Outline

8. Beyond the Standard Model8.1 Recapitulation of the Standard Model8.2 Grand Unified Theories (GUT)8.3 Supersymmetry (SUSY)8.4 Minimal Supersymmetric Standard Model (MSSM)8.5 MSSM phenomenology8.6 Experimental SUSY searches

Brief overview of supersymmetry and its phenomenology

Particle Physics

Beyond the Standard Model Recapitulation of the Standard Model

Components of the Standard Model

fermions(uLdL

),

(cLsL

),

(tLbL

),

uR, dR, cR, sR, tR, bR(νe

e−L

),

(νµ

µ−L

),

(ντ

τ−L

),

e−R, µ−R, τ−R

gauge bosons

SU(3)c × SU(2)L ×U(1)Yelm.: γweak: W±,Z 0

strong: gluons

Higgs

additional scalar weak-isospin doublet with weak hypercharge YH = 12 :

SU(2)L × U(1)YSSB−→ U(1)elm Φ(x) =

(0

1√2ρ(x)

)

Particle Physics

Beyond the Standard Model Recapitulation of the Standard Model

Problems of the Standard Model

I many parameters

I SM describes about 4 % of the matter in the universe only

I hierarchy problem

MSM ∼ 102GeV MPlanck ∼ 1019GeV

I Higgs mass corrections

−|λf |2

8π2Λ2UV + . . . +

λs16π2

Λ2UV (1)

I mass-less neutrinos in contradiction to observed neutrino oscillations

I no underlying symmetry for baryon number conservation

Particle Physics

Beyond the Standard Model Grand Unified Theories (GUT)

Grand unification - SU(5)

I 3 gauge groups in SM⇒ 3 couplings as “free” parameters

I running couplings approach each other for M ∼ 1014 GeV

I unification into 1 group containing the SM gauge groups possible?⇒ only 1 parameter

I smallest such group (Georgi, Glashow, 19??):

SU(5) ⊃ SU(3)× SU(2)× U(1)

I fermion decomposition into SU(3),SU(2):

5 = (1, 2) + (3, 1) = (νe, e−) + dL (2)

10 = (1, 1) + 3, 1) + (3, 2) = eL+ + uL + (uL,dL) (3)

I gauge bosons (N2 − 1 = 24):

24 = (8, 1) + (1, 3) + (1, 1) + (3, 2) + (3, 2) (4)

Particle Physics

Beyond the Standard Model Grand Unified Theories (GUT)

Predictions from SU(5) unification

I weak mixing angle: sin2 θW ∼ 0.2

I quark charges:

Qd =1

3Qe− Qu = −2Qu (5)

I proton decay:consider p→ π0e+ in analogy to weak interaction

GG√2

=g2G

8M2X

(6)

⇒ Γ(p→ π0e+) ∝ G 2Gm

5p ∝

m5p

M4X

(7)

⇒ τp ∼ 1030y (8)

but experimental limit τp→π0e+ > 1034y

Particle Physics

Beyond the Standard Model Supersymmetry (SUSY)

Towards supersymmetry

I trivial cancellation of Higgs mass correctionsif we postulate pairs of fermions and bosons→ supersymmetry

I introduce operator Q, s.t.

Q |fermion〉 = |boson〉 Q |boson〉 = |fermion〉 (9)

Observations:

I Q† also a symmetry generator

I Q, Q† fermionic operators with S = 12

I decomposition into supermultiplets:∣∣Ω′⟩ = αQ |Ω〉+ βQ† |Ω〉 (10)

Beyond the Standard Model Supersymmetry (SUSY)

Supermultipletsconsider members of a given supermultiplets

I [Q,P2] = [Q†,P2] = 0 ⇒ equal masses

I [Q,G ] = [Q†,G ] = 0 for G any generator of a gauge group⇒ same elm. charge, weak isospin, colour

I Nbosons = Nfermions

we get

I scalar supermultiplet:

Weyl fermion (S =1

2)↔ complex scalar (S = 0) (11)

I vector supermultiplet:

Weyl fermion (S =1

2)↔ boson (S = 1) (12)

implies identical gauge transf. for left-/right-handed components

I (gravitational supermultiplet)

Particle Physics

Beyond the Standard Model Minimal Supersymmetric Standard Model (MSSM)

Minimal Supersymmetric Standard Model (MSSM)fermions

I construct a minimal SUSY model which contains the SM particles

I SM fermions must be in scalar supermultiplets

I scalar quarks → squarks:(uLdL

),

(cLsL

),

(tLbL

),

uR, dR, cR, sR, tR, bRI scalar leptons → sleptons:(

νe

e−L

),

(νµ

µ−L

),

(ντ

τ−L

),

e−R, µ−R, τ−RI chiral index refers to handedness of the fermionic parter,

e.g. only (uL, dL) couple to W

Particle Physics

Beyond the Standard Model Minimal Supersymmetric Standard Model (MSSM)

Minimal Supersymmetric Standard Model (MSSM)Higgs

I S = 0 ⇒ scalar supermultiplet

I two supermultiplets needed to avoid anomalies⇒ extend SM Higgs sector

I introduce two weak isospin doublets with Y = ±12 :

(H+u ,H

0u) (H0

d ,H−d ) (13)

I then supersymmetric higgsinos:

(H+u , H

0u) (H0

d , H−d ) (14)

I el. weak symmetry breaking more complicated because of two Higssdoublets . . .

Particle Physics

Beyond the Standard Model Minimal Supersymmetric Standard Model (MSSM)

Minimal Supersymmetric Standard Model (MSSM)gauge bosons

I SM gauge bosons must be in vector supermultiplets:

W+, W 0, W−︸ ︷︷ ︸winos

, B0︸︷︷︸bino

gauginos (15)

I mixing of W 0, B0 to photino γ and zino Z 0

I gluons: 8 gluinosI because of el. weak symmetry breaking mixing:

I neutralinos:

H0u, H

0d , W

0, B0 −→ χ01, χ

02, χ

03, χ

04

I charginos

H+u , W

+, −→ χ+1 , χ

+2

H+u , W

+, −→ χ+1 , χ

+2

Particle Physics

Beyond the Standard Model MSSM phenomenology

R-parity conservation

I introduce new quantum number

PR = (−1)3(B−L)+2S (16)

which is conservedI no mixing between particles and sparticlesI lightest SUSY particle (lsp) must be stableI proton decay, e.g.:

forbidden

Particle Physics

Beyond the Standard Model MSSM phenomenology

MSSM phenomenology

I if SUSY was exact ⇒ equal masses in supermultiplets

I contradicts lack of experimental evidence for SM states

I SUSY must be brokensoft SUSY breaking, not unique

LMSSM = LSUSY + Lsoft (17)

I number of SUSY operators can be increased (here: 1)

⇒ many viable MSSM scenarios possible and proposed

Particle Physics

Beyond the Standard Model MSSM phenomenology

MSSM scenarios

Figure: SUSY scenarios

Particle Physics

Beyond the Standard Model Experimental SUSY searches

Experimental SUSY searches

Problem Too many SUSY scenarios to check one specific prediction

Instead look for signatures which deviate from SM predictions andcan be explaeined by SUSY,e.g. jets and missing ET

e.g. ATLAS:

Particle Physics