2 nd Presentation of Prof. Cho’s Class Hossain Ahmed 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: 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

Anti-matter: An antiparticle is simply a particle with opposing quantum numbers.

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 Z 0 bosons: 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?

Unification:

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 Are the generalized co-ordinates Lagrangian in discrete system A system with continuously varying coordinates 1 3 2

4 From equation 1 ~ Euler-Lagrange equation 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 Where depends on space and time in a completely arbitrary way. This is known as local gauge invariance. But this is not invariant!! Check: 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: 8 The 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: 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

Where transform as Invariance of the Lagrangian (5) is then achieved by replacing by 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)!

Kinetic energies and self-interactions lepton and quark Kinetic energies and their interactions with, and Higgs masses and coupling 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 astr.gsu.edu/hbase/particles/qbag.html Experimental aspects of the standard model. astr.gsu.edu/hbase/particles/qbag.htmlhttp://superstringtheory.com/experm/exper2a.html