martin zur nedden, hu berlin 1 ws 2007/08: physik am lhc 6. super symmetry beyond the standard model...

Martin zur Nedden, HU Berlin 1WS 2007/08: Physik am LHC

6. SUper SYmmetry

● “Beyond the Standard Model”● Introduction into SUper SYmmetry● Minimal Super Symmetric extension of the Standard

Model (MSSM)● Extended Higgs-Model in MSSM● Super Symmetric Interactions● SUSY breaking● Particle spectra of SUSY (phenomenology)● SUSY searches at TEVATRON and strategies for LHC


Global Fit of Standard Model Parameter


Weinberg Angle and Higgs-Masse


Standard Model Symmetry

• SM describes strong and electroweak interactions, L/R asymmetry• Based on symmetries and gauge invariance• All forces propagated by exchange of gauge fields (local gauge fields)

YLC USUSU )1()2()3( Gauge-Bosons (Spin = 1):

gluons Gaμ SU(3) (8,1,0)

vector bosons Wiμ SU(2) (1,3,0)

abelian boson Bμ U(1) (1,1,0)

Fermions Spin = ½:

quarks [Uiα,Di

α]L (3,2,1/3)quarks [Ui

α]R (3,1,4/3)quarks [Di

α]R (3,1,-2/3)

leptons [Lα]L (1,2,-1)leptons [e]R (1,1,-2)

Higgs (Spin = 0):

H-Doublet [H0,H-] (1,2,-1)

Masses of quarks, leptons and vector bosons by spontanous symmetry breaking


Motivation for Super Symmetry

Fermion ↔ Boson Symmetry

basic idea: unification of all forces, no difference between fermions (matter) and bosons (forces)

generator of the SUSY algebra: Q|boson> = |fermion> Q|fermion> = |boson>

Difference in spin = ½, doubling of the number of particles

SUSY transformation: δ|b> = ε|f> (anti-) kommutator relations {f,f} =0, [b,b] = 0,

{ε,ε} = 0 : SUSY generators are fermionic

Q has spin = ½ , may change the helicity 2-component spinor super symmetric algebra: connection of particles with different spins


electron

selectron

quark

squark

photon

photino

Unification ofbosons with fermionsforces with matter

fermios

bosons

bosons

fermions

Supersymmetric Partners


Minimal Super Symmetric Model (MSSM)Most simple case: N=1 generators 2 super multiplets:

NDoF (bosons) = NDoF(fermions)

1. chiral super multiplet [Φ , Ψ] (spin 0, ½), fermions: 2 scalars,

Weyl-spinor with helicity, L/R

2. vector multiplet [λ , A] (spin ½, 1), bosons: gauge boson,

massless spin ½ fermion

● each fundamental particle has to occur in a super multiplet

● each SM particle has a SUSY-partner, Δs = ½ (minimal number of new particles)

● fermions in the vector multiplet transforms like gauge bosons (same for L/R)

● chiral multiplet contains all fermions, also with different transformation behaviour

● unbroken super symmetry: all masses were the same obviously not the case……

SUSY must be (weakly) broken, big masses of super symmetric partners

● More than 100 new parameters for the theory !?


Extended Higgs Model in MSSM

tand

u

H

H

22'2

222

)174(2

GeVgg

MHH Zdu

2 Higgs Dublets needed, to give all particles mass

Complex fields 8 degrees of freedom 3 absorbed in the longitudinal components of W- and Z-bosons 5 higgs bosons remains, 3 are neutral

h0 : light Higgs, scalar H0 : heavy Higgs, scalar A0 : neutral Higgs, pseudo-scalar, PC-odd H+/H- : charged Higgs, scalar

h0/H0 mixing states of Re(Hu

0) and Re(Hd0),

Mixing angle α

A0 mixing state ofRe(Hu

0) and Re(Hd0),

Mixing angle tanβ

H+/H- mixing state ofHu

+ and Hd-,

Mixing angle tanβ

222AWHmMm

2cos42

1 22222222, ZAZAZAhH MmMmMmm

new parameter

For the masses follows:


Higgs Masses in MSSM

● Higgs masses depends on 2 parameters: tan β and mA :

tan β 1 : mh = 0 , mH2 = MZ

2 + mA2

tan β ∞: mh = min(MZ, mA), mH = max(MZ,mA)

Mass terms for A0, H0 and H+/H- could be very big!

If mA big: mA ~ mH ~ m H+/-

Mass of h0 is limited: 0 < mh < |cos2β|MZ

mh < mA < mH

mH > MZ, m H+/- > MW

Radiative corrections important for mh (enlarges the mass)

mh0 < 150 GeV upper limit for MSSM

mh0 < 190 GeV limit for SUSY


MSSM Higgs Masses

All Higgs masses are fixed relative to 2 parameters:


Cancelation of Quantum corrections in SUSY Models


Supersymmetric Particles

Chargino:

(partner of W)

Neutralino:

(partner of Z, g)

Smuon:

(partner of muon)


Super Partners

● qL, qR, lL, lR squarks, sleptons (spin = 0)

● Gauge bosons g, W, B (gluino, Wino, Bino) = gauginos

● SM: coupling of W0/B0 to Z0/γ Zino, Photino

● Higgs (scalar) 2 Higgsinos (chiral super multiplet)

● chiral super multiplet: left handed particles only

● gauge interaction the same for squarks/sleptons and quarks/leptons

● unification with gravity: Graviton Gravitino

● neutral fermionic partners Wino/Bino have the same quantum numbers as the super symmetric Higgs partners: mixing to 4 neutralinos χ0

i (i=1..4) :

the lightest neutralino is the LSP (if R-parity is conserved)

● charged Higgsinos: mixing to charginos χ+/-j, (j=1,2)


SUSY Interactions (R-Parity conserved)

R-parity: +1 for “normal particles, -1 for super symmetric partners

Feynman graphs:

replace at any SM-vertex(3 or 4 particle interaction)two legs by the correspondingsuper symmetric partners

The coupling constants remains the same as in SM (strong or electroweak)


MSUGRA - Parameters

● m0 : universal scalar mass at GUT scale

● m½ : universal gaugino mass at GUT scale

● tan β : ratio of Higgs vacuum expectation value● sgn μ: sing of Higgsino mass parameter

● A0 : universal s-fermion mass mixing parameter

● M(SUSY) < 1 TeV for LSP● important limits from LEP and TEVATRON


MSUGRA Masses


MSUGA Szenarios 1


MSUGRA Szenarios 2


SUSY at Hadron-Colliders

search strategy: Big contribution from standard model QCD-background (Jets) look for high pT leptons and MET

- squarks and gluinos: MET (strong interaction)- neutralinos and charginos: MET and high pT leptons (electro weak interaction)


Squark und Gluino Searches at TEVATRON

production:

decay:

Search for Jets und ETmiss


Result: Upper Limits (exclusions limits)


Search for Neutralinos and Charginos

01

01

021

~~~~~ leepp

01

01

~~ le

No improved SUSY limit foundby TEVATRON up to now


Recostruction of SUSY Particles

Neutralino 2 Sbottom Gluino

CMS MC analysisM = 595 GeV

M = 510 GeV

M = 174 GeV

M = 150 GeV

M = 96 GeV

edge = 78.9 +/- 2.1 GeV M = 499.4 +/- 6.6 GeV M = 585.1 +/- 11.1 GeV


SUSY in R-Parity violating Processes

neutralino (LSP) unstable, no longer a dark matter candidate lepton / and baryon number conservation violated much more possible decay channels ….

L - violation B - violationL - violation


Neutralino in R-Parity violating Decays

production:

decay:

Evidence: 3 charged leptons in FS


Search at Tevatron (Neutralino decay)

production:

decay:

Evidence: 3 charged leptons in FS

Result from D0, TEVATRON:upper limit


Masse of the lightest MSSM-Higgs

Mass of the lightestHiggs as a functionof MA und tan(ß) from 1.6 to 15


Supersymmetric Higgs


Search for the neutral MSSM Higgs

Searches at TEVATON: using multi – jet events


Di-Jet Mass (D0 / Tevatron) MSSM Higgs

Search for overshoot in the invariant mass distribution of the two jets with the highest pT

At least 3 b-flavoured jetare requested per event

BG: multi jet production


Upper Limit for the MSSM-Higgs Mass

based on di-Jet events


Search for the MSSM charged Higgs

Search for MET + J + X:

Direct production in weak IA,compeditiv to t Wb


MSSM – Higgs Search at LHC

All region is covered…


SUSY Mass Spectra


LHC discovery potential

Time Mass sensitivity

1 month ~ 1.3 TeV1 year ~ 1.8 TeV3 years ~ 2.5 TeVMaximum limit ~ 3 TeV

Supersymmetric Particles and dark Matter

The neutralino is a good candidat for dark matter in the univers, if R-parity is conserved.


LEP: Higgsmasse versus tanß

martin zur nedden, hu berlin 1 ws 2007/08: physik am lhc 6. super symmetry beyond the standard model...

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