pratap ppt

8/14/2019 Pratap Ppt

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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.

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