Introduction To The Standard Model Of Elementary Particle .
Introduction to the Standard Model of elementaryparticle physicsAnders Ryd (Anders.Ryd@cornell.edu)May 31, 2011AbstractThis short compendium will try to explain our current understanding of the microscopic universe. This is known as the Standard Model of elementary particlephysics. The Standard Model of elementary particles explains what the fundamental constituents of matter is, what the forces are and how they act on matter.1IntroductionThe Standard Model of particle physics is a bit of a misnomer; in fact it is a very well testedtheory. Calculations based on the Standard Model has been tested in some cases to 1 partin 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 wheremass comes from. This is a rather impressive scope! In the next few pages we will dissectthe 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 isdiscussed. As will be explained the source of mass is yet not experimentally verified andthere are some hints here that the Standard Model does not contain the ultimate explanationof 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 thesepredictions have now been experimentally verified.2MatterOver 2500 years ago the Greek speculated that all of the objects around us were made froma small number of indivisible particles, called atoms. They did not have the ability - orinterest - to experimentally verify this. Skipping about 2300 year forward, in the eighteenthand nineteenth century science had advanced far enough that chemists had started to identifythese elementary building blocks - the atoms. About 100 different atoms were found. Bystudying their chemical properties it was noted that they fell into a pattern and they wereorganized 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 1909it was shown that the atom consisted of a massive nucleus surrounded by electrons. A modelof the atom was developed where the nucleus is built from protons and neutrons that are very1
Figure 1: The periodic table of elements.closely bound. The protons have a positive electric charge, while the neutron is electricallyneutral. The nucleus is surrounded by a ’cloud’ of electrons. The electrons are negativelycharged 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 theknown atoms were built up from these three basic building blocks. However, in the yearsafter the second world war experiments revealed that other particle could be created in highenergy collisions of particles. By the 1960’s well over 100 new particle had been observed. Allof them were short lived and promptly decayed. However, we were again back at a picturethat had 100’s of elementary particles.It was suggested that all these particles could be built from more fundamental constituents, known as quarks. It was postulated that there was an ’up’ quark with an electriccharge equal to 2/3 of the proton and a ’down’ quark with an electric charge equal to 1/3of the proton. The proton would then consist of two up quarks and one down quark whilethe neutron consists of one up quark and two down quarks. In this model one should alsobe able to build a particle that consists of three up quarks and has an electric charge that istwice that of the proton. In fact, such a particle were observed (it is known as the ). Apictorial 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 theprotons and neutrons.Again we have ended up with a fairly simple picture of the mater; we have the up anddown quarks, there is the electron, and also an electrically neutral partner to the electroncalled the neutrino. (Note that the difference in electrical charge between the down quarkand the up quark is the same as the difference in electrical charge between the electron andneutrino. This will be relevant later.) This simple picture got slightly more complicatedwhen 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 thatin turn are built from the up and down quarks plus electrons. However, if you look out inthe universe the picture is a bit different. We will come back to this later.2.1AntimatterFor each of the matter particles discussed in the previous section there exists a correspondingantiparticle. The antiparticle has the same mass as the original particle, but other properties3
Figure 3: The simplified periodic table of quarks and leptons.like the electric charge is the opposite for the antiparticle. The antiparticle of the electronis called the positron. The positron has the same mass as the electron, but the oppositeelectric charge. When the same matter and antimatter particles get in contact with eachother 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 ofmatter1 and there is not yet any evidence for antimatter out in the universe.2.2Problems1. Calculate the number of atoms in one kilogram of iron.2. Estimate the number of protons in the universe. Assume that average galaxy is madefrom 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 somewherein the universe that was made from antimatter the inhabitants would certainly call that antimatter. Is therea 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 chargesof their quark constituents. Consider the sun to be an average star with a mass ofabout 1.99 1030 kg.3ForcesWe are familiar with many forces from our everyday life. The gravitational force keeps us onthe ground, the friction force keeps us from sliding of roads when we drive, the contact forcethat prevents us from slipping into the ground, the electrostatic force between electricallycharged 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 basicconstituents, the standard model also simplifies the description of forces. That is all forcesexcept for gravity. Gravity is not part of the Standard Model.The electric force and magnetism appeared to be different forces, but through the work ofJames Clark Maxwell and others in the nineteenth century it was realized that the electricand magnetic force had the same origin: there was one electromagnetic force. With acommon description it is said that the electric and magnetic forces were unified. Most otherforces, such as friction, contact forces etc. are just manifestations of the electromagneticforce on small scales.The equations that govern the electromagnetic fields allowed for a solution that explainedlight. 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 electricfield of an electrically charged particle fills all of space and generates an electrical potentialthat falls as 1/r, where r is the distance from the electric charge.In the Standard Model a slightly different picture is taken. However, mathematicallyyou can show that the two descriptions give the same observable effects. In this picture theforce comes from ’exchanging’ a photon, see Fig. 4. In this picture two electrically chargedparticles are traveling towards each other, one emits a photon and change direction. Thephoton is absorbed by the other particle within a very short time and it also gets a change indirection. To illustrate how this works, think of a two people standing in boats and tossinga bowling ball back and forth, see Fig. 5. When Alex throws the ball to Jenny, Alex willrecoil against the ball and start moving backwards. When Jenny receives the ball she willabsorb the momentum and start moving to the right. The net effect of this is equivalent toa 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 classicpicture, where the force is proportional to the electric charge. An electrically neutral objectdoes not feel the electromagnetic force.5
Figure 4: Two electrically charged particles exchange a photon.3.1Weak forceIn the Standard Model there are more forces than the electromagnetic force. The weak forceis mediated by two types of particles, the electrically neutral Z 0 and the electrically chargedW . The Z 0 is very similar to the photon but there is one very important difference. TheZ 0 is not massless, like the photon. In fact, the Z 0 is very heavy on the scale of fundamentalparticles. Only the top quark is heavier. The mass of the Z 0 is about the same as 100protons, or one Zirconium (Zr) atom. The fact that the Z 0 is massive has a profound effect.The electric potential around an electrically charged particle was 1/r. For a massiveparticle this changes to e mrc/h̄ /rWhich means that for large distances the potential due to the weak force is exponentiallysuppressed. (If m 0 as for the photon you recover the 1/r form.) But for small distanceswhere mrc/h̄ 1 the exponential is approximately one and there is no exponential suppression. The upshot of this is that the weak for is about as strong as the electromagneticforce at short distances, but for longer distances the weak force is much weaker.The other two particles, the W and W , are also massive. They are just slightly lighterthan the Z 0 . Again, this has the effect that the range of the force is short due to theexponential suppression. However, the fact that they are charged has another importanteffect. Consider the case we had in Fig. 4. If we replaced the photon here with an W or W it would not work - the electric charge would not be conserved. So the type ofinteractions the W generate are different. Instead of just giving the particles a kick, theparticles involved change type. Consider the example in Fig. 6. In this example the initial dquark (with charge 1/3) emits a W and becomes a u quark (with charge 2/3). The W 6
Figure 5: Two people standing on a boat and throw an object between them. This will causethe two to drift apart.in turn splits into an electron and the anti-neutrino. This is an example of a beta decay. Ifthe initial d quark was in an neutron, this would generate the decay n p e ν̄e .3.2Strong forceBesides the electromagnetic and weak forces, there is one more force in the Standard Model:the strong force. This is the force that is responsible for binding the quarks together to formthe protons and neutrons. If you consider the proton as constituting two up quarks and onedown quark it is easily seen that some new force is need to bind these particles together, theelectric repulsion would otherwise make the quarks fly apart.There are several very peculiar properties of the strong force. We will discuss some ofthem here. Like the photon is the mediator of the electromagnetic force, the gluons arethe mediators of the strong force. Similar to the exchange of a photon between two chargedparticle, a gluon can be exchanged between two quarks. This is illustrated in Fig. 7. However,the gluons do not couple to the electric charge, rather they couple a different type of ’charge’called the color. In fact there are three such charges, called red, green, and blue. Like for theelectric charge where we have positive and negative charges the three color charges also havecorresponding anti-charges: anti-red, anti-green, and anti-blue. But even more surprising isthe gluons. Note that the photon was electrically neutral, while the gluons carry one colorcharge (red, green, or blue) and one anti-charge (anti-red, anti-green, or anti-blue). So if wenow look at the diagram again where two quarks exchange gluons and we add the color tothe diagram, as shown in Fig. 8, we have to conserve color in each vertex of the diagram.Since the gluons carry color, gluons also couple to gluons. This is illustrated in Fig. 9.This leads to a much more complicated behavior of the strong interaction. In Fig. 10 aretwo electric charges and two color charges (quarks). Notice that the electric field lines justspread out over all of space, while the color field lines forms a long string, or flux tube. Thereason that the field lines for the strong field bundle up is that there is a force between the7
Figure 6: A neutron can decay to a proton and an electron–anti-neutrino pair. This is knowas beta-decay in nuclear physics. This illustration shows how one d quark is transformed toa u quark when a W is exchanged.gluons as they them self have a color charge. For the electric field the force falls as 1/r2 withdistance. While for the strong field the force is constant. Hence the work needed to separatetwo electric charges is finite, while for the two quarks you would need an infinite amount ofenergy. The property that you can not separate two quarks is known as confinement. Thefact that a quark can never exist free means that it is hard to establish properties of thequarks, such as their masses.Hence quarks are always observed bound together by the strong force. There are twodifferent types of particles that are made from quarks. One type is known as mesons. Theseconsists of a quark and an anti-quark pair. The quark and anti-quark carry opposite color,e.g. red and anti-red. The other type of matter made from quarks is the baryons. Baryonsare made from three quarks, like for example the protons and neutrons. The three quarks,e.g. uud in a proton, each carry a different color. If the color is indicated by r, g, b assubscripts you would for example have ur ug db . We said earlier that free quarks could notexist, why can we have three quarks with three different colors? In some sense this is likewhen you mix red, green, and blue light you get white like on a TV screen, in the same sensethe three quarks that form a proton has no net color charge.3.3Summary of forcesTo summarize this, the Standard Model includes three forces. The electromagnetic force,mediated by the photon, the weak force, mediated by the Z 0 and W and the strong force,mediated by the gluons. In the Standard Model it is shown that the electromagnetic andweak force is actually of the same origin. The strong force is mathematically very similar,but at this point not unified with the electroweak force. Gravity is not included in theStandard Model.8
Figure 7: Two quarks exchange a gluon in the strong interaction.3.4Problems1. As discussed above, the range of the weak force is suppressed by the exponential terme mrc/h̄ . By setting mrc/h̄ 1 we can estimate the range of the weak force. Using themass of the Z boson estimate the range and compare to the size of a typical atom.4Mass and the HiggsThere is one slight issue. In order to mathematically write down the Standard Model oneneed to assume that all particles are massless. This obviously is not consistent with reality.But thanks to a beautiful mathematical trick call ’spontaneous symmetry breaking’ this canbe repaired. Instead of just postulating that the particles in the Standard Model has massone can add the Higgs to the existing particles and forces. The Higgs particle couples tothe different particles with different strengths and this coupling gives the particles in theStandard Model mass.All particles, 6 quarks, 3 leptons, and 3 neutrinos, have been found in particle physicsexperiments. However the Higgs has so far eluded discovery after more than 40 years ofsearches since it was postulated in the late 60’s. The Standard Model makes many predictionsabout the Higgs, but it don’t tell us the Higgs mass. It is likely that the Higgs particle hasnot been discovered as it is just to heavy to be produced in our experiments (so far).9
Figure 8: In this figure the quarks and gluon has been labeled by the color to more carefullyindicate how the strong force works.5OutlookThe Standard Model has been incredibly successful. All experiments done so far has beenconsistent with the predictions of the Standard Model. However, there are a few hints thatthere are something beyond the Standard model. A few of these are mentioned below.5.1Dark Matter and Dark EnergyWhen astronomers study galaxies they can look at the rotation curves of the stars. Thislooks at the velocity of the stars in galaxies as a function of the radius from the center ofthe galaxy. It has been observed since the 1930’s that the velocity is consistent with muchmore mass in the galaxy than what you see from the light emitted by stars.Using gravitational lensing where light is bent by the mass of galaxies and clusters ofgalaxies, astronomers have made made maps of the mass distributions and seen that thereis much more mass than what you expect from the observed number of stars.These observations point to a large fraction of dark matter in the universe. The termdark is used to mean that it does not emit light. That is it does not couple to the photon it is electrically neutral.Even more strange are the observations from the cosmic microwave background studies.In these studies small temperature variations from the time when the universe was onlyabout 300,000 years old are used to probe the early universe. These observation tells usthat the universe is full of a substance known as dark energy. The dark energy providing anegative pressure that is driving an expansion of the universe.10
Figure 9: This diagram shows an example of how gluons can couple to each other andgenerate very complicated diagrams.All of these, and other, observations tells us that the universe is made from about 4% of’regular’ matter that we have here on earth. Dark energy makes up about 23% and mostlythe universe is made from dark energy, 73%. So the Standard Model is only useful to explainabout 4% of the ’stuff’ in the universe.5.2The Higgs MassAnother problem with the Standard Model is Higgs itself. Though it does an remarkable jobat giving mass to all the other particles in the Standard Model, its own mass suffers froma theoretical problem known as ’fine tuning’. It turns out that in order to give the Higgs aFigure 10: Illustration of how the electric and color fields differs. The electric field spreadsout all over space, while the color field tends to stick together (like glue) and form a bundle.11
mass that makes the theory consistent one has to tune a parameter in the model to about36 significant digits. This is what is meant by fine tuning. This seems exceedingly unlikelyso theorists have thought of ways to solve this problem. The most popular idea is knownas super symmetry. Super symmetry adds more particles and solves the problem with finetuning. But then there should be many more particles, and so far none of them has beenseen. Again it is likely that they are heavy and has not been seen yet in experiments.It is clear from all the experiments done so far that the Standard Model is an excellentmodel for the physics we have explored so far. This is similar to classical mechanics. It worksvery well for macroscopic objects in our everyday life. But if you start to look at objectsthat travel at speeds close to the speed of light you will need to use special relativity whichprovides a correct description for objects that travel at very high speeds. Similar if you lookat very small objects you need to use quantum mechanics. As experiments in particle physicsprobe higher and higher energies it is expected that one day we will run into a ’crack’ inthe Standard Model and it will give us an hint about the new physics beyond the StandardModel.12
Figure 4: Two electrically charged particles exchange a photon. 3.1 Weak force In the Standard Model there are more forces than the electromagnetic force. The weak force is mediated by two types of particles, the electrically neutral Z0 and the electrically charged W . The Z0 is very sim
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Le genou de Lucy. Odile Jacob. 1999. Coppens Y. Pré-textes. L’homme préhistorique en morceaux. Eds Odile Jacob. 2011. Costentin J., Delaveau P. Café, thé, chocolat, les bons effets sur le cerveau et pour le corps. Editions Odile Jacob. 2010. 3 Crawford M., Marsh D. The driving force : food in human evolution and the future.
