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Introduction to the Standard Model of Elementary Particle Physics

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Introduction to the Standard Model of elementary particle physics Anders Ryd ([email protected]) May 31, 2011 Abstract This short compendium will try to explain our current understanding of the mi- croscopic universe. This is known as the Standard Model of elementary particle physics. The Standard Model of elementary particles explains what the fundamen- tal constituents of matter is, what the forces are and how they act on matter. 1 Introduction The Standard Model of particle physics is a bit of a misnomer; in fact it is a very well tested theory. Calculations based on the Standard Model has been tested in some cases to 1 part in 10 billion. So far all experimental data is consistent with the Standard Model. At the heart, the Standard Model explains what matter is, what the forces are, and where mass comes from. This is a rather impressive scope! In the next few pages we will dissect the different components of the Standard Model to understand what it tells us. First, we discuss what matter is. Then we move on to the forces, and last mass is discussed. As will be explained the source of mass is yet not experimentally verified and there are some hints here that the Standard Model does not contain the ultimate explanation of how the universe works. The Standard Model of particle physics was developed in the late 1960's and early 1970's. At this point many aspects of the model were theoretical predictions. Basically all of these predictions have now been experimentally verified. 2 Matter Over 2500 years ago the Greek speculated that all of the objects around us were made from a small number of indivisible particles, called atoms. They did not have the ability - or interest - to experimentally verify this. Skipping about 2300 year forward, in the eighteenth and nineteenth century science had advanced far enough that chemists had started to identify these elementary building blocks - the atoms. About 100 different atoms were found. By studying their chemical properties it was noted that they fell into a pattern and they were organized in the 'periodic table of the elements' as shown in Fig. 1. In a famous experiment by Hans Geiger, Ernest Marsden, and Ernest Rutherford in 1909 it was shown that the atom consisted of a massive nucleus surrounded by electrons. A model of the atom was developed where the nucleus is built from protons and neutrons that are very 1 Figure 1: The periodic table of elements. closely bound. The protons have a positive electric charge, while the neutron is electrically neutral. The nucleus is surrounded by a 'cloud' of electrons. The electrons are negatively charged and balance the charge from the protons to make an atom electrically neutral. This lead to a fairly simple picture; there were electrons, protons, and neutrons. All the known atoms were built up from these three basic building blocks. However, in the years after the second world war experiments revealed that other particle could be created in high energy collisions of particles. By the 1960's well over 100 new particle had been observed. All of them were short lived and promptly decayed. However, we were again back at a picture that had 100's of elementary particles. It was suggested that all these particles could be built from more fundamental con- stituents, known as quarks. It was postulated that there was an 'up' quark with an electric charge equal to 2=3 of the proton and a 'down' quark with an electric charge equal to −1=3 of the proton. The proton would then consist of two up quarks and one down quark while the neutron consists of one up quark and two down quarks. In this model one should also be able to build a particle that consists of three up quarks and has an electric charge that is twice that of the proton. In fact, such a particle were observed (it is known as the ∆++). A pictorial view of the structure of matter is shown in Fig. 2. 2 Figure 2: Matter as you zoom in more and more until you get to resolve the quarks in the protons and neutrons. Again we have ended up with a fairly simple picture of the mater; we have the up and down quarks, there is the electron, and also an electrically neutral partner to the electron called the neutrino. (Note that the difference in electrical charge between the down quark and the up quark is the same as the difference in electrical charge between the electron and neutrino. This will be relevant later.) This simple picture got slightly more complicated when it was discovered that each of these 4 particles (the up, down, electron, and neutrino) each had 2 heavier partners. These heavier partners basically have the same properties, except that their mass is larger. In Fig. 3 is a summary of these different particles. In the world around us that we can see an touch, all matter is made up from atoms that in turn are built from the up and down quarks plus electrons. However, if you look out in the universe the picture is a bit different. We will come back to this later. 2.1 Antimatter For each of the matter particles discussed in the previous section there exists a corresponding antiparticle. The antiparticle has the same mass as the original particle, but other properties 3 Figure 3: The simplified periodic table of quarks and leptons. like the electric charge is the opposite for the antiparticle. The antiparticle of the electron is called the positron. The positron has the same mass as the electron, but the opposite electric charge. When the same matter and antimatter particles get in contact with each other they can annihilate each other and turn into pure energy (photons). One of the mysterious still of the universe is why it seems to be made up mostly of matter1 and there is not yet any evidence for antimatter out in the universe. 2.2 Problems 1. Calculate the number of atoms in one kilogram of iron. 2. Estimate the number of protons in the universe. Assume that average galaxy is made from 10 billion stars and that there are about 10 billion galaxies in the universe. 1Of course what we call matter vs. antimatter is an arbitrary choice. It is just more convenient to call the ’stuff' that we are made from matter as supposed to antimatter. However, if there were a planet somewhere in the universe that was made from antimatter the inhabitants would certainly call that antimatter. Is there a way to tell if they are made from antimatter before we make contact with them? 4 3. Verify the the electric charge of the proton and neutron is correct based on the charges of their quark constituents. Consider the sun to be an average star with a mass of about 1:99 × 1030 kg. 3 Forces We are familiar with many forces from our everyday life. The gravitational force keeps us on the ground, the friction force keeps us from sliding of roads when we drive, the contact force that prevents us from slipping into the ground, the electrostatic force between electrically charged objects, the magnetic force that makes the compass point to the north, etc. Similar to how the Standard Model explained how all matter is built out of a few basic constituents, the standard model also simplifies the description of forces. That is all forces except for gravity. Gravity is not part of the Standard Model. The electric force and magnetism appeared to be different forces, but through the work of James Clark Maxwell and others in the nineteenth century it was realized that the electric and magnetic force had the same origin: there was one electromagnetic force. With a common description it is said that the electric and magnetic forces were unified. Most other forces, such as friction, contact forces etc. are just manifestations of the electromagnetic force on small scales. The equations that govern the electromagnetic fields allowed for a solution that explained light. Light was electromagnetic waves that travel by the speed of light (in vacuum). Hence, besides unifying the electromagnetic force, Maxwell explained what light was. In classical physics the electric field is defined as the force a test charge feels. The electric field of an electrically charged particle fills all of space and generates an electrical potential that falls as / 1=r, where r is the distance from the electric charge. In the Standard Model a slightly different picture is taken. However, mathematically you can show that the two descriptions give the same observable effects. In this picture the force comes from 'exchanging' a photon, see Fig. 4. In this picture two electrically charged particles are traveling towards each other, one emits a photon and change direction. The photon is absorbed by the other particle within a very short time and it also gets a change in direction. To illustrate how this works, think of a two people standing in boats and tossing a bowling ball back and forth, see Fig. 5. When Alex throws the ball to Jenny, Alex will recoil against the ball and start moving backwards. When Jenny receives the ball she will absorb the momentum and start moving to the right. The net effect of this is equivalent to a repulsive force that pushes the boats away. In the Standard Model the electromagnetic force is described by the exchange of photons. We say that the 'photons couple to the electric charge'. This is consistent with the classic picture, where the force is proportional to the electric charge.
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