Pratap Ppt

Under The Guidance Of Dr. S. Sahoo

Presented by Pratap Kumar Swain 07/PH/406

1. Fundamental Interaction 2. Standard Model

(a) Particles of Matter (b) Force mediating particles (c) Quantum-chromodynamics (d) Electroweak Interaction 3. Draw back of SM 4. Beyond SM & Origin of SUSY 5. Basic ingredient of SUSY 6. SYSY in QM 7. Supersymmetric Oscillator 8. Future Plan 9. Reference 10. Accowdgelement

The mechanism by which the particles interact with each other and which can not be explained in 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

It is the mathematical model to explain the fundamental interaction, based upon the group theory of SU(3)×SU(2) ×U(1). It explain three fundamental interaction out of four interactions. therefore it is also called three-fourth of fundamental interaction. The SM consists elementary particles, grouped into two classes : bosons (particles that transmits force) and fermions ( particles that make up matter ). The bosons have particle spin

All the fermions in the standard model are spin-half and the Pauli exclusion principle in accordance with the spin statistic Fermions

Generation-1 Generation-2 Generation3

Leptons

Electron Neutrino

νe

Muon neutrino

Electron

e-

Muon

Quarks

νµ

Tau ντ neutrino

μ−

Up

u

Charm

c

Down

d

Strange

s

Tau − τ Top Bottom b

t

Force mediating particle(bosons) Due

to fundamental interactions, the matter particles exchange from one form to another, in between 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 the weak interactions between particles of different flavors (all quarks and leptons). Gluons mediate the strong interactions between color charged particles.

Force Mediating Particles NAME

SPIN

CHARGE

MASS

OBSERVED

(GeV/c2)

Graviton

2

0

0

Photon

1 1 1 1 1 0

0 0 +1 -1 0 0

0 0 80 80 91 95

Gluon W+ WZ0 Higgs Boson

Not yet Yes Indirectly Yes Yes Yes Not yet

Similar to QED, a theory is developed for quark interaction is called (QCD). This was first given by DJ Gross, F. Wilczek and H.D Politzer in 1973. The strong interaction involves the exchange of mesons and baryons made of quarks. Each of quarks occure in three varieties and this new variety of quark is named as “ color ”. The idea of color is first put forwarded by Oscar Gruenberg in 1965. The statement that QCD is renormalizable gauge theory based on the group SU(3) with color triplet quark matter field fixes the QCD Lagrangian density to be

In late 1960 Sheldon Glashow, Steven Wienberg and Abdus Salam gave a unified theory of electromagnetic interaction and weak interaction known as electroweak theory. Fundament Exchange Mass (in Relative The electroweak theoryRange predicts, there al force d ( Gev/c ) m) strength are four vector0 boson ≤fields. They are Particle strong Gluon 10 1 W+,W-, Z0 and Higgs boson. 2

-15

electromagn Photon etic

0

∞

~ 10-2

weak

80.4; 91.2

≤ 10-18

~ 10-6

0

∞

~ 10-39

w±, Z0

gravitational Graviton

Draw back of the standard model This model has many demerits. It can’t explain the mechanism of electroweak

symmetry breaking. It can’t say whether the Higgs boson is fundamental or composite. The CP-violation is not well understood by SM. It can’t say about dark matter and dark energy. It also gives wrong prediction about neutrino mass.

Beyond the standard model The electroweak “gauge” theory only has

conserved currents for its weak charges if the W’s 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 particle’s 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

Three extra Higgs fields, H+, H-, anti-H0 make up the extra component of the W and Z spins needed to make them massive. The W’s have a mass of 81 GeV, and the Z of 90 GeV. The H0 has a constant vacuum density, and can also make a physical particle.

H +  H 0   ,   H 0  H −    

How to Find the Higgs The Higgs vacuum value is uniform, neutral,

appears the same at all velocities, and undetectable – except for the fact that it gives mass to everything. A particle’s mass is proportional to its coupling to the Higgs and therefore to its vacuum 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

- Grand Unified Theories of electroweak and strong interactions - Supersymmetry - Superstring Theories – 10 dimensions with gravity - Superstring Unification to M Theory

Running Coupling Constants Charged particles have virtual quantum allowed

clouds around them of photons and electronpositron 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 energy from 1/137 to 1/40 at 1017 GeV Unification Scale Strong coupling decreases from ~1 to 1/40 Weak coupling to W’s also reaches 1/40 So couplings come together at unification scale

This graph is obtained by group of physicsts at CERN in 2002

A Bit of History of Unification

 Electricity unified with magnetism (M. Faraday and J. C.

Maxwell).  Relativity and General Relativity (A. Einstein).  Quantum Mechanics (Planck, Bohr, Schrodinger and Heisenberg).  Relativistic quantum mechanics (P. Dirac).  Quantum Electrodynamics (R. Feynman, Tomonaga, Schwinger).  Quarks and Quantum Chromodynamics (Nemann, M. GellMann and G. Zweig).  Unification of Electromagnetism with Weak Interactions to form Electroweak theory (S. Weinberg, A. Salam).  Grand Unified Theories  Supersymmetry  Superstring Theory of Everything including gravity.

Particle Supersymmetry In a Grand Unified Theory, all quarks and leptons are in

a 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 into another. A grander symmetry would be to transform all gauge

bosons to fermions with the same charges, and vice versa. Thus for every spin ½ fermion there would be a spin 0

boson with the same charges and flavor, and to every

Why Supersymmetry (SUSY)? It’s believers think it is a beautiful symmetry between

fermions and bosons, and should be a part of nature. If the sparticles are at about 1 TeV, then the running coupling constants actually do meet at a GUT scale of 1017 GeV. GUT scale (mass) Higgs’s 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 Hierarchy problem. String Theory requires SUSY, again for similar cancellations.

angular momentum is quantized to integer units of Planck’s constant over 2π. Quarks and leptons have half a unit of angular momentum as spin, or are spin 1/2 particles, also called fermions. Photons and W’s and Z are spin 1 particles, also called bosons. Gravitons have spin 2, and are bosons.

Evolution of Gauge Couplings (reciprocals)

Standard Model

Supersymmetry

This fig. is collected from Czechoslovak j.of physics.vol(52)

A supersymmetric operator changes boson into a fermion. We may write as Qα+ boson = fermion Qα fermion = boson

a

α α

are Lorentz spionors obeying the ant communication

relation as

{Q

+ α

, Qβ } = p µ ( σ µ ) α β

Like creation and annihilation operator in quantum mechanics we can define Q and Q+ as Q = a+b(ћω)1/2 and Q+ = ab+(ћω)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) exited state

. The

have the energy given by En = (n +

Energy

Boson state

Q|n,1> Fermion state +

= (n+1) ½|n+1,0> Q |n+1,0> = (n+1) ½|n,1>

0

|0,0>

ћω

|1,0>

|0,1>

2ћω

|2,0>

|1,1>

|3,0>

|2,1>

3ћω

Supersymmetric oscillator Supersymmetric oscillator operator is formed

by the combination of one bosonic and one fermionic oscillator operator We define Q = abaf+ and its conjugate as Q+ = afab+ The action of these operators on the

combined of bosonic and fermionic state as follows 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 = ћω(ab+ab +

a +a )

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 and E.amaldi. 4. S.M Bilenky, E.Kh.Khristova and N.P Nedelcheva

I thank my project supervisor Dr. S.Sahoo

who

has been instrumental in helping and showing me the direction and approach of study.

I thank all the faculty members and my friends who have been supportive to me for this work.