Introduction to Supersymmetry Implications from the LHC Dataromao/Public/... · 2012-12-06 · Instituto Superior T´ecnico Jorge C. Rom˜ao Introduction to SUSY – 1 Introduction

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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


Quarks

The quark supermultiplets are given in the Table. The supermultiplet Qi isalso a doublet of SUL(2), that is


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


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.


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


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


•R-Parity

•Kinetic Terms

• Self Gauge Int

•Gauge & Matter

• Self Matter Int

• Superpotential

• Soft breaking

•CMSSM

LEP Results

LHC Results

Conclusions


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


•R-Parity

•Kinetic Terms

• Self Gauge Int

•Gauge & Matter

• Self Matter Int

• Superpotential

• Soft breaking

•CMSSM

LEP Results

LHC Results

Conclusions


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


•R-Parity

•Kinetic Terms

• Self Gauge Int

•Gauge & Matter

• Self Matter Int

• Superpotential

• Soft breaking

•CMSSM

LEP Results

LHC Results

Conclusions


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


•R-Parity

•Kinetic Terms

• Self Gauge Int

•Gauge & Matter

• Self Matter Int

• Superpotential

• Soft breaking

•CMSSM

LEP Results

LHC Results

Conclusions


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


•R-Parity

•Kinetic Terms

• Self Gauge Int

•Gauge & Matter

• Self Matter Int

• Superpotential

• Soft breaking

•CMSSM

LEP Results

LHC Results

Conclusions


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


•R-Parity

•Kinetic Terms

• Self Gauge Int

•Gauge & Matter

• Self Matter Int

• Superpotential

• Soft breaking

•CMSSM

LEP Results

LHC Results

Conclusions


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


•R-Parity

•Kinetic Terms

• Self Gauge Int

•Gauge & Matter

• Self Matter Int

• Superpotential

• Soft breaking

•CMSSM

LEP Results

LHC Results

Conclusions


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


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


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


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


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


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


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

Summary

Motivation

SUSY Algebra

MSSM

Couplings

• couplings

•New vertices

•Unification

LEP Results

LHC Results

Conclusions


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

Summary

Motivation

SUSY Algebra

MSSM

Couplings

• couplings

•New vertices

•Unification

LEP Results

LHC Results

Conclusions


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

Summary

Motivation

SUSY Algebra

MSSM

Couplings

• couplings

•New vertices

•Unification

LEP Results

LHC Results

Conclusions


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

Summary

Motivation

SUSY Algebra

MSSM

LEP Results

•Higgs

•Charginos ...

•Neutralinos

•Dark Matter

LHC Results

Conclusions


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

Summary

Motivation

SUSY Algebra

MSSM

LEP Results

•Higgs

•Charginos ...

•Neutralinos

•Dark Matter

LHC Results

Conclusions


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

Summary

Motivation

SUSY Algebra

MSSM

LEP Results

•Higgs

•Charginos ...

•Neutralinos

•Dark Matter

LHC Results

Conclusions


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


µ > 0

Excluded at 95% C.L.

3035404550556065707580

10 20 30 40tanβ

Mχ lim

(G

eV/c

2 )



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

Summary

Motivation

SUSY Algebra

MSSM

LEP Results

•Higgs

•Charginos ...

•Neutralinos

•Dark Matter

LHC Results

Conclusions


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

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


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

Summary

Motivation

SUSY Algebra

MSSM

LEP Results

LHC Results

• LHC Overview

•Basic Physics

•H: 2photons

•H: 4Leptons

• SUSY at LHC

• Signatures


• 2012 Results

Conclusions


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

Summary

Motivation

SUSY Algebra

MSSM

LEP Results

LHC Results

• LHC Overview

•Basic Physics

•H: 2photons

•H: 4Leptons

• SUSY at LHC

• Signatures


• 2012 Results

Conclusions


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

Summary

Motivation

SUSY Algebra

MSSM

LEP Results

LHC Results

• LHC Overview

•Basic Physics

•H: 2photons

•H: 4Leptons

• SUSY at LHC

• Signatures


• 2012 Results

Conclusions


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

Summary

Motivation

SUSY Algebra

MSSM

LEP Results

LHC Results

• LHC Overview

•Basic Physics

•H: 2photons

•H: 4Leptons

• SUSY at LHC

• Signatures


• 2012 Results

Conclusions


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)

Summary

Motivation

SUSY Algebra

MSSM

LEP Results

LHC Results

• LHC Overview

•Basic Physics

•H: 2photons

•H: 4Leptons

• SUSY at LHC

• Signatures


• 2012 Results

Conclusions


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IST First Results from the LHC in 2011

Summary

Motivation

SUSY Algebra

MSSM

LEP Results

LHC Results

• LHC Overview

•Basic Physics

•H: 2photons

•H: 4Leptons

• SUSY at LHC

• Signatures


• 2012 Results

Conclusions


!"" "*

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2@"7$%R1'<$%+'

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IST Results from the LHC in 2012

Summary

Motivation

SUSY Algebra

MSSM

LEP Results

LHC Results

• LHC Overview

•Basic Physics

•H: 2photons

•H: 4Leptons

• SUSY at LHC

• Signatures


• 2012 Results

Conclusions


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

Summary

Motivation

SUSY Algebra

MSSM

LEP Results

LHC Results

• LHC Overview

•Basic Physics

•H: 2photons

•H: 4Leptons

• SUSY at LHC

• Signatures


• 2012 Results

Conclusions


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

Summary

Motivation

SUSY Algebra

MSSM

LEP Results

LHC Results

• LHC Overview

•Basic Physics

•H: 2photons

•H: 4Leptons

• SUSY at LHC

• Signatures


• 2012 Results

Conclusions


Higgs combined results

Significance 6.9σ versus 7.8σ expected.

Combination of 5 channels: bb, ττ, WW, ZZ, γγ


IST Results from the LHC in 2012

Summary

Motivation

SUSY Algebra

MSSM

LEP Results

LHC Results

• LHC Overview

•Basic Physics

•H: 2photons

•H: 4Leptons

• SUSY at LHC

• Signatures


• 2012 Results

Conclusions



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


• 2012 Results

Conclusions


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


Summary

Motivation

SUSY Algebra

MSSM

LEP Results

LHC Results

• LHC Overview

•Basic Physics

•H: 2photons

•H: 4Leptons

• SUSY at LHC

• Signatures


• 2012 Results

Conclusions


CMSSM interpretation



Summary

Motivation

SUSY Algebra

MSSM

LEP Results

LHC Results

• LHC Overview

•Basic Physics

•H: 2photons

•H: 4Leptons

• SUSY at LHC

• Signatures


• 2012 Results

Conclusions


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


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) =

±


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


masst~

) = 10 GeV)±

1χ∼(m)-t

~(m) = 0 GeV,

0


masst~

) = 150 GeV)±

1χ∼(m) = 0 GeV,

0


masst~

) = 55 GeV)0

1χ∼(m(167 GeV , 7 TeV [1208.4305, 1209.2102]-1=4.7 fbL

massb~

))0

1χ∼(m) = 2

±


massb~

) < 120 GeV)0


massg~ ) < 200 GeV)0

1χ∼(m(1.15 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


• 2012 Results

Conclusions


χ+χ0 exclusion limits

7 TeV result New 8 TeV result

SUS-12-022 SUS-12-006


IST Conclusions

Summary

Motivation

SUSY Algebra

MSSM

LEP Results

LHC Results

Conclusions


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

Documents

Introduction to Supersymmetry Implications from the LHC Dataromao/Public/... · 2012-12-06 · Instituto Superior T´ecnico Jorge C. Rom˜ao Introduction to SUSY – 1 Introduction