Instituto Superior Tecnico
Jorge C. Romao Introduction to SUSY – 1
Introduction to Supersymmetry
&
Implications from the LHC Data
Jorge C. RomaoInstituto Superior Tecnico, Departamento de Fısica & CFTP
A. Rovisco Pais 1, 1049-001 Lisboa, Portugal
5 de Dezembro de 2012
IST Summary
Summary
Motivation
SUSY Algebra
MSSM
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 2
Motivation
SUSY Algebra and Representations
MSSM
Particle Content
Superpotential
Masses
Couplings
Bounds: LEP, Tevatron, · · ·
Higgs
Chargino, Neutralinos, · · · Dark Matter
Results from LHC
Conclusions
IST Bibliography
Summary
Motivation
SUSY Algebra
MSSM
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 3
Books
Supersymmetry and Supergravity, Julius Wess and Jonathan Bagger.(−,+,+,+)
Supersymmetric Gauge Field Theory and String Theory, David Bailinand Alexander Love. (+,−,−,−)
Supersymmetry in Particle Physics, Ian Aitchison. (+,−,−,−)
Other Texts
The search for supersymmetry: Probing physics beyond the standard
model, H. E. Haber and G. L. Kane, Phys. Rep. 117 (1985) 75.(+,−,−,−)
A Supersymmetry primer, Stephen Martin, hep-ph/9709356.(−,+,+,+)
BUSSTEPP Lectures on Supersymmetry, Jose M. Figueroa-O’Farrill,hep-ph/0109172. (−,+,+,+)
The Minimal Supersymmetric Standard Model, Jorge C. Romao, (seemy homepage). (+,−,−,−)
IST Motivation
Summary
Motivation
•Naturalness
SUSY Algebra
MSSM
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 4
Although there is not yet direct experimental evidence forsupersymmetry (SUSY), there are many theoretical arguments indicatingthat SUSY might be of relevance for physics around the 1 TeV scale.
The most commonly invoked theoretical arguments for SUSY are:
Interrelates matter fields (leptons and quarks) with force fields (gauge and/orHiggs bosons).
As local SUSY implies gravity (supergravity) it could provide a way to unifygravity with the other interactions.
As SUSY and supergravity have fewer divergences than conventional fieldtheories, the hope is that it could provide a consistent (finite) quantum gravitytheory.
SUSY can help to understand the mass problem, in particular solve the nat-uralness problem (and in some models even the hierarchy problem) if SUSYparticles have masses ≤ O(1TeV).
IST The Naturalness Problem: I
Summary
Motivation
•Naturalness
SUSY Algebra
MSSM
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 5
As the SM is not asymptotically free, at some energy scale Λ, the inter-actions must become strong indicating the existence of new physics. Can-didates for this scale: MX ≃ O(1016 GeV) in GUT’s or the Planck scaleMP ≃ O(1019GeV).
The only consistent way to give masses to the gauge bosons and fermions isthrough the Higgs mechanism involving at least one spin zero Higgs boson.
Although the Higgs boson mass is not fixed by the theory, a value much bigger
than < H0 >≃ G−1/2F ≃ 250 GeV would imply that the Higgs sector would
be strongly coupled making it difficult to understand why we are seeing anapparently successful perturbation theory at low energies.
The one loop radiative corrections to the Higgs boson mass
δm2H = O
(λ2
16π2
)Λ2 + · · ·
would be too large if Λ is identified with ΛGUT or ΛPlanck.
IST The Naturalness Problem: II
Summary
Motivation
•Naturalness
SUSY Algebra
MSSM
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 6
SUSY cures this problem in the following way. If SUSY were exact, radiativecorrections to the scalar masses squared would be absent because thecontribution of fermion loops exactly cancels against the boson loops.
Therefore if SUSY is broken, as it must, we should have
δm2H = O
(λ
16π2
)(m2
F −m2B) ln
Λ
mB+ · · ·
We conclude that
SUSY provides a solution for the the naturalness problem if the massesof the superpartners are around O(1 TeV). This is the main reason
behind all the phenomenological interest in SUSY.
IST The Poincare Algebra
Summary
Motivation
SUSY Algebra
•Poincare algebra
• SUSY algebra
• Simple Results
•Multipletos
• Superfields
MSSM
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 7
The Poincare group is made up of the Lorentz group plus the translations. Wedenote by Jµν the generators of the Lorentz group and by Pµ the generators of thetranslations. The algebra is defined by,
[Jµν , Jρσ] = i (gνρJµσ − gνσJµρ − gµρJνσ + gµσJνρ)
[Pα, Jµν ] = i (gµαPν − gναPµ)
[Pµ, Pν ] = 0
One can show that[P 2, Jµν
]=[P 2, Pµ
]= 0
[W 2, Jµν
]=[W 2, Pµ
]=[W 2, P 2
]= 0
where
Wµ = −1
2εµνρσ J
νρ P σ
is the Pauli-Lubanski vector operator.
IST SUSY Algebra
Summary
Motivation
SUSY Algebra
•Poincare algebra
• SUSY algebra
• Simple Results
•Multipletos
• Superfields
MSSM
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 8
The SUSY generators carry Spin 1/2 and obey the following algebra
Qα, Qβ = 0Qα, Qβ
= 0
Qα, Qβ
= 2 (σµ)αβ Pµ
where
σµ ≡ (1, σi) ; σµ ≡ (1,−σi)
and α, β, α, β = 1, 2 (Weyl 2–component spinor notation).
IST SUSY Algebra and the Poincare Group
Summary
Motivation
SUSY Algebra
•Poincare algebra
• SUSY algebra
• Simple Results
•Multipletos
• Superfields
MSSM
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 9
The commutation relations with the generators of the Poincare group
[Pµ, Qα] = 0 [Jµν , Qα] = −i (σµν)αβ Qβ
One can easily derive that the two invariants of the Poincare group,
P 2 = PαPα W 2 =WαW
α Wµ = − 12ǫµνρσJ
νρP σ
P 2 |m, s〉 = m2 |m, s〉 W 2 |m, s〉 = −m2s(s+ 1) |m, s〉
where Wµ is the Pauli–Lubanski vector operator, are no longer invariants of theSuper Poincare group:
[Qα, P2] = 0 [Qα,W
2] 6= 0
Irreducible multiplets will have particles of thesame mass but different spin.
IST Simple Results from the Algebra
Summary
Motivation
SUSY Algebra
•Poincare algebra
• SUSY algebra
• Simple Results
•Multipletos
• Superfields
MSSM
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 10
Number of Bosons = Number of Fermions
Qα|B >= |F > (−1)NF |B >= |B >
Qα|F >= |B > (−1)NF |F >= −|F >
where (−1)NF is the fermion number of a given state. Then we obtain
Qα(−1)NF = −(−1)NFQα
Using this relation we can show that
Tr[(−1)NF
Qα, Qα
]= Tr
[(−1)NFQαQα + (−1)NFQαQα
]
= Tr[−Qα(−1)NFQα +Qα(−1)NFQα
]= 0
But we also have
Tr[(−1)NF
Qα, Qα
]
= Tr[(−1)NF 2σµ
ααPµ
] Tr[(−1)NF
]= #Bosons−#Fermions = 0
IST SUSY Representations: Massive case
Summary
Motivation
SUSY Algebra
•Poincare algebra
• SUSY algebra
• Simple Results
•Multipletos
• Superfields
MSSM
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 11
In the rest frameQα, Qα
= 2m δαα
This algebra is similar to the algebra of the spin 1/2 creation and annihilationoperators. Choose |Ω〉 such that
Q1 |Ω〉 = Q2 |Ω〉 = 0
Then we have 4 states |Ω〉 ; Q1 |Ω〉 ; Q2 |Ω〉 ; Q1Q2 |Ω〉If J3 |Ω〉 = j3 |Ω〉
State J3 Eigenvalue
|Ω〉 j3Q1 |Ω〉 j3 +
12
Q2 |Ω〉 j3 − 12
Q1Q2 |Ω〉 j3
Two bosons and two fermionsstates separated byone half unit of spin.
IST SUSY Representations: Massless case
Summary
Motivation
SUSY Algebra
•Poincare algebra
• SUSY algebra
• Simple Results
•Multipletos
• Superfields
MSSM
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 12
If m = 0 then we can choose Pµ = (E, 0, 0, E). In this frameQα, Qα
=Mαα
where the matrix M takes the form
M =
(0 00 4E
)
ThenQ2, Q2
= 4E all others vanish.
We have then just two states |Ω〉 ; Q2 |Ω〉
If J3 |Ω〉 = λ |Ω〉
State J3 Eigenvalue
|Ω〉 λQ2 |Ω〉 λ− 1
2
Two states, one fermionone boson separated byone half unit of spin.
IST Superfields for Massless Particles
Summary
Motivation
SUSY Algebra
•Poincare algebra
• SUSY algebra
• Simple Results
•Multipletos
• Superfields
MSSM
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 13
Chiral Superfields: Spin 0 + Spin 12
Φ = Φ(φ, χL)φ Complex Scalar: 2 d.o.fχL Chiral Fermion: 2 d.o.f (on-shell)
Vector Superfields: Spin 12 + Spin 1
V = V (λ,Wµ)λ Chiral Fermion: 2 d.o.fWµ Massless Vector: 2 d.o.f (on-shell)
φ superpartner of the fermion: sfermion
λ superpartner of gauge field: gaugino
IST Particle Content: Gauge Fields
Summary
Motivation
SUSY Algebra
MSSM
Content
•Gauge
• Leptons
•Quarks
•Higgs
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 14
Gauge Fields
We want to have gauge fields for the gauge groupG = SUc(3)⊗ SUL(2)⊗ UY (1). Therefore we will need three vector
superfields (or vector supermultiplets) Vi with the following components:
V1 ≡ (λ′,Wµ1 ) → UY (1)
V2 ≡ (λa,Wµa2 ) → SUL(2) , a = 1, 2, 3
V3 ≡ (gb,Wµb3 ) → SUc(3) , b = 1, . . . , 8
where Wµi are the gauge fields and λ′, λ and g are the UY (1) and SUL(2)
gauginos and the gluino, respectively.
IST Particle Content: Leptons
Summary
Motivation
SUSY Algebra
MSSM
Content
•Gauge
• Leptons
•Quarks
•Higgs
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 15
Leptons
As each chiral multiplet only describes one helicity state, we will need twochiral multiplets for each charged lepton (We will assume that the neutrinosdo not have mass).
Supermultiplet SUc(3)⊗ SUL(2)⊗ UY (1)Quantum Numbers
Li ≡ (L, L)i (1, 2,− 12 )
Ri ≡ (ℓR, ℓcL)i (1, 1, 1)
Each helicity state corresponds to a complex scalar and we have that Li is adoublet of SUL(2)
Li =
(νLi
ℓLi
); Li =
(νLi
ℓLi
)
IST Particle Content: Quarks
Summary
Motivation
SUSY Algebra
MSSM
Content
•Gauge
• Leptons
•Quarks
•Higgs
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 16
Quarks
The quark supermultiplets are given in the Table. The supermultiplet Qi isalso a doublet of SUL(2), that is
Supermultiplet SUc(3)⊗ SUL(2)⊗ UY (1)Quantum Numbers
Qi ≡ (Q,Q)i (3, 2, 16 )
Di ≡ (dR, dcL)i (3, 1, 13 )
Ui ≡ (uR, ucL)i (3, 1,− 2
3 )
Qi =
(uLi
dLi
); Qi =
(uLi
dLi
)
IST Particle Content: Higgs Bosons
Summary
Motivation
SUSY Algebra
MSSM
Content
•Gauge
• Leptons
•Quarks
•Higgs
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 17
Higgs Bosons
Finally the Higgs sector. In the MSSM we need at least two Higgs doublets.This is in contrast with the SM where only one Higgs doublet is enough togive masses to all the particles. The reason can be explained in two ways.Either the need to cancel the anomalies, or the fact that, due to theanalyticity of the superpotential, we have to have two Higgs doublets ofopposite hypercharges to give masses to the up and down type of quarks.
Supermultiplet SUc(3)⊗ SUL(2)⊗ UY (1)Quantum Numbers
H1 ≡ (H1, H1) (1, 2,− 12 )
H2 ≡ (H2, H2) (1, 2,+ 12 )
IST R-Parity
Summary
Motivation
SUSY Algebra
MSSM
Building MSSM· · ·
•R-Parity
•Kinetic Terms
• Self Gauge Int
•Gauge & Matter
• Self Matter Int
• Superpotential
• Soft breaking
•CMSSM
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 18
Most discussions of SUSY phenomenology assume R-Parity conservation where,
RP = (−1)2J+3B+L
This is the case of the MSSM. It implies:
SUSY particles are pair produced.
Every SUSY particle decays into another SUSY particle.
There is a LSP that it is stable ( E/ signature ).
But this is just an ad hoc assumption without a deepjustification. We will see later what are the
consequences of non conservation of R-Parity.
IST Kinetic Terms
Summary
Motivation
SUSY Algebra
MSSM
Building MSSM· · ·
•R-Parity
•Kinetic Terms
• Self Gauge Int
•Gauge & Matter
• Self Matter Int
• Superpotential
• Soft breaking
•CMSSM
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 19
Like in any gauge theory we have
Lkin = − 14F
aµνF
aµν + iλaσµDµλa + (Dµφ)
†Dµφ+ iχσµDµχ
where the field strength F aµν is given by
F aµν = ∂µW
aν − ∂νW
aµ − gfabcW b
µWcν
and fabc are the structure constants of the gauge group G. The covariantderivative is
Dµ = ∂µ + igW aµT
a
One should note that χ and λ are left handed chiral spinors.
IST Self Interactions of the Gauge Multiplet
Summary
Motivation
SUSY Algebra
MSSM
Building MSSM· · ·
•R-Parity
•Kinetic Terms
• Self Gauge Int
•Gauge & Matter
• Self Matter Int
• Superpotential
• Soft breaking
•CMSSM
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 20
For a non Abelian gauge group G we have the usual self–interactions, (cubic andquartic), of the gauge bosons with themselves. But we have a new interaction ofthe gauge bosons with the gauginos. In two component spinor notation it reads
LλλW = igfabc λaσµλ
bW c
µ + h.c.
where fabc are the structure constants of the gauge group G and the matrices σµ
are the equivalent of the γ matrices in two component language.
IST Interactions of the Gauge and Matter Multiplets
Summary
Motivation
SUSY Algebra
MSSM
Building MSSM· · ·
•R-Parity
•Kinetic Terms
• Self Gauge Int
•Gauge & Matter
• Self Matter Int
• Superpotential
• Soft breaking
•CMSSM
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 21
In the usual non Abelian gauge theories we have the interactions of the gaugebosons with the fermions and scalars of the theory. In the supersymmetric case wealso have interactions of the gauginos with the fermions and scalars of the chiralmatter multiplet. The general form, in two component spinor notation is,
LΦW = −gT aijW
aµ
(χiσ
µχj + iφ∗i ∂
↔µφj
)+ g2
(T aT b
)ijW a
µWµb φ∗iφj
+ig√2T a
ij
(λaχjφ
∗i − λ
aχiφj
)
where the new interactions of the gauginos with the fermions and scalars are givenin the last term.
IST Self Interactions of the Matter Multiplet
Summary
Motivation
SUSY Algebra
MSSM
Building MSSM· · ·
•R-Parity
•Kinetic Terms
• Self Gauge Int
•Gauge & Matter
• Self Matter Int
• Superpotential
• Soft breaking
•CMSSM
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 22
These correspond in non supersymmetric gauge theories both to the Yukawainteractions and to the scalar potential. In supersymmetric gauge theories we haveless freedom to construct these terms. The first step is to construct thesuperpotential W . This must be a gauge invariant polynomial function of thescalar components of the chiral multiplet Φi, that is φi. It does not depend on φ∗i .In order to have renormalizable theories the degree of the polynomial must be atmost three.The Yukawa interactions are
LY ukawa = − 12
[∂2W
∂φi∂φjχiχj +
(∂2W
∂φi∂φj
)∗χiχj
]
and the scalar potential is
Vscalar = 12D
aDa + FiF∗i
where
Fi =∂W
∂φi, Da = g φ∗iT
aijφj
IST The Superpotential and SUSY Breaking Lagrangian
Summary
Motivation
SUSY Algebra
MSSM
Building MSSM· · ·
•R-Parity
•Kinetic Terms
• Self Gauge Int
•Gauge & Matter
• Self Matter Int
• Superpotential
• Soft breaking
•CMSSM
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 23
The MSSM Lagrangian is specified by the R–parity conserving superpotential W
W = εab
[hijU Q
ai UjH
b2 + hijDQ
biDjH
a1 + hijE L
bi RjH
a1 − µHa
1 Hb2
]
where i, j = 1, 2, 3 are generation indices, a, b = 1, 2 are SU(2) indices, and ε is acompletely antisymmetric 2× 2 matrix, with ε12 = 1. The coupling matriceshU , hD and hE will give rise to the usual Yukawa interactions needed to givemasses to the leptons and quarks.
If it were not for the need to break SUSYthe number of parameters involved
would be less than in the SM.
IST SUSY Soft Breaking
Summary
Motivation
SUSY Algebra
MSSM
Building MSSM· · ·
•R-Parity
•Kinetic Terms
• Self Gauge Int
•Gauge & Matter
• Self Matter Int
• Superpotential
• Soft breaking
•CMSSM
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 24
The most general SUSY soft breaking is
− LSB = M ij2Q Qa∗
i Qaj +M ij2
U UiU∗j +M ij2
D DiD∗j +M ij2
L La∗i L
aj +M ij2
R RiR∗j
+m2H1Ha∗
1 Ha1 +m2
H2Ha∗
2 Ha2 −
[1
2Msλsλs +
1
2Mλλ+
1
2M ′λ′λ′ + h.c.
]
+εab
[Aij
UhijU Q
ai UjH
b2 +Aij
DhijDQ
biDjH
a1 +Aij
EhijE L
bi RjH
a1 −BµHa
1Hb2
]
Parameter Counting
Theory Gauge Fermion HiggsSector Sector Sector
SM e, g, αs hU , hD, hE µ2, λMSSM e, g, αs hU , hD, hE µ
Broken MSSM e, g, αs hU , hD, hE µ,M1,M2,M3, AU , AD, AE , Bm2
H2,m2
H1,m2
Q,m2U ,m
2D,m
2L,m
2R
IST The Constrained MSSM
Summary
Motivation
SUSY Algebra
MSSM
Building MSSM· · ·
•R-Parity
•Kinetic Terms
• Self Gauge Int
•Gauge & Matter
• Self Matter Int
• Superpotential
• Soft breaking
•CMSSM
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 25
The number of independent parameters can be reduced if we impose some furtherconstraints. The most popular is the MSSM coupled to N = 1 Supergravity(mSUGRA).
At = Ab = Aτ ≡ A ,
m2H1
= m2H2
=M2L =M2
R = m20 ,M
2Q =M2
U =M2D = m2
0 ,
M3 =M2 =M1 =M1/2
Parameter Counting
Parameters Conditions Free Parameters
ht, hb, hτ , v1, v2 mW , mt, mb, mτ tanβ = v2/v1A, B, m0, M1/2, µ ti = 0, i = 1, 2 A, m0, M1/2, sign(µ)
Total = 10 Total = 6 Total = 4+”1”
It is remarkable that with so few parameters we can get the correctvalues for the parameters, in particular m2
H2< 0. For this to happen
the top Yukawa coupling has to be large which we know to be true.
IST The Chargino Mass Matrices
Summary
Motivation
SUSY Algebra
MSSM
Mass Matrices
• chargino
• neutralino
• Scalar Higgs
• SM Higgs Mass
•Higgs Mass RC
• Spectra
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 26
The charged gauginos mix with the charged higgsinos giving the so–calledcharginos. In a basis where ψ+T = (−iλ+, H+
2 ) and ψ−T = (−iλ−, H−1 ), the
chargino mass terms in the Lagrangian are
Lm = − 12 (ψ
+T , ψ−T )
(000 MMMT
C
MMMC 000
)(ψ+
ψ−
)+ h.c.
where the chargino mass matrix is given by
MMMC =
M21√2gv2
1√2gv1 µ
and M2 is the SU(2) gaugino soft mass. We can write this as
MMMC =
M2
√2mW sin β
√2mW cosβ µ
IST The Neutralino Mass Matrix
Summary
Motivation
SUSY Algebra
MSSM
Mass Matrices
• chargino
• neutralino
• Scalar Higgs
• SM Higgs Mass
•Higgs Mass RC
• Spectra
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 27
The neutral gauginos mix with the neutral higgsinos giving the so–calledneutralinos. In the basis ψ0T = (−iλ′,−iλ3, H1
1 , H22 ) the neutral fermions mass
terms in the Lagrangian are given by
Lm = − 12 (ψ
0)TMMMNψ0 + h.c.
where the neutralino mass matrix is
MMMN =
M1 0 − 12g
′v112g
′v20 M2
12gv1 − 1
2gv2− 1
2g′v1
12gv1 0 −µ
12g
′v2 − 12gv2 −µ 0
and M1,M2 are the gaugino soft mass.
IST Neutral Higgs Mass Matrices
Summary
Motivation
SUSY Algebra
MSSM
Mass Matrices
• chargino
• neutralino
• Scalar Higgs
• SM Higgs Mass
•Higgs Mass RC
• Spectra
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 28
MMM2S0 =
(tanβ −1
−1 cot β
)Bµ+
(cotβ −1
−1 tanβ
)12m
2Z sin2 β
with masses
m2h,H = 1
2
[m2
A +m2Z ∓
√(m2
A +m2Z)
2 − 4m2Am
2Z cos 2β
]
MMM2P 0 =
(tanβ −1
−1 cotβ
)Bµ with mass m2
A =Bµ
sin 2β
Sum Rule
m2h +m2
H = m2A +m2
Z
mh < mA < mH
mh < mZ < mH
IST Higgs Boson Mass: Standard Model
Summary
Motivation
SUSY Algebra
MSSM
Mass Matrices
• chargino
• neutralino
• Scalar Higgs
• SM Higgs Mass
•Higgs Mass RC
• Spectra
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 29
In the Standard Model
LHiggs = (DµΦ)†DµΦ− λ
4
(Φ†Φ− v2
2
)2
where
Φ =
(ϕ+
v+H+iϕZ√2
)
Therefore
LHiggs = ∂µH∂µH − λv2
4H2
or
MH =
√λ
2v v = 246 GeV fixed but λ free. MH free.
IST Higgs Boson Mass: Radiative corrections
Summary
Motivation
SUSY Algebra
MSSM
Mass Matrices
• chargino
• neutralino
• Scalar Higgs
• SM Higgs Mass
•Higgs Mass RC
• Spectra
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 30
As the top mass is very large there are important radiative corrections to the Higgsboson mass. The most important are:
m2h = m
(0)h
2 +3g2
16π2m2W
m4t
sin2 βln
(m2
t1m2t2
m4t
)
0 100 200 300 400
1
10
100
1000
A
h
H
Masses
(GeV
)
mH+ (GeV)
0 100 200 300 400
1
10
100
1000
A
h
H
Masses
(GeV
)
mH+ (GeV)
0 200 400 600 800 1000
60
80
100
120
140
Masses
(GeV
)
tan β = 10
tan β = 2
mt1,t2(GeV)
tanβ = 2 tanβ = 10 mh with RC
IST Example of Spectra
Summary
Motivation
SUSY Algebra
MSSM
Mass Matrices
• chargino
• neutralino
• Scalar Higgs
• SM Higgs Mass
•Higgs Mass RC
• Spectra
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 31
SPS1a SPS1b
0
100
200
300
400
500
600
700
800
m [GeV]
lR
lLνl
τ1
τ2
χ0
1
χ0
2
χ0
3
χ0
4
χ±
1
χ±
2
uL, dRuR, dL
g
t1
t2
b1
b2
h0
H0, A0 H±
0
100
200
300
400
500
600
700
800
900
1000
m [GeV]
lR
lL νl
τ−
1
τ−
2
ντ
χ0
1
χ0
2
χ0
3
χ0
4
χ±
1
χ±
2
qR
qL
g
t1
t2
b1
b2
h0
H0, A0 H±
m0 = 100GeV, m1/2 = 250GeVA0 = −100GeV, tanβ = 10, µ > 0
m0 = 200GeV, m1/2 = 400GeVA0 = 0, tanβ = 30, µ > 0
IST Couplings in the MSSM
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Jorge C. Romao Introduction to SUSY – 32
Name Type
Gauge VVVSelf-Interaction VVVV3-Point Gauge V ff
Coupling V f fV χχV HHV GHVGG
3-Point Higgs Hff
Coupling HffHχχHV V
3-Point Goldstone Gff
Coupling GffGχχGV V
Other 3-Point ff χ
Name Type
4-Point V V ffCoupling HHV V
HGV VGGV V
f fHH
ffGH
ffGG
f f f fGoldstone-Higgs HHGInteraction HGG
HHHGHHGGHGGGGGGG
Ghost ωω Vωω Hωω G
IST Examples of New Couplings: Conserving R-Parity
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Jorge C. Romao Introduction to SUSY – 33
γγ χ0χ0
W+W+
W−W−
χ+χ+
χ−χ−
γγ χ0χ0
e+e+
e−e−
e+e+
e−e−
Rule: Change any two lines into the superpartners.
IST Gauge Couplings Unification
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Jorge C. Romao Introduction to SUSY – 34
Standard Model Supersymmetry
0 5 10 15 20Log(Q/GeV)
0
10
20
30
40
50
60
1/α i
0 5 10 15 20Log(Q/GeV)
0
20
40
60
1/α i
α−11
α−12
α−13
α−11
α−12
α−13
αi =g2i4π
g1g2g3
UY (1)
SUL(2)
SUc(3)
Electroweak Theory
QuantumChromodynamics
IST Higgs Boson
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•Charginos ...
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Jorge C. Romao Introduction to SUSY – 35
160
180
200
10 102
103
mH [GeV]
mt
[GeV
]
Excluded
High Q2 except mt
68% CL
mt (Tevatron)0
1
2
3
4
5
6
10030 300
mH [GeV]
∆χ2
Excluded Preliminary
∆αhad =∆α(5)
0.02758±0.00035
0.02749±0.00012
incl. low Q2 data
Theory uncertainty
mLimit = 144 GeV
MH = 114+69−45 GeV
MH < 260 GeV @ 95%CL
MH > 114.4 GeV
IST Limits on Charginos, Sneutrinos & Sleptons
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Jorge C. Romao Introduction to SUSY – 36
99
100
101
102
103
104
105
200 400 600 800 1000
√s > 206.5 GeVADLO
Mν~
(GeV)
Mχ~
1+ (
GeV
)
Excluded at 95 % C.L.
tanβ=2 µ= -200 GeV
0
20
40
60
80
100
50 60 70 80 90 100Ml (GeV/c2)
Mχ
(GeV
/c2 )
R
Ml < MχR
e eR R+ -
µ µR R+ -
τ τR R+ -
√s = 183-208 GeV ADLO
Excluded at 95% CL(µ=-200 GeV/c2, tanβ=1.5)
ObservedExpected
Limits on χ±, l± ≃ 100 GeV.
IST Limits on Neutralinos
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Jorge C. Romao Introduction to SUSY – 37
3035404550556065707580
10 20 30 40tanβ
Mχ lim
(G
eV/c
2 )
ADLO preliminary Any A0, m0<1 TeV/c2, Mtop= 175 GeV/c2
A0=0, Mtop= 175 GeV/c2
A0=0, Mtop= 180 GeV/c2
µ > 0
Excluded at 95% C.L.
3035404550556065707580
10 20 30 40tanβ
Mχ lim
(G
eV/c
2 )
A0=0, Mtop= 175 GeV/c2
A0=0, Mtop= 180 GeV/c2
µ < 0
Excluded at 95% C.L.
ADLO preliminary
0
50
100
150
200
250
300
350
400
0 200 400 600 800 1000
m0 (GeV/c2)
m1/
2 (G
eV/c
2 )
tanβ = 30, µ>0Mtop=175 GeV/c2
A0=0
A0= -1 TeV/c2
Excluded any A0
Limits on χ0 ≥ 50 GeV. More model dependent.
IST Neutralino as Dark Matter
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Jorge C. Romao Introduction to SUSY – 38
m0
(GeV
)
M1/2 (GeV)
tanβ=10, A0=0 (GeV)
0
250
500
750
1000
1250
1500
1750
0 200 400 600 800 1000
Blue region: Neutralino consistent with dark matter.
IST LHC Overview
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Jorge C. Romao Introduction to SUSY – 39
Superconductingmagnets
SPS
PS
CMSCompact Muon Solenoid
Beams Energy Luminosity
e+ e- 200 GeV 1032 cm-2s-1
p p 14 TeV 1034
Pb Pb 1312 TeV 1027
LEP
LHC
The Large Hadron Collider (LHC)
ATLAS
LHC-B
ALICE
From LEP to LHC
IST Basic Physics at LHC
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Jorge C. Romao Introduction to SUSY – 40
l
l
jet
Particle
jet
Proton-Proton (2835 x 2835 bunches)
Protons/bunch 1011
Beam energy 7 TeV (7x1012 eV)Luminosity 1034 cm-2 s-1
Crossing rate 40 MHz
Collisions ≈ 107 - 109 Hz
SUSY.....
Higgs
Zo
Zo
Parton(quark, gluon)
Proton
Selection of 1 in 10,000,000,000,000
Collisions at LHC
Bunch
Higgs
e+
e+
e-
e-
IST SM Higgs at LHC: Two photons
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Jorge C. Romao Introduction to SUSY – 41
p p
γ
γ
H
MHiggs
= 100 GeV
H0 → γγ is the most promising channel if M
H is in the range 80 – 140 GeV.
The high performance PbWO4 crystal
electromagnetic calorimeter in CMS has been optimized for this search.The γγ mass resolution at Mγγ ~ 100 GeV is better than 1%, resulting in a S/B of ≈1/20
4000
5000
6000
7000
8000
110 120 130 140
Eve
nts/
500
MeV
for
100
fb–1
Higgs signal
H → γγ
Mγγ (GeV)
Higgs to 2 photons (MH < 140 GeV)
IST SM Higgs at LHC: Four Leptons
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Jorge C. Romao Introduction to SUSY – 42
Higgs to 4 leptons (140 < MH< 700 GeV)
p pH
µ+
µ-
µ+
µ-
Z
Z
In the MH range 130 - 700 GeV the most
promising channel is H0 → ZZ*→ 2,+ 2,–
or H0 → ZZ → 2,+ 2,– . The detection relies on the excellent performance of the muon chambers, the tracker and the electromagnetic calorimeter. For M
H≤ 170 GeV a mass resolution of
~1 GeV should be achieved with the combination of the 4 Tesla magnetic field and the high resolution of the crystal calorimeter
6080
2040
120 140 160 180
M4± (GeV)
Eve
nts
/ 2 G
eV
H→ZZ*→ 4 ±
MHiggs
= 150 GeV
IST SUSY Discovery Potential at LHC
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Jorge C. Romao Introduction to SUSY – 43
Domains of mSUGRA parameter space (m0,m1/2)where various sparticles can be identified
1000
800
600
400
200
0 400 800 1200 1600 2000m0 GeV
m1/
2, G
eV
q (2000)
~
g (2000)~
tan β = 2, A0 = 0, µ < 0
(40
0)
Ω h2= 0.4
Ω h2= 0.15
~
L
105pb-1
g,q → n + X~~
Sparticles cannot escape discovery at the LHC
Gluinos and squarks can be searched for in various channels with leptons + E
tmiss
+ jets and discovered for masses up to ~ 2.2 TeV.Sleptons can be discovered for masses up to ~ 350 GeV. The region of parameter space 0.15 < Ω h2 < 0.4 — where LSP would be the Cold Dark Matter particle — is contained well within the explorable region
Sparticles: discovery ranges
IST Results from the LHC (LP2011)
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Jorge C. Romao Introduction to SUSY – 44
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IST First Results from the LHC in 2011
Summary
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• LHC Overview
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Jorge C. Romao Introduction to SUSY – 45
!"" "*
"5S94() +
2@"7$%R1'<$%+'
$%!%&$$'(
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"!=B
S""!!*
IST Results from the LHC in 2012
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• LHC Overview
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Jorge C. Romao Introduction to SUSY – 46
Situation in early 2012
Exclusions of MH: − LEP < 114 GeV (arXiv:0602042v1)
− Tevatron [156,177] GeV ( arXiv:1107.5518) − LHC [~127, 600] GeV arXiv:1202.1408 (ATLAS)
arXiv:1202.1488 (CMS)
Very precise measurement of
MW = 80.390 ± 0.016 GeV,
driven mainly by the Tevatron. .
Much of the SM Higgs
range had been ruled out
by 2011 LHC running.
Excess of events in the low mass region seen in
ATLAS and CMS
DISCRETE 2012, CMS overview, J. Varela 12
IST Results from the LHC in 2012: Higgs
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Jorge C. Romao Introduction to SUSY – 47
2. The 4th of July and after
After 48 years of postulat, 30 years of search (and a few heart attacks),
the Higgs is discovered at LHC on the 4th of July: Higgstorical day!
[GeV]H
m110 115 120 125 130 135 140 145 150
0Local p
-1110
-1010
-910
-810
-710
-610
-510
-410
-310
-210
-110
1
Obs.
Exp.
σ1±-1Ldt = 5.8-5.9 fb∫ = 8 TeV: s
-1Ldt = 4.6-4.8 fb∫ = 7 TeV: s
ATLAS 2011 - 2012
σ0σ1σ2
σ3
σ4
σ5
σ6
Higgs boson mass (GeV)110 115 120 125 130 135 140 145
of S
M H
iggs
hyp
othe
sis
SC
L
-710
-610
-510
-410
-310
-210
-110
1
10
99.9%
95%
99%
Observed
Expected (68%)
Expected (95%)
CMS Preliminary-1 = 7 TeV, L = 5.1 fbs-1 = 8 TeV, L = 5.3 fbs
Discrete–Lisbon, 03/12/2012 Implicatons of Higgs discovery – A. Djouadi – p.7/23
IST Results from the LHC in 2012: Higgs
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Jorge C. Romao Introduction to SUSY – 48
Higgs combined results
Significance 6.9σ versus 7.8σ expected.
Combination of 5 channels: bb, ττ, WW, ZZ, γγ
DISCRETE 2012, CMS overview, J. Varela 37
IST Results from the LHC in 2012
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Jorge C. Romao Introduction to SUSY – 49
DISCRETE 2012, CMS overview, J. Varela 16
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Jorge C. Romao Introduction to SUSY – 50
4. Implications for pMSSM: mass
Main results:
• LargeMS values needed:
–MS ≈ 1 TeV: only maximal mixing
–MS ≈ 3 TeV: only typical mixing.
• Large tanβ values favored
but tanβ≈3 possible ifMS≈3TeV
How light sparticles can be with
the constraintMh = 126 GeV?
• 1s/2s gen. q should be heavy...
But not main player here: the stops:
⇒ mt1
<∼
500 GeV still possible!
•M1,M2 and µ unconstrained,
• non-univ. mf: decouple ℓ from q
EW sparticles can be still very light
but watch out the new limits..
Discrete–Lisbon, 03/12/2012 Implicatons of Higgs discovery – A. Djouadi – p.15/23
IST Results from the LHC in 2012: SUSY
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Jorge C. Romao Introduction to SUSY – 51
CMSSM interpretation
DISCRETE 2012, CMS overview, J. Varela 44
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Jorge C. Romao Introduction to SUSY – 52
Mass scale [TeV]
-110 1 10
RP
VLo
ng-li
ved
part
icle
sE
Wdi
rect
3rd
gen.
squ
arks
dire
ct p
rodu
ctio
n3r
d ge
n. s
q.gl
uino
med
.In
clus
ive
sear
ches
,missTE) : ’monojet’ + χWIMP interaction (D5, Dirac
Scalar gluon : 2-jet resonance pair qqq : 3-jet resonance pair→ g~
,missTE : 4 lep + e
νµ,eµνee→0
1χ∼,
0
1χ∼l→Ll
~,
-
Ll~+Ll
~ ,missTE : 4 lep + e
νµ,eµνee→0
1χ∼, 0
1χ∼W→+
1χ∼, -
1χ∼+
1χ∼
,missTEBilinear RPV CMSSM : 1 lep + 7 j’s + resonanceτ)+µe(→τν∼+X, τν∼→LFV : pp resonanceµe+→τν∼+X, τν∼→LFV : pp
+ heavy displaced vertexµ (RPV) : µ qq→ 0
1χ∼
τ∼GMSB : stable (full detector)γβ, β R-hadrons : low t~Stable (full detector)γβ, β R-hadrons : low g~Stable
±
1χ∼ pair prod. (AMSB) : long-lived ±
1χ∼Direct
,missTE : 3 lep + 0
1χ∼)*(Z
0
1χ∼)*( W→ 0
2χ∼±
1χ∼
,missTE) : 3 lep + νν∼l(Ll
~ν∼), lνν∼l(Ll~νLl
~ → 0
2χ∼±
1χ∼
,missTE : 2 lep + 0
1χ∼νl→)ν∼(lνl~→+
1χ∼,
-
1χ∼+
1χ∼
,missTE : 2 lep + 0
1χ∼l→l~, Ll
~Ll
~ ,missTEll) + b-jet + → (natural GMSB) : Z(t~t~
,missTE : 0/1/2 lep (+ b-jets) + 0
1χ∼t→t~, t
~t~ ,missTE : 1 lep + b-jet +
0
1χ∼t→t~, t
~t~ ,missTE : 2 lep + ±
1χ∼b→t~ (medium), t~t~
,missTE : 1 lep + b-jet + ±
1χ∼b→t~ (medium), t~t~
,missTE : 1/2 lep (+ b-jet) + ±
1χ∼b→t~ (light), t~t~
,missTE : 3 lep + j’s + ±
1χ∼t→1b
~, b
~b~ ,missTE : 0 lep + 2-b-jets +
0
1χ∼b→1b
~, b
~b~ ,missTE) : 0 lep + 3 b-j’s + t
~ (virtual
0
1χ∼tt→g~
,missTE) : 0 lep + multi-j’s + t~
(virtual 0
1χ∼tt→g~
,missTE) : 3 lep + j’s + t~
(virtual 0
1χ∼tt→g~
,missTE) : 2 lep (SS) + j’s + t~
(virtual 0
1χ∼tt→g~
,missTE) : 0 lep + 3 b-j’s + b~
(virtual 0
1χ∼bb→g~
,missTEGravitino LSP : ’monojet’ + ,missTEGGM (higgsino NLSP) : Z + jets + ,missT
E + b + γGGM (higgsino-bino NLSP) : ,missTE + lep + γGGM (wino NLSP) : ,missTE + γγGGM (bino NLSP) : ,missTE + 0-1 lep + j’s + τ NLSP) : 1-2 τ∼GMSB ( ,missTE NLSP) : 2 lep (OS) + j’s + l
~GMSB (
,missTE) : 1 lep + j’s + ±χ∼qq→g~ (±χ∼Gluino med. ,missTEPheno model : 0 lep + j’s + ,missTEPheno model : 0 lep + j’s + ,missTEMSUGRA/CMSSM : 1 lep + j’s + ,missTEMSUGRA/CMSSM : 0 lep + j’s +
M* scale < 80 GeV, limit of < 687 GeV for D8)χm(704 GeV , 8 TeV [ATLAS-CONF-2012-147]-1=10.5 fbL
sgluon mass (incl. limit from 1110.2693)100-287 GeV , 7 TeV [1210.4826]-1=4.6 fbL
massg~666 GeV , 7 TeV [1210.4813]-1=4.6 fbL
massl~
> 0)122λ or 121λ), τl~(m)=µl
~(m)=el
~(m) > 100 GeV,
0
1χ∼(m(430 GeV , 8 TeV [ATLAS-CONF-2012-153]-1=13.0 fbL
mass+
1χ∼∼
> 0)122λ or 121λ) > 300 GeV, 0
1χ∼(m(700 GeV , 8 TeV [ATLAS-CONF-2012-153]-1=13.0 fbL
massg~ = q~ < 1 mm)LSPτ(c1.2 TeV , 7 TeV [ATLAS-CONF-2012-140]-1=4.7 fbL
massτν∼ =0.05)1(2)33λ=0.10, ,311λ(1.10 TeV , 7 TeV [Preliminary]-1=4.6 fbL
massτν∼ =0.05)132λ=0.10, ,311λ(1.61 TeV , 7 TeV [Preliminary]-1=4.6 fbL
massq~ decoupled)g~
< 1 m, τ, 1 mm < c-5
10× < 1.5211,λ <
-510×(0.3700 GeV , 7 TeV [1210.7451]-1=4.4 fbL
massτ∼ < 20)β(5 < tan300 GeV , 7 TeV [1211.1597]-1=4.7 fbL
masst~
683 GeV , 7 TeV [1211.1597]-1=4.7 fbL
massg~985 GeV , 7 TeV [1211.1597]-1=4.7 fbL
mass±
1χ∼ ) < 10 ns)
±
1χ∼(τ(1 < 220 GeV , 7 TeV [1210.2852]-1=4.7 fbL
mass±
1χ∼ ) = 0, sleptons decoupled)
0
1χ∼(m),
0
2χ∼(m) =
±
1χ∼(m(140-295 GeV , 8 TeV [ATLAS-CONF-2012-154]-1=13.0 fbL
mass±
1χ∼ ) as above)ν∼,l
~(m) = 0,
0
1χ∼(m),
0
2χ∼(m) =
±
1χ∼(m(580 GeV , 8 TeV [ATLAS-CONF-2012-154]-1=13.0 fbL
mass±
1χ∼ )))
0
1χ∼(m) +
±
1χ∼(m(
21) = ν∼,l
~(m) < 10 GeV,
0
1χ∼(m(110-340 GeV , 7 TeV [1208.2884]-1=4.7 fbL
massl~
) = 0)0
1χ∼(m(85-195 GeV , 7 TeV [1208.2884]-1=4.7 fbL
masst~
) < 230 GeV)0
1χ∼(m(115 < 310 GeV , 7 TeV [1204.6736]-1=2.1 fbL
masst~
) = 0)0
1χ∼(m(230-465 GeV , 7 TeV [1208.1447,1208.2590,1209.4186]-1=4.7 fbL
masst~
) = 0)0
1χ∼(m(230-560 GeV , 8 TeV [ATLAS-CONF-2012-166]-1=13.0 fbL
masst~
) = 10 GeV)±
1χ∼(m)-t
~(m) = 0 GeV,
0
1χ∼(m(160-440 GeV , 8 TeV [ATLAS-CONF-2012-167]-1=13.0 fbL
masst~
) = 150 GeV)±
1χ∼(m) = 0 GeV,
0
1χ∼(m(160-350 GeV , 8 TeV [ATLAS-CONF-2012-166]-1=13.0 fbL
masst~
) = 55 GeV)0
1χ∼(m(167 GeV , 7 TeV [1208.4305, 1209.2102]-1=4.7 fbL
massb~
))0
1χ∼(m) = 2
±
1χ∼(m(405 GeV , 8 TeV [ATLAS-CONF-2012-151]-1=13.0 fbL
massb~
) < 120 GeV)0
1χ∼(m(620 GeV , 8 TeV [ATLAS-CONF-2012-165]-1=12.8 fbL
massg~ ) < 200 GeV)0
1χ∼(m(1.15 TeV , 8 TeV [ATLAS-CONF-2012-145]-1=12.8 fbL
massg~ ) < 300 GeV)0
1χ∼(m(1.00 TeV , 8 TeV [ATLAS-CONF-2012-103]-1=5.8 fbL
massg~ ) < 300 GeV)0
1χ∼(m(860 GeV , 8 TeV [ATLAS-CONF-2012-151]-1=13.0 fbL
massg~ ) < 300 GeV)0
1χ∼(m(850 GeV , 8 TeV [ATLAS-CONF-2012-105]-1=5.8 fbL
massg~ ) < 200 GeV)0
1χ∼(m(1.24 TeV , 8 TeV [ATLAS-CONF-2012-145]-1=12.8 fbL
scale1/2F eV)-4) > 10G~
(m(645 GeV , 8 TeV [ATLAS-CONF-2012-147]-1=10.5 fbL
massg~ ) > 200 GeV)H~
(m(690 GeV , 8 TeV [ATLAS-CONF-2012-152]-1=5.8 fbL
massg~ ) > 220 GeV)0
1χ∼(m(900 GeV , 7 TeV [1211.1167]-1=4.8 fbL
massg~619 GeV , 7 TeV [ATLAS-CONF-2012-144]-1=4.8 fbL
massg~ ) > 50 GeV)0
1χ∼(m(1.07 TeV , 7 TeV [1209.0753]-1=4.8 fbL
massg~ > 20)β(tan1.20 TeV , 7 TeV [1210.1314]-1=4.7 fbL
massg~ < 15)β(tan1.24 TeV , 7 TeV [1208.4688]-1=4.7 fbL
massg~ ))g~(m)+
0χ∼(m(
21) =
±χ∼(m) < 200 GeV, 0
1χ∼(m(900 GeV , 7 TeV [1208.4688]-1=4.7 fbL
massq~ )0
1χ∼) < 2 TeV, light g
~(m(1.38 TeV , 8 TeV [ATLAS-CONF-2012-109]-1=5.8 fbL
massg~ )0
1χ∼) < 2 TeV, light q
~(m(1.18 TeV , 8 TeV [ATLAS-CONF-2012-109]-1=5.8 fbL
massg~ = q~1.24 TeV , 8 TeV [ATLAS-CONF-2012-104]-1=5.8 fbL
massg~ = q~1.50 TeV , 8 TeV [ATLAS-CONF-2012-109]-1=5.8 fbL
Only a selection of the available mass limits on new states or phenomena shown.* theoretical signal cross section uncertainty.σAll limits quoted are observed minus 1
-1 = (2.1 - 13.0) fbLdt∫ = 7, 8 TeVs
ATLASPreliminary
7 TeV results
8 TeV results
ATLAS SUSY Searches* - 95% CL Lower Limits (Status: Dec 2012)
IST Results from the LHC in 2012:SUSY
Summary
Motivation
SUSY Algebra
MSSM
LEP Results
LHC Results
• LHC Overview
•Basic Physics
•H: 2photons
•H: 4Leptons
• SUSY at LHC
• Signatures
•First Results 2011
• 2012 Results
Conclusions
Jorge C. Romao Introduction to SUSY – 53
χ+χ0 exclusion limits
7 TeV result New 8 TeV result
SUS-12-022 SUS-12-006
DISCRETE 2012, CMS overview, J. Varela 51
IST Conclusions
Summary
Motivation
SUSY Algebra
MSSM
LEP Results
LHC Results
Conclusions
Jorge C. Romao Introduction to SUSY – 54
Although there is not yet direct experimental evidence forsupersymmetry (SUSY), there are many theoretical arguments indicatingthat SUSY might be of relevance for physics around the 1 TeV scale.
We will be waiting for the LHC verdict!
Lots of things to be done by Experimentalists and Theoreticians