Extra-dimension, Compositness, Grand Unified Theory, …
Vector-like ?
42
Vector-Like Quark (VLQ)
Predicted by many theories
Extra-dimension, Compositness, Grand Unified Theory, …
Vector-like ?
L. Panizzi
43
Vector-Like Quark (VLQ)
Predicted by many theories
Extra-dimension, Compositness, Grand Unified Theory, …
Vector-like ?
L. Panizzi
44
VLQ
VLQ mix with SM quarks
… and interact through Yukawa interactions
Various incarnation possible:
L. Panizzi
45
Searching for VLQ
Production / decay
46
Searching for VLQ
Production / decay
47
Searching for VLQ
Production / decay
48
Searching for VLQ
Production / decay
49
Searching for VLQ
Production / decay
50
Conclusion
Lots of models on the market
… trying to address
–
dark matter
–
naturalness
Of course, I could not present
many other models
many other problems (ν mass, ...)
Hors-Série
Beyond SM
Higgs
t
H
Un avenir
pour le TeVatron?
51
Backup
52
Top-quark mass
Important parameter of the SM
(meta-)stability of the Higgs field ?
Larger mtop →
larger corrections
M
et
ast
ab
il i
ty
ty
Our vacuum
St
ab
i li
Energy of
empty space
vev
Exotic vacuum
53