Standard Model of Physics Project Supervisor: Dr. Babar Qureshi Project by: M. Anadil Saeed Occasional Helper: Dr. Amer Iqbal

What does the information given in the previous slide mean? Let me illustrate a little. What are quarks? What are leptons? What are bosons?

What are quarks? Briefly, they constitute hadrons. Hadrons are heavier particles, most of them very unstable, and not lasting long. The most stable hadrons are neutrons and protons. Hadrons are composite particles that are held together by the ‘strong force’, analogous to electromagnetic forces which bind the atoms and molecules together. Hadrons are classified into two families: Baryons and Mesons. Baryons are made up of three quarks e.g. Protons (uud) Mesons are made up of one quark and one anti-quark e.g. Pion + (ud*) Quarks are never observed alone (in isolation), but exist always in combinations. The rule which is followed here is documented by ‘color confinement’.

A little on color confinement Of the fields that we are usually accustomed to, force decreases with distance e.g. the electric field. This does not seem to be the case for quarks. We have posited the existence of gluons to account for the strange behavior of these particles (which we can’t see). When it is attempted to separate two quarks, the force between them does not decrease with distance. It is fact does not behave as a traditional electric or magnetic field either. It acts in ‘tubes’. And when we increase our energies (as in accelerators), instead of breaking up and giving us jets of isolated quarks, we receive jets of hadrons. Thus we conclude, that the first impulse of the quarks is to stick together. But when it becomes energetically feasible a quark /anti-quark pair is spontaneously produced. It means that the gluon tubes are not stretched further than a point. After the critical point, a pair is produced from within nature… This is the strong interaction. And we end up with ‘color neutral’ particles in the end.

Color Charge Pauli-Exclusion Principle says, no two identical fermions may occupy the same quantum state. We introduce a new quantum property for quarks, called ‘color charge’. To keep this rule intact Greenborg after 1964, introduced the notion of color to account for fermions existing in the same quantum states within hadrons. These are three colors Red, Blue and Green, for every quark. Similarly, we have anti-Red, anti-Blue and anti-Green for every anti-quark. Red, Blue and Green whenever present together will make color neutral. anti-Red, anti-Blue and anti-Green whenever present together will make color neutral. A color and its anti-color will also make color neutral The color assignment of individual quarks is not important, because we can’t observe them. It is only important to know that all three colors are present. And thus, we have color conserved in all observable particles.

An example of a particle decay Delta ++ with a mass of MeV is a very heavy and a very unstable particle produced in collisions. It thus rapidly decays. As an example we can consider to decay into pion + with a mass of MeV and proton with a mass of MeV. uuu goes to uud + ud* Its diagrammatic representation is on the following page.

Leptons and Bosons? I leave them for now… I will return to bosons by the end.

The Current Abstract In this project I will study the standard model of particle physics. The current understanding of all the particles in nature and the forces among them is in terms of gauge theories. These gauge theories are actually quantum field theories with a local symmetry under certain group transformations. To make the matters complicated, the local symmetry, and the coupling structure of matter and gauge fields, does not allow any particle to have mass, which has to be generated via Higgs mechanism. I will study the group structure underlying this model and study how different particles and forces come out of it and fit together. I will also study the extensions of this group structure to other models of current interest, namely the grand unified theories and super symmetric theories.

Questions What are gauge theories? How do we understand particles and forces in terms of them? What is meant by ‘local symmetry’ under group transformations? What is the coupling structure of matter? How does local symmetry and coupling structure of matter and gauge fields disallow particles to have mass? How is this compensated via Higgs Mechanism? These are the questions I will review.

Questions For now I will give you an intuitive picture of some of the questions: What are gauge theories? What is meant by local transformations? What do we mean and seek to accomplish by introducing ‘gauge invariance’?

Gauge Invariance (in brief) “… if certain forms of matter exist and are to interact in a way consistent with quantum theory, then the structure of the interaction can be deduced. This is a great departure from the historical situation, where we are simply given the form of the interaction, which was itself guessed by clever physicists. Theories where the interaction is determined (because of the invariance of the theory under some local transformations) are called "gauge theories?” - Kane, p.35, Modern Elementary Particle Physics

What I have done so far is just provided an overview of the subject. Of course delving into a deeper understanding will include detailed mathematics, particularly an understanding of Lie Groups and their Representations.

Reference Texts. Literature and Texts I am aiming to (or have) looked at: Clifford Algebras and Spinors by Pertti Lounesto, London Mathematical Society. Quantum Field Theory by Lewish H. Ryder. Quantum Field Theory in a Nutshell by A. Zee. Modern Elementary Particle Physics by Gordon Kane. An Introduction to Quantum Field Theory by Michael Peskin and Dan Shroeder. Quantum Theory of Fields by Steven Weinberg. Lie Groups, Lie Algebras, and Representations by Brian C. Hall. Representation Theory by William Fulton and Joe Harris.

Thank You.