aa r X i v : . [ phy s i c s . pop - ph ] J un FLAVORS OF RESEARCH IN PHYSICS
Copyright @ 2010, Indian National Science Academy, New Delhi, India
The Heart of Matter
Rohini M. Godbole
Theoretical Physics, CERN, CH-1211, Geneva-23,SwitzerlandCenter for High Energy Physics, Indian Institute of Science, Bangalore 560 012, India
Abstract
In this article I trace the development of the human understanding of the “Heartof Matter” from early concepts of “elements” (or alternatively “Panchmahab-hootas”) to the current status of “quarks” and “leptons” as the fundamental con-stituents of matter, interacting together via exchange of the various force carrierparticles called “gauge bosons” such as the photon, W/Z-boson etc. I would liketo show how our understanding of the fundamental constituents of matter hasgone hand in hand with our understanding of the fundamental forces in nature.I will also outline how the knowledge of particle physics at the “micro” scaleof less than a Fermi(one millionth of a nanometer), enables us to offer expla-nations of Cosmological observations at the “macro” scale. Consequently theseobservations, may in turn, help us address some very fundamental questions ofthe Physics at the “Heart of the Matter”.
1. Concept of “elementarity” through ages.
In addressing any problem in any walk of life, the recognition of the central issue isalways essential. A query of what lies at the “heart” of a given problem is of utmostimportance to all of us, in dealing with various issues in everyday life. It is therefore,not surprising that, since the dawn of humanity, a major part of the scientific endeavorof the humankind has been devoted to gain an understanding as to what lies at the‘Heart of the Matter’. The scientific knowledge and process as we know today, hasdeveloped through a desire to know how nature operates. One of the central themesin these explorations has been the wish to know whether all the matter is made up ofelemental building blocks and if so how these elemental constituents are held together.In more colloquial words one might call this a quest for deciphering what the “bricks”and ”mortar’ of this wonderful edifice of life around us are. Funnily enough throughthe ages, the development of our understanding of what the fundamental constituentsof matter are, has grown hand in hand along with our knowledge of the working ofvarious fundamental processes and the fundamental forces of nature. It is this interplaythat I find most fascinating. FlavorsofResearchinPhysicsAt present particle physicists have arrived at an understanding of the basic laws ofphysics which govern the behaviour of the fundamental building blocks of matter, thequarks and the leptons. The interesting fact is that the same laws, in principle ,allow us to predict the behavior of all the matter around us under all circumstances.Indeed we have come a long way since the early days of the Greek Empedocles whothought that the world was made up of the four elements : Earth, Water, Fire, Air.So also from the days of the early Indian sages who identified the five entities: theabove four along with the “sky” as the
Panchmahabhootas , as those whose work-ings need to be understood and which need to be conquered. Starting with this really“small” number of fundamental “elements” of nature, our concept of elementarity hasevolved through the ages, starting from molecules, atoms, nuclei and finally ending inquarks/leptons after passing through protons/neutrons on the way, as the candidates forthe basic building blocks of matter. Finally, it seems to have come home, at least tem-porarily, to roost in the wonderful picturesque world of “elementary particle physics”.The particle physicists, for good reason, believe that now we have perhaps peeled thelast layer of the onion and the nature has revealed the ultimate constituents of matter tous. We feel that we have seen the last faceless entity at the heart of this Russian Doll.The currently accepted list of the elementary particles consists of the quarks, leptons,the force carrier particles called gauge bosons: γ, W ± , Z , gluons along with the asyet undiscovered Higgs boson. It is this journey starting from the “elements” of theearly Greeks/Indians to the quarks/leptons as the fundamental constituents, that I wantto sketch out for you.The subject of elementary particle physics, which is the branch of physics thatdeals with the ultimate layer of structure of matter, addresses the following three is-sues. These are: • What are the elementary constituents of matter? • What holds them together? • What is the correct mathematical framework to describe how the constituents are puttogether to form matter, how do they interact with each other and how can one predictits behavior under different conditions?Interesting thing is that the path to the correct answer to the first two questions at agiven level of elementarity, has been indicated only by the answers to the last questionat the earlier level of elementarity. A detailed account of the aspect of the elementaryparticle physics mentioned under point (3) above, is to be found in the article of Prof.A. Raychaudhuri, elsewhere in this volume. I would therefore not really spend muchtime on it, rather, I would like to chart out for you how our ideas of elementarity havechanged and why we believe that quarks and leptons are indeed the ‘fundamental’ constituents. This means I will not discuss much about the “force carriers”. One basicpoint I want to make is, that in the end the essential process by which structure hasbeen revealed has been more or less the same at all levels.Equally interesting is another development of the past few decades, which havemade us realise that this world at the smallest distance scales holds clues to some of Indeed the size of an electron, if it all it is not a ’point’, has to be less than a million, million, million th of a meter stick heHeartofMatter 3the puzzles of the Cosmos with its huge distance scales of millions of parsecs , suchas why matter dominates over antimatter in the Universe or what might be the “darkmatter” which does not shine but whose existence is revealed through its gravitationaleffects etc. The results of on going investigations in different High Energy Physicsexperiments at the colliders or otherwise should be able to confirm whether the ex-planations offered by the HEP theory to these puzzles are indeed the correct ones.Currently the most important puzzle of them all is why our Universe is accelerating?A new development in Particle physics theory extended to include gravitation, calledthe String theory, might have a solution for that as well! This interplay between the”micro” and the ”macro” scale is one of the most amazing things and reminds me ofa saying by Albert Einstein, which I freely paraphrase: ‘The most incomprehensiblething about our Universe is that it is comprehensible to human thought’.
2. Standard Model of Particle Physics
Let me begin by summarising the currently accepted picture of the fundamental con-stituents and interactions among them, the Standard Model of Particle Physics(SM),before I venture into a retracing of the tortuous path taken by the scientific commu-nity from the time of the Demorkritos and Kanad to arrive at the SM. According toour current understanding, not only the bricks but even the mortar (the force carriers)are elementary particles. Fig. 1 shows the constituents of matter at different distancescales, beginning from atoms with a size of one tenth of a billionth meter, ending with quarks and leptons . Experiments put an upper limit on their size, which itself is ahundred million times smaller than the size of an atom and today are believed to betruly indivisible. These are considered to be the fundamental constituents of matter.Experiments at high energy accelerators, and the development of theoretical models,have together helped us arrive at this conclusion.Quarks Leptons (cid:18) ud (cid:19) (cid:18) cs (cid:19) (cid:18) tb (cid:19) (cid:18) e − ν e (cid:19) (cid:18) µ − ν µ (cid:19) (cid:18) τ − ν τ (cid:19) × . The fundamental constituents of matter.
The quarks and leptons come in several different varieties, summarised in Table1. The quarks are called u(p), d(own), c(harm), s(trange),t(op) and b(ottom) whereas One parsec is roughly 180 times the earth-sun distance, i.e.
27 Billion Kilometers.
FlavorsofResearchinPhysicsFigure 1 . Constituents of matter at different distance scales the leptons are the well known electron(e) along with muon( µ ), tau-lepton ( τ ) and thecorresponding neutrinos, ν e , ν µ and ν τ respectively. Later we will get a glimpse ofwhy so many varieties must be present.As for the forces we know today that there are of four basic forces experienced bythe constituents of matter:1. Gravitational Force: The force that holds us on the earth, and gives rise to plan-etary motion as well as tides.2. Electromagnetic Force: The force that holds electrons inside atoms, and that isresponsible for electrostatic effects, electric currents, and magnetic poles.3. Weak Force: The force that causes the decay of radioactive nuclei, in which aproton changes into a neutron or vice versa.4. Strong Force : The force that binds together the quarks inside protons and neu-trons, and also makes the latter stick to each other to form the atomic nucleus.The force responsible for holding the nucleons (protons and neutrons) together in anucleus, is derived from the Strong Force above in a similar way that the “Van derWaals” force (the force between neutral atoms holding them together in a molecule) isderived from the Coulomb interaction among the charged constituents of the otherwiseheHeartofMatter 5neutral atom. These forces are familiar to us to varying degrees, depending on theireffects on the kind of objects that we encounter in daily life. The first two forces inthe above list have been known almost since the dawn of scientific thought, while thelast two are nuclear forces and were discovered only in the twentieth century. Theeffects of the latter two forces cannot be observed directly by the human senses, butthey are just as real as the first two, since experimental equipment is certainly able todetect them. For the strong, electromagnetic and weak interaction, we have been ableto show that these interactions between the constituents of matter are conveyed via themediation of the force carriers. The interactions along with these force carriers arelisted in Table 2.Interaction Description Carrier ParticleGravitation Long-range but extremely weak attrac-tion between all particles. ????Electromagnetic Long-range interaction of a quark or lep-ton with another quark or lepton Photon γ Weak Short-range interaction that can causedifferent quarks and leptons to changeinto each other
W/Z
BosonsStrong Short-range interaction among quarksonly Gluons g Table 2 . Four basic forces in Nature, and the carriers for three of them.
The lighter quarks manifest themselves only as bound states like protons, pionsand kaons. The neutrinos have only weak interactions, whereas the colourless chargedleptons have weak and electromagnetic interactions and the coloured quarks feel all thethree interactions. The properties of all the particles, the constituent matter particlesand the force carriers, have been measured to a high degree of accuracy.Let us recall here that most elementary particles carry a “spin”, or intrinsic angularmomentum. We believe this because of experiments in which particles are found tobehave as if they are spinning on their own axis. This is not literally true: if it were, oneshould be able to change their amount of spin, or stop them from spinning, while in facttheir spin angular momentum is an unchangeable property. So we must treat it as anintrinsic property of the particle. It turns out that it has to be always an integer or half-integer multiple of a basic unit called ~ or Planck’s constant. This multiple is calledthe ’spin’ of the particle. Particles of integer spin are called “bosons” and those ofhalf-integer spin, “fermions”. All these particles have a few other intrinsic propertieswhich have been given very imaginative and descriptive names such as strangeness,colour etc. by particle physicists and I will get back to that a little later. FlavorsofResearchinPhysicsThe achievement of the last fifty odd years of the particle physicists as a commu-nity has been to arrive at an understanding of the working of the matter particles, thequarks and leptons, and the force carriers, the bosons and develop the mathematicalframework in which this can be described. The latest in this series of developmentsis to develop a mathematical framework which will also might make it possible to de-scribe workings of gravity at the same level. As already mentioned this subject doesnot concern us here. We will now proceed to discuss how particle physicists arrived atan understanding that these quarks and leptons are the building blocks of nature.
3. A tale of molecules, atoms and nuclei
Our concept of elementarity has undergone a change in the centuries; so has the branchof science in general and physics in particular, that has dealt with the issue. Demokritossaid ‘By convention there is colour, by convention sweetness, by convention bitterness,but in reality there are only atoms and space’ . In the above statement and a similar oneby Kanad in Vaishyashik Sutras, there was only a conviction that all the observed prop-erties of things around us are result of how the ’atoms’ (the smallest, indivisible part ofmatter) are put together. This was postulated without any idea of what the atoms wereand/or how they are to be put together. It was a philosophical statement. It took SirIssac Newton, the father of Physics as we know it, to tell us how we should go aboutsubstantiating this and finding these atoms. He said in his Optics, ’
Now the smallestParticles of matter may cohere by the strongest attractions and compose bigger parti-cles of weaker virtue....There are therefore agents in nature able to make particles ofBodies stick together by very strong attractions and it is the Business of experimentalPhilosophy to find them out ’. Thus ’experimental Philosophy’ is the earliest name onecould give to this branch of science which dealt with the issue. Issac Newton wasalso the first one to put forward the theory of ’action at a distance’ which explainedthe proverbial falling down of the apple, earth’s going around the sun and the strangeappearance of comets in the sky from time to time, in terms of the same interaction;viz. Gravitation. At the time of Newton and for quite some time after that, thermody-namics might have been termed as the branch of science that dealt with the structureof matter, as one could describe the behavior of three states of matter; the solid, theliquid and the gas, in terms of the laws of thermodynamics. However, already at thistime a further classification was known. Chemists already knew that one can classifyobjects by some properties which they seem to retain, independent of the state of mat-ter: gaseous, liquid or solid. So Chemistry, the study of these chemical “elements”,could have been considered to be the branch of science dealing with this issue at thattime. The regularity of patterns observed in masses, ionisation of various compounds,elements etc had led to the idea of “atoms”. The ordering of these chemical elements inthe Periodic Table according to their properties, put forward by Mendeleev in 1876, isone of the earliest examples of recognising order/patterns which can then be used as anexperimental indication of the presence of underlying constituents. This phenomenonof an observed order/pattern/regularity in the properties of ‘elemental’ objects, beinga smoking gun signal of a possible underlying structure, was to repeat oft in the yearsto follow.The modern saga of atomicity, after the Greeks/Vedantas, begins with Dalton at theend of 18 th Century. He observed that the chemical elements always combined in theheHeartofMatter 7same ratio to make a given compound. He postulated therefore that the chemical ele-ments were made of units, which he termed “atoms” . Avagadro further found that allthe gases combine in definite proportion of volume. That is the number of moleculesin a given volume, at a given temperature are the same. This then led to the determina-tion of molecular weights, molecular formulae and hence also of atomic weights. Soalready, by the early 19 th century the Chemists knew that all the molecular weightswere rough integral multiples of that of the hydrogen. So it was likely that the Hydro-gen atom was the basic unit of them all! Thus the order in the atomic and molecularweights gave an indication of the possible existence of a basic building block in termsof the Hydrogen atom. Chemists kept on using the “atomic” theory without believingin the existence of the atoms till the advent of the kinetic theory of gases which gave afirst principle derivation of all the observed property of gases . The importance of theidea of atomicity to the world of science is very graphically expressed in the words ofone of the greatest minds in physics of the 20 th century, arguably next only to Einstein,Richard Feynman. He says, ’ If all the scientific knowledge in the world were to be de-stroyed and I can choose only one piece of understanding to be passed on to future,I would choose to pass on the message that matter is composed of atoms, ceaselesslymoving and bouncing against each other ’. So at this point in the human history, onecould have said that the scientists had found the “atoms” which the Greeks /Kanad hadpostulated and which Newton had exhorted the practitioners of “experimental Philos-ophy” to find.Then in the later half of the nineteenth century came the discovery which effec-tively defined the shape of physical and chemical sciences for the next century: thediscovery by the great Michael Faraday that the electricity too comes in multiples of abasic unit. This and the experiments J.J. Thompson performed with the Cathode Rays,helped him discover the electron, the first elementary particle, in 1897. The world ofparticle physics was born then. Indeed, Thompson went on to claim boldly ’
Cathoderays are matter in a new state, a state in which the subdivision of matter is carriedmuch further than in the normal gaseous state, a state in which all matter, - that ismatter derived from different sources such as Oxygen, Hydrogen etc. - is one and thesame kind, the matter being the substance from which all chemical elements are builtup. ’ Thompson had thus split the “atom” by proclaiming that it was made up of elec-tricity : positive and negative ! Existence of an electron with the mass to charge ratioas measured by Thompson was shown to explain fine details of the atomic spectrallines under the effect of a magnetic field, as calculated using an idea by Lorenz andmeasured by Zeeman. These experiments in 1899, helped electron make a transitionfrom being a “mathematical entity” to being a “physical reality”. As a matter of factthe last mentioned was an important step so that people could believe in the existenceof the electrons in reality,In the above description of the discovery of the electron, we see at work, all the By necessity his “atoms” were essentially what we call “molecules” today. It is interesting to note that Einstein’s famous first work in physics in 1905 on Brownian Motion wasfueled by a wish to provide ’direct’ evidence for ’atoms’ to the straggling nonbelievers. To be honest this was a very bold speculation on part of Thompson, not quite justified by the results hehad gotten then.
FlavorsofResearchinPhysicsthree basic processes which have helped the physicists to arrive at the current pictureof the basic constituents of matter. These were1) Observation by Faraday that the electricity comes in units, from patterns in ion-isation,2) The experiments made by Thompson which showed him that the Cathode raysbehave under the action of electric and magnetic fields as though they consistedof particles with a ratio of charge to mass (the famous e/m ) quite different fromthe Hydrogen ion,3) The measurement by Zeeman of the splitting of the atomic spectral lines in amagnetic field and finding a value in agreement with that predicted using ideasby Lorenz, assuming that a particle with that value of e/m exists inside the atom.In achieving the last it was necessary to have an understanding of how to describemathematically the interactions of the electron (a charged particle) with electromag-netic fields. This was in place by then, thanks to Faraday and Maxwell. This is anexample of the synergy mentioned in the beginning of the article, between discoveringwhat lies at the heart of the matter and figuring out the correct mathematical frameworkto describe interactions among the constituents of matter.As a matter of fact Thompson did not stop at making the bold speculation thatmatter was made of electrons, but gave a specific model for the Hydrogen atom calledthe “plum pudding model” and had worked out in detail how the very “light” electrons could make up the atom. Then came another discovery that shaped our thinking aboutmatter again for decades to come: the famous Rutherford scattering experiment whichmany of us study in physics in the last years of our school these days. As a matterof fact, this is a classic example of one of the two paths to “elementarity” that hasbeen followed by scientists in their pursuit of what lies at the heart of matter. It iscomplementary to the other path mentioned earlier, where one uses indications givenby observing the pattern and order in properties of “elemental” objects. Very oftenprogress in these two paths, took place side by side! I will give specific examples ofthis synergy in the context of Nuclear Physics and Elementary Particle Physics as wego along.Fig. 2 depicts schematically the experiment conducted by Rutherford in whichhe bombarded a thin gold foil with a beam of α particles emitted by the radioactivesalts. The α particles carried a positive charge twice as much as the Hydrogen ion andweighed four times as much. He then measured their angles of deflection after hittingthe gold foil. In technical terms he scattered a beam of the α particles off the target of a gold foil and detected the scattered α particles in a detector made up of the zincsulphide screen which produced scintillations when α particles hit it. Though it maynot be very obvious at this stage, it was an attempt to “look” inside the atom usingthe α particles. In this case the “known” piece of theory was the good old ClassicalMechanics started by Newton and Electrodynamics : the theory of how charged bodies Electrons were found to be about 1800 times lighter than the Hydrogen atom. heHeartofMatter 9
Target
Thin gold foil
Detector
MicroscopeZincSulphideScreen
Beam
Alphaparticlesource
Figure 2 . Schematic depiction of Rutherford’s experiment. moved under the action of electric and magnetic fields, honed to perfection by Fara-day and Maxwell. Using these two one could predict the trajectory of an α particlepassing through the distribution of the positive charge in the atom, which accordingto Thompson’s Plum Pudding Model, was spread all over the atom uniformly with the e ′ s sticking up like plums. Recall that Thompson’s experiment had revealed that the e/m ratio for the electron was much smaller than for the hydrogen ion and thus themass of the atom was expected to be concentrated in the positive charge. Thus it wasexpected that all the α particles will mainly feel the positive charge and thus be de-flected through very small angles. Imagine you are traversing through a big group ofpeople uniformly spread over an area. You will have to change your “trajectory” everyso often as to avoid directly colliding with another person and thus your trajectory willsuffer small “deflections”. Now what Rutherford discovered was something exactlyopposite to the expectations of Thompson’s model. Most of the α particles traversedthrough the foil without suffering any deflections at all, but those which did deflect didso violently. Some of them even rebounded. In Rutherford’s own words, ’ It was aboutas credible as if you had fired a fifteen inch shell at a piece of tissue paper and it cameback and hit you ’.This was a watershed of a discovery. Qualitatively it meant that all the mass andthe positive charge of an atom was concentrated in a “point”. So for most of the time α particles saw no charge which could repel them, i.e. most of the atom was empty space.To carry the above mentioned analogy further, consider now that you had to traversethe same road but the group of people now had gathered in a tight crowd around someobject of interest in the middle of the road. If you tried to pass through the crowd youwill be pushed back, but if you were initially headed in the region away from this knotof people you don’t need to change your direction at all to pass through the road. Thisis exactly what was being observed by Rutherford with his α particles and the goldfoil. Of course, what fraction of time you will be repelled back will be decided by howwidely spread the “knot” of people in the centre of the road is. In more technical words,the fraction of α particles scattered at a particular angle, called the angular distribution,can give information on the spatial extent of the charge distribution. Thus they can be0 FlavorsofResearchinPhysicsused to “see” whether the positive charge in the atom had a structure or whether itwas concentrated in a point. Rutherford showed that the angular distribution observedby him, agreed with the one calculated using electromagnetism and Newton’s laws ofmotion, assuming the positive charge to be a “point” particle. He termed this point tobe the “nucleus” of an atom. Thus now the next step in revelation of the structure ofmatter was taken: the nucleus had arrived. The “atom” has been truly split and shownto consist of a point nucleus and a whole lot of empty space containing the electrons.At this point the fundamental constituents of matter were nuclei and electrons and theymade up atoms, which in turn made up the molecules and so on.The next decades then saw further progress in the understanding of atoms in termsof a central nucleus and electrons as well as in that of the nuclei themselves. AtomicPhysics and Nuclear Physics could then have been said to be the branch of Physicsdealing with the fundamental constituents of matter around us. Emergence of patternsin the properties of nuclei, such as their masses, the spin angular momenta they car-ried, already indicated that the nuclei, though seen to be point-like, a-la Rutherford’smeasurements, perhaps had constituents. Note that while finite size of an object indi-cates that it has constituents, just because a particular object has a size smaller thanthe least count of our best measuring stick, we can not automatically conclude thatthe object may not have constituents. All the observed regularities in the propertiesof the nuclei could be explained by assuming that they were made up of protons (thehydrogen nucleus), and neutrons, neutron being an electrically neutral particle withthe same mass as that of the proton. Thus the list of the “fundamental” objects atthis point would have contained only a few “particles”: the photon γ whose existencewas deduced from “Photoelectric Effect” by Einstein, the electron e , the proton(p)and the neutron (n). To jump a few years in this so far chronological narration, wecould also include in addition the small “neutron”, i.e., the neutrino ν that WolfgangPauli, another intellectual giant, had had to reluctantly postulate to reconcile with theconservation of energy, linear momentum and angular momentum, the experimentallyobserved properties of the β particles observed in the decay of the radioactive nuclei.Let us note, as an aside, that perhaps this was one of the early examples wherethe requirement of such conservation principles, indicative of symmetries of the fun-damental processes of physics, were used to postulate a new particle. In this case thesymmetry was the fact that the laws of physics are unchanged if we shift the originof our coordinate system by a constant amount, rotate the coordinate axes and/or goto a frame of coordinates in a state of uniform relative motion. Note that this is yetanother way in which some of the fundamental constituents of matter announced theirpresence. We will have some more examples of the same later.
4. The tale of Nucleons
But frankly this was just the tip of an iceberg. The heady developments of the earlypart of the 20 th century on the theoretical fronts, some of which were arrived at inan attempt to describe mathematically how the nuclei and the e ′ s are held together inatoms and some which sprang from the genius of one mind (that of Albert Einstein),changed the way we thought about mechanics, space and time. Till then our ideasabout these were solidly grounded in the laws laid down by Newton and Galileo. AheHeartofMatter 11quantum world in which time was no longer absolute was born. This is not the place tosketch out the developments of these desperately exciting times for physics which sawthe emergence of Quantum Mechanics and the Theory of Relativity. We will, however,make use of one very important concept of these times, that of the wave-particle dualityto take further this story of the hunt for the constituents of matter.The question of whether a beam of light was made of corpuscles as Newton calledthem or whether it was a wave, was a topic of very hot discussions and dissensions onthe two sides of the English Channel. The issue was decided in favor of Huygens andthe wave description of light by the late 19 th century. However, Einstein’s explanationof the Photo-Electric effect proved conclusively that light can be seen as made up ofquanta of energies. Thus by the early twentieth century the dual nature of light: as awave as well as a particle, was an established fact. De Broglie hypothesized extensionof this dual existence to all the other particles such as the electron, postulating thatassociated with a particle of momentum p , there is a characteristic wavelength λ = h πp , (1)where h is Planck’s constant given by . × − joule-sec. At distance scalesmuch larger than λ we see particle behavior and at distance scales comparable orsmaller than λ the experiments will notice evidence of wave like behavior. This wasindeed verified in a famous experiment by J.J. Thompson’s son G. J. Thompson.The above has a very interesting implication for the search of what lies at the heartof matter. I mentioned two ways of doing this search, that have been used historically.The first being the use of patterns/regularities to learn about possible constituents andsecond being scattering experiments of Rutherford. However, so far I made no mentionof the much more rudimentary ways such as1) breaking the system into its constituents by supplying enough energy: electricdissociation of molecules, photoelectric effect being a few examples2) using microscopes with better and better resolving power. This is what was donewith biological systems helping us to arrive at the cellular theory of organisms.In fact, the experiments of the type performed by Rutherford are but a logicalextension of this “visual” process mentioned in (2) above, just with a “microscope” ofhigher resolving power. To understand this let us recall that if we want to decrease theminimum distance between two points up to which they can be told apart, we need touse light of shorter and shorter wavelength. The phenomenon of diffraction, or bendingof light around obstacles, is used to measure shorter and shorter distance scales and thelimiting value is then the wavelength of the radiation used. The wavelength of visiblelight is several thousand Angstroms (one Angstrom is 100 million th of a cm.). Using X –rays, which have a wavelength of a few Angstroms, we can measure distance scalesof the order of a few Angstroms such as distance between atoms in a molecule etc.Note however, that this “seeing” is no longer strictly visual. The above wave-particleduality means that we can probe shorter and shorter wavelengths by replacing lightwith beams of accelerated particles. The higher the energy (and hence the momentum)2 FlavorsofResearchinPhysicsthe shorter is the distance which we can probe. This thus is the genesis of electronmicroscopy.Again, let me make a small digression and once again jump ahead a few decades.Electron Microscopy has proved a very useful tool indeed once we learned how toaccelerate electrons to high energies. It has now been more than 50 years since the firstimage of an Atom that was taken with a Field Ion Microscope. In 1956, E. Mueller(an Indian physicist Dr. Bahadur was crucially involved in this exercise) presented theimage of a tungsten tip showing individual atoms. This is shown in the Fig. 3. SureFigure 3 . Image of an atom. enough, by 1956 we knew atoms existed, we knew what their sizes were and so on,without ever having “sighted” the atom itself. Still this achievement was a milestonein itself as it provided the direct image of the atom and also because this marks the endof “visual” sighting of constituents of matter.Let us get back to Rutherford and his scattering experiment. In his experiment,he was using a beam of α particles which were being emitted by the radioactive nu-clei. These had revealed that the atom was not “indivisible” and consisted of a “point”nucleus and electrons around it. However, further studies in Nuclear Physics had re-vealed that the nuclei themselves must be made up of protons and neutrons, boundtogether by an attractive force. If they were indeed made up of constituents why is itthat Rutherford’s experiment “saw” them as a “point”? We can answer this question bylooking at the energies of the α particles used and their “resolving” power. These hadenergies of the order of MeV and hence the corresponding wavelength given by Eq. 1was about one tenth of a billionth of a cm. or about a 100 th of an Angstrom. Thus itcould resolve an object as not being a point, only if it was bigger than this distance. SoRutherford’s experiment simply meant that the nuclei, if they had a size, were smallerthan this. On the other hand, since this wavelength is much smaller than an Angstrom,heHeartofMatter 13which is roughly the size of (say) Hydrogen atom, this beam was capable of revealingthat the atom was not a point particle, but had a distribution where the positive chargewas concentrated in a very small region of the atom.You see that we can thus use the high energy particle beams as a meter stick tomeasure the size of an object, by scattering the beam off the object. The De-Brogliewavelength defined by Eq. 1 gives the limit of the length scale which such scatteringcan probe. These high energy scattering experiments thus are, but an extension of theprocess of trying to put an object under microscope to determine its structure and see-ing its constituents. Of course, the information is indirect and it is necessary to knowthe laws that govern the interaction between the “probe” and the “target” to be ableto convert the observed results into an information on the “size” of the object. Thusa knowledge of the laws of dynamics at level “n” is necessary to probe the structureat level “n + 1”. This point can not be overemphasized. Since one needs beams ofhigher and higher energies to probe smaller and smaller distance scales for existenceof structure and/or constituents, the subject of ‘elementary particle physics’ is some-times also called the subject of ‘high energy physics’. The tools we use to measuresizes of objects changes with the size that they have! This fact is illustrated in Fig. 4.Figure 4 . Tools for ‘seeing’ the objects and measuring their sizes.Unveiling the finite size of the nucleus
The discussion so far about the processes which have unveiled the structure of mattertells us that this search proceeds essentially through three steps:1. Seek the regularities/patterns in properties such as masses, spins etc. Very oftenthese reflect possible existence of a more basic fundamental units which makesthe whole: an example would be atomic theory.4 FlavorsofResearchinPhysics2. Measure the “size” of the constituents, which at the level of atomic distances andsmaller, is simply doing scattering experiments using beams of higher energyparticles to get probes of shorter and shorter wavelengths: example at the atomiclevel of this is Rutherford’s experiment3. A parallel and necessary step is also the development of a theory of the dy-namics that holds these units together. See if the observed properties of thecomposites agree with the predictions of the theory: again at the atomic levelthe constituents revealed are nuclei and electrons, the subject dealing with thedynamics is Atomic Physics.Discussions of the earlier sections show that at the next level, in case of nuclei, thefirst step of indirectly inferring existence of the constituents of nuclei, had happenedin the study of Nuclear Physics. The next question was two fold: can one measurethe size of the nucleus and can then one “see” the constituents in the scattering exper-iments. Hence one had to devise an analog of Rutherford’s scattering experiment, butone capable of “resolving” the nucleus beyond the limit of a hundredth of an Angstromthat Rutherford’s experiments could put on its size. Clearly Rutherford knew the im-portance of higher energies already when he said ’
It has been long been my ambitionto have available a copious supply of atoms and electrons which will have energiestranscending those of the α, β particles. ’ This became possible with the advent ofparticle accelerators. Fig. 5 shows actually how such scattering experiments were per-Figure 5 . Nuclear/proton analog of Rutherford experiment formed at the Stanford Linear Accelerator Centre which began by probing how big thenuclei were. In the now famous experiments by Hofstadter, electrons accelerated toenergies of – million electron volts were scattered from nuclear targets. Notethe similarity of the beam-target-detector arrangement with the Rutherford case. Thewavelength of these electrons, λ e , was about a 1000-10,000 times smaller than thatof the α particles used by Rutherford. Again, all that the experimentalists did was tocount the number of electrons scattered at an angle θ as shown in the figure and com-pared it with the number expected for a point-like nucleus. With the arguments madeabove, it is clear that this ratio will be close to as long as λ e ≫ R nucleus and willheHeartofMatter 15start differing from as soon as the λ e ∼ R nucleus . Here the nucleus is assumed tobe a sphere with radius R nucleus . Indeed, it is possible to study this ratio as a func-tion of scattering angle θ and determine how nuclear charge is distributed in space.These experiments indicated that nuclei were about 10,000 – 100,000 times smallerthan atoms. Mind you these experiments only proved that the nucleus has an extensionin space, but could tell nothing whether it had any constituents. Of course since theexistence of neutrons/protons, called collectively a nucleon, was already inferred fromstudies in Nuclear Physics, the fact that the p is not point-like did not come as a bigsurprise. The results of the earlier scattering experiments which had not seen any in-dication of the presence of nucleons inside the nucleus, could be interpreted by sayingthat wavelength λ e was still much bigger than the separation between the nucleonswithin the nucleus and hence it could not be resolved. So at the end of this round ofexperiments, in 1960 or thereabouts (Hofstadter was awarded Nobel Prize in Physicsfor these experiments in 1961),1 The fundamental constituents of matter would have been n, p, γ, e and theneutrino- ν whose existence was postulated by Pauli and confirmed in experi-ments in Nuclear Physics as well as their anti-particles ,2 The elemental block of the earlier atomic level, the nuclei, were shown to havefinite size and the sizes were measured by the scattering experiments,3 Nuclear Physics as a discipline had been able to give a good account of all theobserved nuclear properties by looking at nuclei as composites of the nucleons.The dynamics of interaction between the nucleons was developed and studiedby Nuclear Physicists.The similarity of this description with the corresponding one presented above forthe atomic case can hardly be missed.
5. The last layer?
However, for various reasons none of the physicists around that time would haveagreed with the above list of particles as the list of the fundamental constituents ofmatter. The first and the foremost reason for this, was the observation of a very largenumber of particles similar to n, p , but somewhat heavier than them in the CosmicRay experiments. These experiments studied interactions of very high energy Cosmicradiation impinging on the atmosphere, producing large number of particles. The ob-servation created a suspicion that may be p, n are not fundamental after all. Anotherimportant indication that p/n are not point-like and are a charge/mass distribution,came from the observation that the neutral neutron had a magnetic moment. Accord-ing to Dirac’s equation, mentioned already in the context of anti-particle prediction, theneutral n should have had no magnetic moment at all. Even more interesting was the Dirac’s demand that the laws of Quantum Mechanics should look the same for all observers who are instate of uniform relative motion had predicted existence of an anti-particle for every particle, which wouldhave the same mass, spin but opposite charge. The discovery of an anti-proton and existence of positronshad confirmed this prediction. th Century who used Dalton’s atoms as a mathematicalentity without believing in them.According to the quark hypothesis, all the particles which experience strong inter-actions are made up of quarks: a proton is a bound state of two “ u -quarks” and one“ d -quark” and so on. The names u and d stand for “up” and “down”, but just likecolour, these are abstract concepts and could easily be given any other names. Indeed,the attribute of being “up” or “down” is called “flavour”.To account for the particles then known, one required only three different flavoursof quarks: u(p), d(own) and s(trange). A number of different high energy experimentsgave results consistent with the quark hypothesis. With the advent of higher energiesand the discovery of new particles, these three flavours proved insufficient for the quarkhypothesis to work. So three more flavours were added: c(harm), b(eauty) and t(op).This (almost) accounts for the quarks mentioned in Table 1.Figure 6 . How quarks and anti quarks of different types make up the strongly interact-ing particles.
Today we believe that there exist precisely these six flavours of quarks. Theirpresence is strongly, though indirectly, confirmed by experiments, and is also requiredfor consistency of the corresponding theory, the Standard Model. Fig. 6 shows thecomposition of some of the known strongly interacting particles in terms of differentheHeartofMatter 17quarks and (anti)quarks.In 1965, soon after the original quark postulate, Greenberg, Han and Nambu pro-posed that each flavour of quark comes in three different species, differing only in anadditional attribute which they called “colour”. They were led to this hypothesis byformal considerations. Pauli’s Exclusion Principle tells us that the wave function of acollection of identical fermions must be antisymmetric under the exchange of any two.Alternatively you may know this as a statement that no electrons with the same energyand spin can be in the same position. However, the existence of a particle called ∆ ++ posed a paradox for this principle. The paradox is straightforward to explain usingideas of quantum mechanics.The electric charge of ∆ ++ is 2 in units of electron charge, and its spin is inunits of ~ . In terms of the quark model, ∆ ++ must consist of three u quarks. Forit to have a spin , the spins of the three identical quarks (each of spin ) have tobe all aligned. Thus all the quarks would be able to occupy the same position withthe same spin orientation. More technically, this says that the net wave function for ∆ ++ is symmetric under the exchange of any two u quarks. That would contradictthe exclusion principle, a fundamental tenet of quantum mechanics. Thus the quarkmodel, as understood at the time, had to be wrong, or incomplete.To resolve the paradox, Greenberg, Han and Nambu were led to introduce an addi-tional attribute, which they called “colour”, taking three different values (for examplered, yellow and blue), solely so that the wave function could be made antisymmetricunder an exchange of colour labels. In particular, the ∆ ++ would contain not threeidentical u quarks, but rather, one u quark of each colour. Then it would not be aproblem to make the wave function antisymmetric and save the exclusion principle.A large number of measurements, such as the rate of decay of a neutral pion intoa pair of photons, gave evidence that the number of quark species is really three timeswhat was previously thought, consistent with the colour hypothesis. However, at thistime there was no evidence which would compel one to accept quarks, “colourful” orotherwise, as genuine physical entities. All attempts to observe spin particles withfractional electromagnetic charges had failed. Thus, for a large class of physicists, thequark hypothesis was just a kind of “mathematics” that explained very neatly a wholelot of observed properties but did not require quarks to actually exist.In the meanwhile, indirect evidence for both the quark hypothesis as well as thecolour hypothesis was mounting, in different experiments such as muon-antimuon pairproduction in pion-proton collisions, or the production of strongly interacting particlesin electron-positron collisions.One of the obvious things to do, as per the list given in the earlier section, was thento perform scattering experiments to see if indeed p has a spatial extension to beginwith. One could think later of addressing the question whether the scattering couldreveal existence of these funny objects postulated from the requirements of patterns.As mentioned above, results of the various high energy experiments had agreed withthe prediction of the “quark” model any way. So in that sense the third item on the “todo” list of the earlier section had been taken care of.Similar to the experiments with the Nuclear targets, Hofstadter actually confirmedthat indeed the p/n were charge distributions and the radius of this distribution was8 FlavorsofResearchinPhysics100,000 times smaller than one Angstrom : it was ∼ Fermi. One thing to note hereis that when we consider the scattering process, e ( E e ) + p → e ( E ′ e ) + p (2) e scattered at a given angle θ for a given energy of the incoming electron E e will haveto have a given value of energy E ′ e , (say E ′ ). The real surprise came as the energy ofthe electron was further increased to 10,000 – 20,000 million electron volts, reducingthereby the distance it could probe hundredfold compared to the size of the p/n . Thescattered electrons at a given angle came with all possible energies, indicating therebythat may be the p had something inside it. In principle using the angle at which theelectron travels and its energy, one can back calculate the momentum carried by what-ever might be making up the proton. Thus the observed distribution in the energiesof the scattered electron at a given angle then can thus be transformed into a distribu-tion in momenta carried by these ‘constituents’. The most interesting observation wasthat this distribution was the same when obtained using electrons of different incidentenergies and scattered at different angles. Thus indeed, the assumptions in the backcalculations were correct and the electrons were bouncing off something else inside theproton. Thus not only we knew that the proton had some more things inside but we canalso map the distribution of the momentum of the proton that these constituents car-ried. The results indicated that by now the wavelength of the probe was small enoughto feel the effect of the individual scatterers inside the proton, separately.Needless to say I have oversimplified this second coming of quarks. It sufficesto say that the measurements of the above mentioned distribution in the energy ofthe scattered electrons, for a few different values of the scattering angles, allowed thephysicists to even get information about the possible spin as well as the electric chargeof these elementary constituents. It was indeed gratifying to see that these constituentsseemed to have all the properties (along with “colour”) which they were required tohave in the Quark Model. Thus one could identify these observed constituents of the p with the quarks postulated by Gell-Mann and Zweig.As a matter of fact, results obtained by scattering higher and higher energy e off theprotons, indicated that the proton contains some other point like constituents to whichthe electron beam is blind, as they do not carry any electromagnetic charge. This wasthe first experimental glimpse of gluons. Actually these scattering experiments, theso called Deep Inelastic Scattering experiments, yielded very useful pointers whichallowed physicists to formulate the right mathematical theory describing interactionsof these quarks with each other and gluons. The Nobel Prize for Physics for the year2004 was actually awarded for that theory called Quantum Chromo Dynamics (QCD).But that can be a topic of a separate article. The one feature of this theory that hasimplications for the present discussion is that, with increasing energy the number ofconstituents goes on increasing, since more and more quarks and gluons are createdinside the proton, when one tries to probe it with higher and higher energy. That is,the increasing energies do not reveal any new constituents but reveal only thisincreasing number of quarks and gluons inside. This is in fact a firm predictionof QCD.
In the simplified picture that I mentioned above, the peak in the scatteredenergy electron distribution will keep on shifting to values indicating an increasingnumber of constituents in the proton. Indeed such a rise was observed, precisely in theheHeartofMatter 19manner predicted by QCD, thus proving that electrons and quarks are indeed point likeand QCD the right framework to describe the dynamics of interactions among quarksand gluons!A reasonable question to ask is whether the existence of constituents inside a nu-cleus could also have been inferred from similar experiments with nuclear targets, incase we had not known about them before. The answer is yes. Such experiments wereindeed performed and the results did indicate existence of point-like scattering centersinside the nucleus just as in the case of the proton and even the number of nucleonscould be deduced. The only thing is that the distance scale and hence the energies ofincoming e beams for which it was observed are scaled appropriately.At present experiments have been performed, not just with e beams, but also µ beams and ν beams, with energies about 10-50 times higher than the above. In anexperiment in Germany, 30,000 MeV electrons are collided against protons which havean energy of 920,000 MeV. This corresponds to using an electron beam with an energyof 100 Billion (1 Billion is one thousand million) electron volts in the simple scatteringexperiment we have talked about. None of these experiments revealed any deviationsfrom the expectations of the theory of point-like quarks and gluons, i.e., the abovementioned QCD. Thus there is no indication of any substructure of a quark up to a1000 th Fermi. Thus we believe we have reached the end of the road in substructures.So are we saying this simply because we don’t have high enough energy probes?Indeed not. This is where the part about the Particle Physics, the dynamics, which Ihave left out comes into play with full strength. Recall that this scattering (or equiva-lently “seeing”) of the constituents was only one way in which we hunted for what liesat the heart of the matter. At present every single piece of experimental observationagrees to a very high accuracy, better than to one part in a 100 Millions at times, withthe predictions of a theory which in these calculations, treats these quarks and leptonsas point-like up to energies ∼ billion billion eV. Thus we have an “indirect” butvery strong proof that the quarks and the leptons are indeed point-like and have nofurther substructure.It should be added that I have sketched the path how we have arrived at the idea ofquarks, in great detail and not said much about leptons. In fact they were not huntedfor, but just came uninvited and made their appearance in the cosmic ray as well as inthe high energy experiments. Their properties never gave any indication of substruc-ture, the results of scattering reactions in which only leptons were involved alwaysagreed completely with predictions made assuming that they were point-like. While,theory can not tell how many different repetitions of these pairs of quarks and leptonsshould be there, what the theory IS able to tell is that these should be equal in number.Indeed, this is satisfied by the current list of the fundamental constituents of matter. Ihave also not discussed how the force carriers were “discovered”. But that requires amuch more detailed discussion of dynamics of the particle interactions, which we haveleft out.Thus the discussion now clearly shows that the notion of what is elementary isreally decided by the resolving power of our probes, hence the distance scales we areinterested in. All the discussion in these earlier sections can be summarised as shownin Fig. 7. The figure shows the constituents of matter as we see them at differentdistance (and hence energy) scales.0 FlavorsofResearchinPhysics Solid, Liquid,GasesMoleculesAtomsNucleus + e - NucleonsBound state ofQuarksAlmost freeQuarksQuarks gluons??
ThermalEnergy>10 -9 m 10-100eV>10 -10 m= 1A -14 m= 10fm 1 GeV>10 -15 m= 1fm 20 GeV>10 -16 m quarks+ gluons HH O e - e - nucleusneutronsprotonsquarks EnergySize
Figure 7 . Constituents of matter at different distance and energy scales
Recall here also Fig. 4. This figure tells us that high energy accelerators are ourmicroscopes as we probe distance scales of atoms/nuclei and further. Thus this journeyinto the ’Heart of Matter’ is accompanied by the development of accelerators. Figure 8shows the way the energy frontier has moved through the decades and the distancescale of the new physics that this higher energy has revealed. Through the early partof this journey the higher and higher energy just revealed constituents at smaller andsmaller distance scales. After the discovery of the quarks lying at the heart of protonsand neutrons, the later increase in energy has brought about production of the forcecarriers and helped develop/test the theory which can describe the interactions amongthe fundamental constituents. The Large Hadron Collider (LHC) that has just goneinto operation at CERN in March 2010 and the International Linear Collider (ILC)or CLIC that are under planning are the spearheads of this energy frontier. We willdiscuss these next and present what we expect them to achieve.heHeartofMatter 21Figure 8 . How the energy frontier has moved in the decades.
6. What Next?
Following all the discussions in the earlier sections, one might be tempted to ask, nowthat particle physicists seem to believe that they have arrived at a description of theultimate constituents of matter and the interactions among them, does it mean that thisis the end of the road for the subject? Not at all. There are various reasons which tellus that we still have quite a way to go.1 Firstly, the Higgs Boson which is predicted by these theories has to be found andshown to have exactly the properties that the theorists predict it must have. Thisis almost like checking that the constituents of the p as seen in the scatteringexperiments were indeed the quarks of the Quark Model.2 Even if these experiments were to find this Higgs Boson there are still a lot ofissues that need to be addressed and handled. Even in the case of the StandardModel itself, there are theoretical challenges such as understanding how massless quarks, anti-quarks and gluons make bound states that are massive, why freequarks never appear in nature etc. There are certain unsatisfactory theoreticalissues about the high energy behavior of the dynamical theories involving HiggsBosons. Efforts to cure these problems have led to some popular extensionsbeyond the SM. These predict existence of particles beyond what we have seen.3 The ν ’s have zero mass in the SM. However, the recent Nobel Prize winningexperiments which showed that ν of one type can change into a ν of anothertype, have now firmly established that these have a non-zero mass. Thus thereare indications that the dynamics has something more than the SM.2 FlavorsofResearchinPhysicsFigure 9 . The three frontiers of progress in Particle Physics ν s is indeed an extremely strong indicator for the existence of Physicsbeyond the SM. Studies of the ν sector may therefore provide us with theoretical andexperimental clues to the Physics beyond the SM.It is obvious from the above discussions that the future of particle physics rests onexplorations on different fronts: a) theoretical investigations to address various issuesmentioned above and b) different experiments where these can be tested viz. Theseare i)experiments at high energy accelerators ii)experiments with high energy neutri-nos and iii)the cosmological connections. In fact this state of affairs has been depictedvery succinctly in Fig. 9, taken from the report of the High Energy Physics and Astro-physics Panel (HEPAP), of the National Academy of Sciences, USA. The confluenceof the results obtained at different frontiers will lead to fundamental progress in ourknowledge of the Universe. Indian Scientists are in fact involved in activities on all thefronts.heHeartofMatter 23On the energy frontier there is the Large Hadron Collider (LHC) which has goneinto action in March 2010, albeit with lower energy than was initially foreseen; perhapsthese teething problems remind us of the complexity of the machine. The LHC is aproton-proton collider, where the two beams of protons circulate in opposite directionsin two beam pipes which run inside a tunnel with periphery 27 km long. These twopipes intersect at a few chosen points so that the beams can collide. The beam buncheshave to maintain their micrometer size diameter while traveling the distance of 27 km,which they traverse thousands of time. To achieve collisions of the required number ofhigh energy protons, the beams have to be steered by superconducting magnets whichare kept at a temperature of . ◦ K. Building such complex piece of machinery andmaking it work has been a matter of great joy and pride to the international high en-ergy physics community. We can be very proud that Indian engineers and acceleratorphysicists have been involved in building some part of this machine. The so called Pre-cision Magnet Positioning Systems (PMPS) were manufactured in India. Not just this,Indian physicists have also been involved in building the mammoth detectors whichare capable of making very precise measurements (such as determining the positionof a particle within a micrometer!) and thus can probe the mysteries of the laws ofnature at their deepest level. India participates in the general purpose pp detector CMSas well as the ALICE detector which will study the heavy ion collisions. Figs. 10Figure 10 . The LHC tunnel with its accelerating magnets. and 11, show the LHC tunnel with the accelerating magnets and the cut out view ofthe CMS (Compact Muon Solenoid) detector to which India has contributed. Thus theIndian scientific community is a part of this adventure. Indian theorists are involved inthe development of new and/or more refined theories of the Physics beyond the SM aswell. Indian physicists will also be involved in interpreting what the results coming outof LHC would mean for the SM and for the various theoretical ideas which go beyondthe SM.4 FlavorsofResearchinPhysicsFigure 11 . The CMS detector in which India participates.
The international high energy physics community is convinced that it is neces-sary to have an e + e − collider, which should go in operation after LHC has run fora few years. This is truly an international effort in that even the optimal parametersfor such a collider were decided by the entire international community. The same pat-tern continued in deciding the optimal accelerator technology and now finally even thedesign of this accelerator is being done by an international team. Indian groups arepart of this global exercise as well and there exists an Indian Linear Collider Work-ing Group (ILCWG). A schematic drawing of the radio frequency cavities that wouldhave to be built, in order to construct the ILC is shown in Fig. 12 In fact the futureconsists not just of these collider experiments but also the gigantic Neutrino Experi-ments and India is part of that as well. Indian High Energy Physicists are planning tobuild the Indian (International) Neutrino Observatory (INO). A prototype of the ironcalorimeter they plan to use is shown in Fig. 13. You can get more information on theILC, INO etc. from the websites: and http://imsc.res.in/ ino/ .Actually, there is one more important laboratory where particle physicists can ap-ply/test their theories and that is the Cosmos ! Cosmological observations now havereached a degree of precision rivaling that of the HEP measurements. Measurementsby the Hubble telescope, the Sloan Digital Sky Survey, the Wilkinson MicrowaveAnisotropy Probe etc., have now essentially tested the Standard Model of Big BangCosmology to a great degree and gone beyond it. Very high temperatures are supposedto have existed in the early Universe and at those temperatures all the fundamentalparticles would have existed. Their properties affect the evolution of the Universe inits first three minutes. The number of mass less neutrino species, for example, affectswhat the value of the abundance of different type of elements in the Universe shouldbe. Thus a knowledge of the spectrum of fundamental particles and their interactionsis indispensable in the study of Cosmology. In the reverse, some of the ideas of physicsheHeartofMatter 25Figure 12 . Schematic drawing of a Radio Frequency cavity for the future InternationalLinear Collider.