Embed Size (px)
Citation preview
2nd Presentation of Prof. Cho’s Class
Hossain Ahmed
07.10.2003
Introduction to Standard Model
What is Matter ?Democritus (born about 460BC in Abdera, Thrace,Greece) is credited with introducing this idea, that there must be some set of smallest constituent parts, which are the building blocks of all matter.
How the Matter made of ? Up until 1964, it was believed that there only existed three elementary particles
making up the atom: the electron, the proton and the neutron
-- J.J.Thomson (in 1897): Discovers Electron
-- Rutherford (in 1909): Discovers Nuclear Atom(Proton)
-- Chadwick (in 1932): Discovers Neutron
--SLAC (in 1968): Quarks in Neutrons and Protons
Constituents of Matter:
Quarks are the constituents of nucleons
-------------There are 6 quarks of 3 generation like-------------
u(up) c(charm) t(top)
d(down) s(strange) b(bottom)
Triplet of quark forms Baryon. Nucleons are the most common baryons.
Baryons <=> Fermions
The lightest members of the baryon class are the proton and neutron and the heavier members are known as hyperons.
Pair of quarks and anti-quark makes Meson.These are intermediate mass particles.
Mesons <=> Bosons
What is the conception of anti? later we will discuss !
In 1930 Wolfgang Pauli invented the “Beta radioactivity” means; a neutron transforms into a proton by emitting an electron (beta ray) and another mysterious particle that the italian physicist Enrico Fermi named in 1933 "neutrino"; which in italian means "little neutron".
The neutrino has a Q charge of null and it is 50,000 times smaller than an electron
The neutrino and the electron (light weight particles), are grouped in the family
of leptons (from the Greek "leptos" = light).
Like quarks, there are 6 leptons of three generations like:
e
e
The combination of two leptons and two quarks u and d are thus the building blocks of our world.
The following table represents all of the fundamental fermions known today. These are the building blocks of all matter
Now the question is, how these matter particles hold together??
-- by the basic forces in nature (?)
There are four basic forces in nature. These are:
•Gravitation which makes apples fall on certain peoples heads. It is also this which pulls together
the Earth and the Moon. Newton’s Apple story !
•Electromagnetic interaction which assures the cohesion of our bodies and governs all chemistry. It is this which pulls together the electron and the atomic nucleus like earth around the sun !
•The strong interaction which unites quarks together and thus the nuclei of atoms i.e.world is not broken out !
•Weak interaction which is responsible for beta radioactivity, which gives us the conception of antimatter!
We were talking about forces but why interactions?Before quantum theory, forces were transmitted by virtue of a mysterious force field emitted by particles.According to quantum theory, forces are not exerted between two fermions unless there is an exchange of a mediator particle, called a boson. Now the heavier the boson, the shorter will be the range of the interaction !
For electromagnetic interaction the exchange particle is γ
For strong interaction the exchange particles are gluons.
There are 8 gluons:
For weak interaction the exchange particles are and Z0 bosons:
W
Gravitational interaction has the weakest intensity in particle physics scale!
Up to this we have found the 12 (6 quarks + 6 leptons) fundamental particles as well as four basic forces in nature and also the mediator particles of interactions respectively. What will happen if we try to bring it all together ?
----This synthesis of current knowledge, without any doubt is known as ---- “The Standard Model ”
At a glimpse of Big-Bang !
It is clear from the figure that all 4 forces were created from super force during Big-Bang! In reverse way, we are trying to unify these
forces to reach to super force, aren’t we?
GUT (Grand Unification Theory)
So “the standard model” unifies all four forces?
----No. In reality, and since 1967,the weak and electromagnetic interactions have been unified and named “electroweak theory”, on
which Prof. Salam, Sheldon Lee Glashow and Steven Weinberg awarded the Nobel Prize ----
The interactions are modeled mathematically in the form of a field of forces
having a "gauge symmetry".
Mathematical Aspect of Standard Model
Gauge symmetry is "a group of mathematical transformations for which the
dynamic of particles is invariant".
One of the most profound insights in theoretical physics is that interactions are dedicated by symmetry principles. Einstein made great use of the predictive power of this idea!
How?
By considering invariance under general co-ordinate transformations (together with the equivalence principle), he was led to the general theory of relativity. The present belief is that all particle interactions may be dedicated by so-called “Local Gauge symmetries”.This is intimately connected with the idea that the conserved physical quantities (like electric charge, color etc.) are conserved in local regions of space, and not just globally.
The connection between symmetries and conservation laws is best discussed in the framework of “Lagrangian field theory”.
Lagrange equation of motion in classical mechanics
0)(
ii q
L
q
L
dt
d
sqi ' Are the generalized co-ordinates
VTL Lagrangian in discrete system
),,(),,(
xx
tqqL ii
A system with continuously varying coordinates ),( tx
1
3
2
),,( tqqL ii
0))(
(
xx
4 From equation 1
~ Euler-Lagrange equation
mi
Let’s consider relativistic case. This is Dirac’s Lagrangian! That gives the important information of particles!!
5
This lagrangian should be invariant under the transformation )()( )( xex xi Where depends on space and time in a completely arbitrary way. This is known as local gauge invariance. But this is not invariant!!
)(x
Check:
)()( )( xex xi 7 Anti-particle conception
6
Using equations 6 and 7 in equation 5 we see that only the last term is invariant, first term doesn’t!! Rather:
)()( xixi iee8The term breaks the invariance of
So we have to modified the derivative in order to the invariance of the Lagrangian under local gauge transformation:
The modified derivative, that transforms covariantly under phase transformations, that is , like ψ itself:
D
DeD xi )(
To form the “covariant derivative ” ,we must introduce a vector field with transformation properties such that the unwanted term in equation 8 is canceled.
9
D A
ieAD 10
e
AA1
11
Where transform as A
Invariance of the Lagrangian (5) is then achieved by replacing by D
Aemi
mi
)(
12 This invariance is in U(1) group!
But, in general, standard model holds SU(2) x U(1) symmetries. So what about SU(2)!
aa WigD 2
)(
)().2
.2
(
).2
(
).2
.2
(
4
1.
4
1
21
2
onjugatehermitiancRLGRLG
VBYg
Wg
i
RBYg
iR
LBYg
Wg
iL
BBWW
c
Kinetic energies and self-interactions
,, ZW
lepton and quark Kinetic energies and their interactions with ,, ZW
, and Higgs masses and coupling
,, ZW
Lepton and quark masses and coupling to Higgs
13
14
Conclusion In order to study the particle physics, “standard model” is the key factor for understanding the fundamental particles, their interactions and the creation of particles!
Lagrangian is the term, which can tells us whether the mathematical formula or “model” would be invariant or not under the transformations.
References:
1. An Introduction to the Standard Model of Particle Physics. 2. Modern elementary Particle Physics. 3. Quarks and Leptons. 4. http://perso.club-internet.fr/molaire1/e_quark.html. 5. http://physics.colorado.edu/~nieter/particle.html. 6. http://hyperphysics.phy-astr.gsu.edu/hbase/particles/qbag.html. 7. http://superstringtheory.com/experm/exper2a.html. 8. http://www.nikhef.nl/~henkjan/astro/node11.html. 9. http://www2.slac.stanford.edu/vvc/theory/model.html. 10. Experimental aspects of the standard model.
![[XLS]daffodilvarsity.edu.bd · Web viewMd. Shahriyar Parvez 131-23-3303 Sheikh Tanvir Ahmed 131-23-3304 Md. Nazmul Huda 131-23-3306 Md. Shaharab Hossain 131-23-3307 Md. Amzad Hossain](https://img.pdfslide.us/doc/110x75/5b0db9e77f8b9af65e8e11b5/xls-viewmd-shahriyar-parvez-131-23-3303-sheikh-tanvir-ahmed-131-23-3304-md-nazmul.jpg)
![[XLS] · Web viewJIAUR RAHAMAN KAZI ABEDUR RAHMAN KAZI ASFAR HOSSAIN MD SAMIM SHIKARI NASIR AHMED SK NAZIMUDDIN PAIK](https://img.pdfslide.us/doc/110x75/5afc12b77f8b9a32348fd844/xls-viewjiaur-rahaman-kazi-abedur-rahman-kazi-asfar-hossain-md-samim-shikari-nasir.jpg)