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Presented
by
Pratap Kumar
Swain07/PH/406
Under The Guidance
Of
Dr. S. Sahoo
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1. Fundamental Interaction
2. Standard Model (a) Particles of Matter
(b) Force mediating particles
(c) Quantum-chromodynamics
(d) Electroweak Interaction3.Draw back of SM4. Beyond SM & Origin of SUSY
5. Basic ingredient of SUSY
6. SYSY in QM
7. Supersymmetric Oscillator
8. Future Plan
9. Reference
10. Accowdgelement
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The mechanism by which the particles interactwith each other and which can not be explainedin terms of another interaction is called
fundamental interaction.There are four fundamental interaction.
3.Strong interaction
4.Electromagnetic interaction
5.Weak interaction
6.Gravitational interaction
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It is the mathematical model to explainIt is the mathematical model to explainthe fundamental interaction, basedthe fundamental interaction, basedupon the group theory of SU(3)SU(2)upon the group theory of SU(3)SU(2)
U(1).U(1).It explain three fundamental interactionIt explain three fundamental interactionout of four interactions. therefore it isout of four interactions. therefore it isalso called three-fourth of fundamentalalso called three-fourth of fundamental
interaction.interaction.The SM consists elementary particles,The SM consists elementary particles,
grouped into two classes : bosonsgrouped into two classes : bosons(particles that transmits force) and(particles that transmits force) and
fermions ( particles that make upfermions ( particles that make upmatter ). The bosons have article s inmatter ). The bosons have particle spin
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All the fermions in the standard modelare spin-half and the Pauli exclusionprinciple in accordance with the spinstatistic
Fermions Generation-1 Generation-2 Generation-
3
Leptons Electron eNeutrino
Electron e-
Muon neutrino
Muon
Tauneutrino
TauQuarks Up u
Down d
Charm c
Strange s
Top
Bottom
b
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Force mediating
particle(bosons)Due to fundamental interactions, the matter
particles exchange from one form to another, inbetween a mediating particle is formed called
force mediating particle or bosons.These particles have integral spin.Photon mediate the electromagnetic force
between electrically charged particles.
The W+
, W
, and Z0
gauge bosons mediate theweak interactions between particles of differentflavors (all quarks and leptons).Gluons mediate the strong interactions between
color charged particles.
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NAME SPIN CHARGE MASS
(GeV/c2)
OBSERVED
Graviton 2 0 0 Not yet
Photon 1 0 0 Yes
Gluon 1 0 0 Indirectly
W+ 1 +1 80 Yes
W- 1 -1 80 Yes
Z0 1 0 91 Yes
Higgs Boson 0 0 95 Not yet
Force Mediating Particles
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Similar to QED, a theory is developed for quarkinteraction is called (QCD).
This was first given by DJ Gross, F. Wilczek and H.DPolitzer in 1973.
The strong interaction involves the exchange of mesonsand baryons made of quarks.
Each of quarks occure in three varieties and this newvariety of quark is named as color .
The idea of color is first put forwarded by OscarGruenberg in 1965.
The statement that QCD is renormalizable gauge theorybased on the group SU(3) with color triplet quark matterfield fixes the QCD Lagrangian density to be
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In late 1960 Sheldon Glashow, StevenWienberg and Abdus Salam gave aunified theory of electromagneticinteraction and weak interaction known
as electroweak theory.The electroweak theory predicts, thereare four vector boson fields. They areW+,W-, Z0 and Higgs boson.
Fundamental force
ExchangedParticle
Mass( Gev/c2)
Range (inm)
Relativestrength
strong Gluon 0 10-15 1
electromagnetic Photon 0 ~ 10-2
weak w, Z0 80.4;91.2
10-18 ~ 10-6
gravitational Graviton 0 ~ 10-39
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wmodel
This model has many demerits.
It cant explain the mechanism of electroweak
symmetry breaking.It cant say whether the Higgs boson is
fundamental or composite.
The CP-violation is not well understood by SM.
It cant say about dark matter and darkenergy.
It also gives wrong prediction about neutrinomass.
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Beyond the standard
model The electroweak gauge theory only has
conserved currents for its weak charges if theWs and Z are mass less, like the photon is. It
also helps if quarks and leptons are mass less. To maintain this, but yet have physical
masses, we fill the vacuum with some sludge.A particles mass is then proportional to the
amount each particle couples to this sludge. The sludge is the everywhere constant
vacuum value of the neutral Higgs
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Three extra Higgsfields, H+, H-, anti-H0make up the extra
component of the Wand Z spins needed tomake them massive.The Ws have a mass of81 GeV, and the Z of 90GeV. The H0 has a constantvacuum density, andcan also make aphysical particle.
+
H
H
H
H0
0,
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How to Find the Higgs The Higgs vacuum value is uniform, neutral,
appears the same at all velocities, andundetectable except for the fact that it gives
mass to everything.A particles mass is proportional to its
coupling to the Higgs and therefore to itsvacuum density.
The excitations of the Higgs is a real particle,predicted to be at about 115-130 GeV.This should show up in the LHC in some rare
decays.
It would have shown up at the Fermi lab
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- Grand Unified Theories of electroweak andstrong interactions
- Supersymmetry
- Superstring Theories 10 dimensions withgravity
- Superstring Unification to M Theory
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Constants
Charged particles have virtual quantum allowedclouds around them of photons and electron-positron pairs.
Colored particles have virtual gluons and q-anti-q
pairs.So the total coupling at long distance or charge,
is different from the coupling at short distance,where the cloud is penetrated.
Electromagnetic coupling increases with energyfrom 1/137 to 1/40 at 1017 GeV Unification Scale
Strong coupling decreases from ~1 to 1/40
Weak coupling to Ws also reaches 1/40
So couplings come together at unification scale
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This graph is obtained by group of physicsts at CERN in2002
A B t H t
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A B t o H story oUnification
Electricity unified with magnetism (M. Faraday and J. C.
Maxwell).Relativity and General Relativity (A. Einstein).
Quantum Mechanics (Planck, Bohr, Schrodinger andHeisenberg).
Relativistic quantum mechanics (P. Dirac).
Quantum Electrodynamics (R. Feynman, Tomonaga,Schwinger).
Quarks and Quantum Chromodynamics (Nemann, M. Gell-Mann and G. Zweig).
Unification of Electromagnetism with Weak Interactions toform Electroweak theory (S. Weinberg, A. Salam).
Grand Unified Theories
Supersymmetry
Superstring Theory of Everything including gravity.
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Particle Supersymmetry
In a Grand Unified Theory, all quarks and leptons are ina generation and are united into one family.
The GUT gauge bosons transform one quark or lepton to
another, such as gluon changing one color quark intoanother.
A grander symmetry would be to transform all gauge
bosons to fermions with the same charges, and viceversa.
Thus for every spin fermion there would be a spin 0
boson with the same charges and flavor, and to every
W t
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W y upersymmetry(SUSY)?
Its believers think it is a beautiful symmetry betweenfermions and bosons, and should be a part of nature.
If the sparticles are at about 1 TeV, then the runningcoupling constants actually do meet at a GUT scale of
1017 GeV.GUT scale (mass) Higgss would normally couple to the
light SM Higgs and bring its mass up to the GUT scale.
Adding sparticles to particles cancel this coupling to
leave the SM Higgs light, solving the so-called Hierarchyproblem.
String Theory requires SUSY, again for similarcancellations.
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angular momentum is quantized to integerunits of Plancks constant over 2.
Quarks and leptons have half a unit of angularmomentum as spin, or are spin 1/2 particles,also called fermions.Photons and Ws and Z are spin 1 particles,also called bosons.
Gravitons have spin 2, and are bosons.
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Evolution of Gauge Couplings
(reciprocals)
Standard ModelSupersymmetry
This fig. is collected from Czechoslovak j.ofphysics.vol(52)
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A supersymmetric operator changes a
boson into a fermion. We may write as
are Lorentz spionors obeying the ant communicationrelation as
fermionbosonQ =+
bosonfermionQ =
{ } ( )
pQQ =+
,
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Like creation and annihilation operator in quantum
mechanics we can define Q and Q+ as
Q = a+b()1/2 and Q+ = ab+()1/2
And the anti-commutation relation of Q and Q+ form
the Hamiltonian of the system
{Q, Q+} = H = Hosc + Hspin = (a+a + b+b) . The
exited state have the energy given by En = (n +
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Q|n,1> = (n+1) |n+1,0>
Q+|n+1,0> = (n+1) |n,1>
Energy Boson
state
Fermion
state
0 |0,0>
|1,0> |0,1>
2 |2,0> |1,1>
3 |3,0> |2,1>
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Supersymmetric oscillatorSupersymmetric oscillator operator is formed
by the combination of one bosonic and onefermionic oscillator operator
We define Q = abaf+ and its conjugate as Q+ =
afab+
The action of these operators on thecombined of bosonic and fermionic state asfollows
Q|nb,nf=0> = abaf+
|nb,nf=0> = (nb)1/2
|nb,nf=1>Q+|nb,nf=1> = afab
+|nb,nf=1> = (nb+1)1/2|
nb,nf=0>
The Hamiltonian H = Hb + Hf = (ab+ab +
a +a )
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1. Czechoslovak journal of physics.voi(52)2002,Suppl.C
2. Shoji.Asai et,al. EPJdirect C.4 si,17 (2002)3. The standard model of particle physics
CERN-PH-TH/2005 by Guido Altorelli andE.amaldi.
4. S.M Bilenky, E.Kh.Khristova and N.PNedelcheva
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I thank my project supervisor Dr. S.Sahoo who
has been instrumental in helping and showing methe direction and approach of study.
I thank all the faculty members and my friends
who have been supportive to me for this work.