minimal supersymmetric standard model (mssm) · n=1 broken susy lagrangian local gauge invariance,...
TRANSCRIPT
Athanasios Dedes
Institute for Particle Physics Phenomenology (IPPP), Durham, UK
YETI’05, IPPP, January 8, 2005
Minimal Supersymmetric Standard Model
(MSSM)
1. What is and Why Supersymmetry (SUSY)?
2. What are the SUSY interactions ?
3. What is MSSM ?
4. How can I discover SUSY today?Direct SUSY Trileptons searches
Indirect rare decay Bs → µ+µ−
5. Conclusions
The present is a basic introduction to Beate’s talkthat follows
Minimal Supersymmetric Standard Model 1
What is and Why Supersymmetry ?
• Consider the Lagrangian of a free complex scalar field anda free Weyl spinor field :
L = i Ψ σµ∂µ Ψ + ∂µΦ∗ ∂µΦ
1 deriv 2 deriv
Ψ→ eiβ Ψ Φ→ eiγ Φ
Seen Unseen?←→
Question : Is there any symmetry relating the two ?
δΦ = a ξ Ψ
l Supersymmetry
δΨ = i a∗ ξ σµ (∂µΦ)
Supersymmetric masses and interactions :
∆L =∣
∣
∣
∣
∂W(Φ)
∂Φ
∣
∣
∣
∣
2 −[ 1
2
∂2W(Φ)
∂Φ ∂ΦΨ Ψ + H.c
]
W(Φ) is an analytic function (superpotential)
IPPP, University of Durham 1 Athanasios Dedes
Minimal Supersymmetric Standard Model 2
Masses : W [Φ] = 12 µ Φ2
∆L = |µ|2 Φ2 − (µ
2ΨΨ + H.c)
... all fields entering a supermultiplet {Φ, Ψ} have the samemass...
↓Supersymmetry must be broken at our energies
↓∆LBreaking = M 2
0 Φ2
Interactions :
WReal World[Φ] = YD QL HD DR + YU QL HU UR
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IPPP, University of Durham 2 Athanasios Dedes
Minimal Supersymmetric Standard Model 3
More SM and SUSY interactions
We started with
L = i Ψ σµ ∂µ Ψ
+ ∂µ Φ∗ ∂µ Φ
IPPP, University of Durham 3 Athanasios Dedes
Minimal Supersymmetric Standard Model 4
More SM and SUSY interactions
Local gauge invariance and global supersymmetry result in
L = i Ψ σµ(∂µ − igAµ) Ψ
+ (∂µ − igAµ)∗ Φ∗ (∂µ − igAµ) Φ
IPPP, University of Durham 4 Athanasios Dedes
Minimal Supersymmetric Standard Model 5
More SM and SUSY interactions
Local gauge invariance and global supersymmetry result in
L = i Ψ σµ(∂µ − igAµ) Ψ
+ (∂µ − igAµ)∗ Φ∗ (∂µ − igAµ) Φ
− 1
4Fµν Fµν
IPPP, University of Durham 5 Athanasios Dedes
Minimal Supersymmetric Standard Model 6
More SM and SUSY interactions
Local gauge invariance and global supersymmetry result in
L = i Ψ σµ(∂µ − igAµ) Ψ
+ (∂µ − igAµ)∗ Φ∗ (∂µ − igAµ) Φ
− 1
4Fµν Fµν
+ iλ σµ∂µ λ
IPPP, University of Durham 6 Athanasios Dedes
Minimal Supersymmetric Standard Model 7
More SM and SUSY interactions
Local gauge invariance and global supersymmetry result in
L = i Ψ σµ(∂µ − igAµ) Ψ
+ (∂µ − igAµ)∗ Φ∗ (∂µ − igAµ) Φ
− 1
4Fµν Fµν
+ iλ σµ(∂µ − igAµ) λ
IPPP, University of Durham 7 Athanasios Dedes
Minimal Supersymmetric Standard Model 8
More SM and SUSY interactions
Local gauge invariance and global supersymmetry result in
L = i Ψ σµ(∂µ − igAµ) Ψ
+ (∂µ − igAµ)∗ Φ∗ (∂µ − igAµ) Φ
− 1
4Fµν Fµν
+ iλ σµ(∂µ − igAµ) λ
− 1
2
∂2W∂Φ ∂Φ
Ψ Ψ + H.c
where W = 12 µ Φ2 + 1
3 Y Φ3
IPPP, University of Durham 8 Athanasios Dedes
Minimal Supersymmetric Standard Model 9
More SM and SUSY interactions
Local gauge invariance and global supersymmetry result in
L = i Ψ σµ(∂µ − igAµ) Ψ
+ (∂µ − igAµ)∗ Φ∗ (∂µ − igAµ) Φ
− 1
4Fµν Fµν
+ iλ σµ(∂µ − igAµ) λ
− 1
2
∂2W∂Φ ∂Φ
Ψ Ψ + H.c
+ i√
2 g Φ∗ Ψ λ + H.c
IPPP, University of Durham 9 Athanasios Dedes
Minimal Supersymmetric Standard Model 10
N=1 SUSY Lagrangian
Local gauge invariance and global supersymmetry result in
L = i Ψ σµ(∂µ − igAµ) Ψ
+ (∂µ − igAµ)∗ Φ∗ (∂µ − igAµ) Φ
− 1
4Fµν Fµν
+ iλ σµ(∂µ − igAµ) λ
− 1
2
∂2W∂Φ ∂Φ
Ψ Ψ + H.c
+ i√
2 g Φ∗ Ψ λ + H.c
− |∂W∂Φ|2 − g2
2(Φ∗ Φ)2
where W = 12µ Φ2 + 1
3Y Φ3
IPPP, University of Durham 10 Athanasios Dedes
Minimal Supersymmetric Standard Model 11
N=1 broken SUSY Lagrangian
Local gauge invariance, global supersymmetry and supersym-metry breaking result in
L = i Ψ σµ(∂µ − igAµ) Ψ
+ (∂µ − igAµ)∗ Φ∗ (∂µ − igAµ) Φ
− 1
4Fµν Fµν
+ iλ σµ(∂µ − igAµ) λ
− 1
2
∂2W∂Φ ∂Φ
Ψ Ψ + H.c
+ i√
2 g Φ∗ Ψ λ + H.c
− |∂W∂Φ|2 − g2
2(Φ∗ Φ)2
− M 20 Φ∗ Φ − B0 Φ Φ − A0 Φ Φ Φ + H.c
IPPP, University of Durham 11 Athanasios Dedes
Minimal Supersymmetric Standard Model 12
N=1 broken SUSY Lagrangian
Local gauge invariance and global supersymmetry result in
L = i Ψ σµ(∂µ − igAµ) Ψ
+ (∂µ − igAµ)∗ Φ∗ (∂µ − igAµ) Φ
− 1
4Fµν Fµν
+ iλ σµ(∂µ − igAµ) λ
− 1
2
∂2W∂Φ ∂Φ
Ψ Ψ + H.c
+ i√
2 g Φ∗ Ψ λ + H.c
− |∂W∂Φ|2 − g2
2(Φ∗ Φ)2
− M 20 Φ∗ Φ − B0 Φ Φ − A0 Φ Φ Φ + H.c
− M1/2
2λ λ + H.c
IPPP, University of Durham 12 Athanasios Dedes
Minimal Supersymmetric Standard Model 13
What is MSSM ?
Fields SU(3)C × SU(2)L × U(1)Y Φ Ψ
Qi,αr (3,2, 1
6)
u
d
L
,
ud
L
Dr,α (3,1, 13) dR , dR
Ur,α (3,1,−23) uR , uR
Lir (1,2,−1
2)
νe
e
L
,
νe
e
L
Er (1,1, 1) eR , eR
H id (1,2,−1
2)
H0d
H−d
,
H0d
H−d
H iu (1,2, 1
2)
H+u
H0u
,
H+u
H0u
Fields SU(3)C × SU(2)L × U(1)Y λ Aµ
V(R)3 (8,1, 0) G(R) , G(R)
µ
V(Γ)2 (1,3, 0) W (Γ) , W (Γ)
µ
V1 (1,1, 0) B , Bµ
IPPP, University of Durham 13 Athanasios Dedes
Minimal Supersymmetric Standard Model 14
What is tan β ??
tan β =〈H0
u〉〈H0
d〉or
tan β =vu
vd
IPPP, University of Durham 14 Athanasios Dedes
Minimal Supersymmetric Standard Model 15
How to Discover SUSY today ?
1. Start with your favorite Standard Model process
2. Supersymmetrize the intermediate legs of thisprocess
3. Decide whether you want the SUSY particles tobe produced in pairs or not i.e., R-parity symme-try on or off
4. Estimate the rate before you start typing...
Example : Electron-Muon Scattering
IPPP, University of Durham 15 Athanasios Dedes
Minimal Supersymmetric Standard Model 16
Trileptons
“Gold plated” mode at Tevatron
,
A. D, H. Dreiner, U. Nierste, P. Richardson, arXiv:hep-ph/0207026.
IPPP, University of Durham 16 Athanasios Dedes
Minimal Supersymmetric Standard Model 17
Bd,s→ µ+µ−�
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CS,P ∝ mµtan3 βM2
H3
f(MSUSY )⇒ B(Bs → µ+µ−) ∝ tan6 βM4
H3
!!
A. D., and A. Pilaftsis, Phys. Rev. D 67, 015012 (2003) [arXiv:hep-ph/0209306].
For a review see A. D., Mod. Phys. Lett. A 18 (2003) 2627
IPPP, University of Durham 17 Athanasios Dedes
Minimal Supersymmetric Standard Model 18
• Standard Model Prediction :
B(Bs→ µ+µ−) = (3.7± 1.2)× 10−9
B(Bd→ µ+µ−) = (1.0± 0.3± 0.3)× 10−10
• General MSSM prediction :
B(Bs → µ+µ−) = up to 10−5
B(Bd→ µ+µ−) = up to 10−6
• Tevatron CDF/D0 Run II experimental bound :
B(Bs → µ+µ−) < 5.8/4.1× 10−7 at 90% CL
• BaBar/Belle experimental bound :
B(Bd→ µ+µ−) < 8.3/16× 10−8 at 90% CL
...any evidence at Tevatron or at
BaBar/Belle
will be a SUSY footprint...
IPPP, University of Durham 18 Athanasios Dedes
Minimal Supersymmetric Standard Model 19
Correlation with the muon g − 2
M0 = 350 GeV,M1/2 = 450 GeV, A0 = 0 GeV, µ > 0
A.D, H. K. Dreiner and U. Nierste, Phys. Rev. Lett. 87, 251804 (2001)
IPPP, University of Durham 19 Athanasios Dedes
Minimal Supersymmetric Standard Model 20
Bounding M0, M1/2 and A0 from above!
MA <∼ 660 GeV with x = 0.5 fb−1
MA <∼ 790 GeV with x = 2 fb−1
MA <∼ 970 GeV with x = 10 fb−1 ,
A.D., and B. T. Huffman, Phys. Lett. B 600 (2004) 261 [arXiv:hep-ph/0407285].
IPPP, University of Durham 20 Athanasios Dedes
Minimal Supersymmetric Standard Model 21
Conclusions
1. Supersymmetry is a symmetry which relates particles ofdifferent spins.
2. It has a virtue of allowing non trivial interactions betweenfermions and bosons.
3. Our ignorance about the breaking of supersymmetry bringsthe unknown parameters : M0, M1/2, A0
4. A Realization of broken SUSY exists and called MSSM
5. Tevatron can see MSSM signatures today directly or indi-rectly. Examples are : SUSY trileptons and Bs → µ+µ−.
6. Supersymmetry will receive great support if a light Higgsboson is found. After all, there must be a reason whyNature decided to entertain us with particles of differentspin.
IPPP, University of Durham 21 Athanasios Dedes