Unification of Nature's Fundamental Forces

Home , Force carrier, George Zweig, Unification (physics)

Unification of Nature’s Geoffrey B. West Fredrick M. Cooper Fundamental Forces Emil Mottola a continuing search Michael P. Mattis

it was explicitly recognized at the time that basic research had an important and seminal role to play even in the highly programmatic en- vironment of the Manhattan Project. Not surprisingly this mode of opera- tion evolved into the remarkable and unique admixture of pure, applied, programmatic, and technological research that is the hallmark of the present Laboratory structure. No- where in the world today can one find under one roof such diversity of talent dealing with such a broad range of scientific and technological challenges—from questions concerning the evolution of the universe and the nature of elementary particles to the structure of new materials, the design and control of weapons, the mysteries of the gene, and the nature of AIDS! Many of the original scientists would have, in today’s parlance, identified themselves as nuclear or particle physicists. They explored the most basic laws of physics and continued the search for and understanding of the “fundamental building blocks of nature’’ and the princi- t is a well-known, and much- grappled with deep questions con- ples that govern their interactions. overworked, adage that the group cerning the consequences of quan- It is therefore fitting that this area of Iof scientists brought to Los tum mechanics, the structure of the science has remained a highly visi- Alamos to work on the Manhattan atom and its nucleus, and the devel- ble and active component of the Project constituted the greatest as- opment of quantum electrodynamics basic research activity at Los Alam- semblage of scientific talent ever (QED, the relativistic quantum field os. Furthermore, in keeping with put together. Many of those scien- theory describing the interaction of the historical development of the tists had made (or in some cases charged particles with radiation). Laboratory, there continues to be a were destined to make) highly sig- Although those questions had to be vigorous and productive interplay nificant contributions to the devel- put on the back burner for the dura- with other more applied and pro- opment of our understanding of the tion of the project, the pot, so to grammatic parts of the Laboratory basic laws of physics. They had speak, continued to simmer. Indeed, (see “Testing the Standard Model of

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Particle Interactions using State-of- The initial major breakthrough the quantum fields describing all el- the-Art Computers”). occurred around 1970 when a theory ementary particles. This article will give a brief was proposed that unified the weak The unification of electromagnet- overview of some of the exciting de- force with the electromagnetc force ism with the weak interactions was velopments in this area of science in a mathematically consistent fash- accomplished in the context of that have taken place in recent years ion. This unification came almost a quantum field theory by extending and in which scientists at Los Alam- century after Maxwell had shown the principle of gauge symmetry and os have played significant roles. that electric and magnetic phenome- the idea of a force-carrier to the From the end of the Manhattan na could themselves be unified in a case where the force-carrier can it- Project until approximately 1970, single force carried by the electro- self carry electric charge and there- the general taxonomy and phenome- magnetic field. In the modern lan- fore interact with itself. (In QED nology of the elementary particles guage of QED, all electromagnetic the photon is neutral and therefore was intensely studied. When the phenomena can be understood in cannot interact with itself.) A various mesons (such as the pions terms of a force-carrier that is ex- force-carrier of the weak interac- and the kaons) and baryons (such as changed between electrically tions must have electric charge be- the proton, neutron, §, ß, and •) charged particles such as electrons. cause some weak interactions cause were classified, it was discovered This force-carrier, called the photon, the charge of a particle to change. that there were four apparently quite is the quantum of the electromagnet- For example, the neutron, which is distinct ways in which they interact- ic field and can be thought of as a neutral, decays through the weak in- ed among themselves: (1) gravita- massless elementary particle with no teractions to a proton, which has tionally, (2) electromagnetically, (3) electric charge and spin angular mo- one unit of positive charge. Fur- weakly and (4) strongly. The first mentum equal to one (in units of -hÅ). ther, the force-carrier of the weak two interactions, or forces, are the The masslessness of the photon is a interaction must be massive rather 2 most familiar since they are long- consequence of the so-called gaugee4¼ sin thanw=® ¼massless10¡ 170 because the range of range and so manifest themselves (or phase) symmetry of the electro- the weak force is so short, less than macroscopically even over astro- magnetic field and gives rise to the 10−14 centimeter. (This follows nomical distances. The second two long-range nature of the electrostatic from the original observation of have very short ranges (less than 1 force between charged particles. Yukawa that the range of a force fermi, or 10−13 centimeter) and so Furthermore, it guarantees that elec- varies inversely with the mass of are only important at the nuclear and tric charge is conserved. Technical- the force-carrier.) subnuclear level. The weak interac- ly, the gauge symmetry responsible The remarkable accomplishment tion is the one responsible for beta for the masslessness of the photon is of Glashow, Weinberg and Salam decay (such as the decay of the neu- a reflection of the invariance of was to fashion a well-defined quan- tron to a proton, an electron, and a Maxwell’s equations to arbitrary tum field theory like QED for the neutrino), and the strong interaction phase changes in the quantum fields weak interaction. It is based on an is the one responsible for the bind- associated with the electron and the extended notion of gauge symmetry ing of protons and neutrons to form photon. (Specifically, an arbitrary that Yang and Mills had invented the nuclei of atoms. phase change of the electron field earlier in an attempt to describe the One of the great intellectual can be compensated for by a redefi- strong interactions, but, in addition, achievements of the twentieth century nition of the photon field, which is ideally suited for describing the has been the realization that these leaves the form and structure of the charge-changing and charge-con- four wildly different “fundamental’’ equations of motion for electromag- serving interactions of the weak forces may, in fact, be viewed as netic interactions unchanged.) Be- force. To obtain massive force-car- manifestations of a single unified cause of its deep and seminal role, riers, called the W+, W−, and Z0, the force. Although this paradigm was this local phase, or gauge, invari- gauge (or phase) symmetry of the originally the dream of Einstein, not ance of the electromagnetic fields is quantum fields had to be dynamical- until the 1970s was any serious now viewed as a fundamental princi- ly broken in a rather subtle way progress made toward developing the ple, or constraint, used to derive the analogous to the way the sponta- theoretical framework for unification. form of the basic interactions among neous symmetry breaking in a super-

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conductor produces the Meissner ef- plest version small fluctuations of Baryon-Number fect. This dynamical symmetry the Higgs alignment field manifest Nonconservation and the breaking is referred to as the Higgs themselves as an elementary mas- Stability of Matter mechanism. It was designed to yield sive particle, dubbed the Higgs par- massive mediators of the weak force ticle. The mass of the Higgs parti- One of the most intriguing possi- while preserving the masslessness of cle is not certainly known, but it bilities for new physics at the SSC the photon. As mentioned above, must be less than approximately and an area in which Los Alamos the masslessness of the photon is the 1 TeV = 1012 eV. has been heavily involved is the origin of both the long-range nature The existence of the Higgs parti- possibility of experimentally observ- of the electrostatic force and the cle and the origin of electroweak ing the violation of baryon-number conservation of electric charge, so symmetry breaking are therefore in- (B) conservation. Baryon number these properties of electromagnetism timately related to the ancient and appears to be an exactly conserved are sacrosanct and had to be main- vexing question of the origin of quantum number in nature. Its con- tained in any attempt at unifying mass itself. Indeed the hope of veri- servation, for example, prevents a electromagnetic and weak forces fying this line of thinking has been proton (B = 1) from decaying into a into a unified force law. These con- one of the main justifications for state with B = 0 such as an electron straints turn out to be so tight that constructing the $10 billion Super- and a pion or an electron and a pho- they lead to precise predictions for conducting Super Collider (SSC) ton, even though these decays are the masses of the W+, W−, and Z0, just outside of Dallas. The SSC will energetically very favorable. In- which were brilliantly confirmed by collide two proton beams, each com- deed, it is the conservation of bary- experiment. The prediction and dis- posed of protons accelerated to ener- on number that keeps ordinary mat- covery of the mediators of the weak gies of 20 TeV. Compelling argu- ter stable against radioactive decay force can be likened in their profun- ments suggest the collision energies (“diamonds are forever’’). dity to the prediction and discovery are ample to either create and dis- Notwithstanding a complete lack of electromagnetic waves that fol- cover the elusive Higgs particle or, of experimental evidence for the vio- lowed from Maxwell’s formulation even if it doesn’t exist, to unravel lation of baryon-number conserva- of electromagnetism. the deep mystery as to the “origin of tion, the absolute validity of this law The Higgs mechanism of dynami- mass.” has always been viewed with some cal symmetry breaking can be Scientists at Los Alamos have suspicion by theorists. Indeed, it has thought of as a spontaneous align- been actively involved in several as- always appeared as a somewhat ad ment of the vacuum (the state of pects of SSC physics. These have hoc phenomenological law with no lowest energy). The alignment is included theoretical studies concern- fundamental basis for its understand- roughly analogous to the sponta- ing the nature and phenomenological ing. There are two basic reasons for neous magnetization encountered in implications of the Higgs mecha- this skepticism. (1) Unlike the con- ferromagnetic materials such as or- nism as well as vigorous involve- servation of electric charge (which is dinary bar magnets. As particles ment in designing the huge (and believed to be exactly conserved) such as the W+, W−, and Z0 propa- very expensive) detectors needed to there is no known long-range force gate through this aligned vacuum, investigate these questions experi- between baryons or local gauge sym- they become massive as a result of mentally. Indeed the Los Alamos metries associated with baryon num- their coherent interaction with the contribution to the SSC nicely ex- ber. Thus there is no fundamental Higgs field (analogous to a magnetic emplifies the breadth of the Labora- reason for the exact conservation of field). It is believed at present that tory’s unique and special character- baryon number; if exact, it would the dynamical interaction of parti- istics: fundamental theoretical stud- have to be viewed as an “accident’’ cles with the vacuum is the origin of ies, detailed physics involvement from our present viewpoint. (2) The all the mass in the universe (includ- with the design of the detectors, and second reason for skepticism is the ing us!). The precise nature of the superb engineering capability for its well-known and remarkable fact that Higgs mechanism is not, however, actual construction. This year over the universe appears to be over- well understood and remains the $7 million of SSC engineering funds whelmingly dominated by matter, subject of intense study. In its sim- will be spent at Los Alamos. which has positive baryon number,

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West fig1 3/31/93

rather than antimatter, which has Vacuum negative baryon number. This domi- potential ∆ ∆ nance is particularly hard to under- B = Ð1 B = +1 Jumping

stand if baryon number is exactly Energy conserved; in that case one would ~10 TeV have to postulate that this gross Quantum tunneling asymmetry in the universe was put in “by hand’’ as an initial boundary condition at the moment of creation! Figure 1. Structure of the Vacuum for the Electroweak Theory and the Suggestively, the unified electro- Possibility of Baryon-Number Nonconservation weak theory has, as a dynamical This figure illustrates the periodic structure of the vacuum in the electroweak sector of consequence, the breakdown of the standard model. A system usually sits in the minimum of ar well of the vacuum baryon-number conservation. As potential where it is separated from adjacent minima by a very high energy barrier of with the Higgs mechanism and the about 10 TeV. Baryon number is conserved as long as the system remains in a single generation of mass, so here, the ori- well of the potential. In principle, baryon-number conservation can be violated by two gin of the violation has its roots in mechanisms: Either a system acquires enough energy, through heating or high-ener- the terribly complicated vacuum gy collisions, to jump over the barrier, or a system leaks through the barrier by quan- structure of the theory. It turns out tum tunneling. A system will change its baryon number by one unit each time it jumps that the field configuration of the over or tunnels through the barrier. Collision energies at the SSC will be high enough vacuum has a periodic structure in to test the former mechanism of baryon-number violation. which the different minima are separated by a potential barrier whose pen; diamonds are not going to sent mean temperature is only 3 α ≈ height is Mw/ 10 TeV (where Mw spontaneously decay into radiation kelvins), this asymmetry of matter is the mass of the W+,− and α is the any time soon! over antimatter was frozen in since strength of the electromagnetic in- However, the second possibility, tunneling through the potential barri- teraction). Furthermore these differ- namely jumping over the barrier, er is so strongly suppressed. So, we ent minima correspond to different brings up two intriguing alternatives. are led to the satisfying possibility values of baryon number. Normally, One can, in principle, pump suffi- that the unified electroweak theory an isolated system (such as “the uni- cient energy into a system either (1) can potentially explain both the dom- verse’’) sits at the bottom of a spe- by heating it up or (2) by performing inance of matter over anti-matter, cific minimum with a given value of some high-energy collision. In the which requires the violation of bary- B. Now, B can change if either the former case one needs to heat the on-number conservation at an earlier system quantum mechanically tun- system to a temperature greater than epoch and, at the same time, explain nels through the barrier separating it roughly 1015 kelvins (100 million the apparent exact conservation of from its neighboring vacuum (analo- times hotter than the center of the baryon number today (and, conse- gous to the way in which α particles sun!). Although this is clearly not quently, the stability of matter). tunnel through the nuclear potential feasible in the laboratory, the uni- The Elementary Particles and barriers in the radioactive α decay verse itself was at those extreme tem- Field Theory Group at the Laborato- of a nucleus), or the system has suf- peratures during its evolution follow- ry began to study the breakdown of ficient energy (nominally greater ing the big bang. The theory predicts baryon-number conservation in elec- than about 10 TeV) to jump over the that during that period baryon-num- troweak theory at high temperatures barrier (see Figure 1). It turns out ber conservation was significantly vi- in 1987, and soon after, it was real- that the probability for quantum-me- olated by the system’s jumping over ized that the baryon-number-violat- chanical tunneling is ridiculously the 10-TeV potential barrier. It is ing processes described above could small, on the order of 10−170. So therefore conceivable, though not yet be important in the evolution of the even though baryon number can in- proven, that the present overwhelm- early universe. Los Alamos re- deed change in the electroweak the- ing domination of matter over anti- search played a major role in clari- ory, the universe is still waiting for matter was generated at that time. fying the mechanism of the process the first event of this kind to hap- As the universe cooled down (its pre- and convincing a skeptical scientific

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establishment of its importance. such a case a very dramatic effect the “fundamental building blocks” Today we are investigating the very would occur: the copious production and have the curious property of exciting possibility that violations of of W’s and Z’s (and Higgs particles) carrying an electric charge that baryon-number conservation could (see Figure 2). Recall that ordinari- comes in units of e/3, where e is the be directly observed in the very ly the probability of producing just magnitude of the charge carried by high-energy collisions at the SSC. one of these particles is, as with electrons and protons; previously, e This research is being carried out in photons, at best on the order of the was thought to be the smallest unit collaboration with the Institute of electromagnetic interaction strength, of electric charge carried by any Nuclear Research in Moscow. By or less than 1 percent! Unfortunate- particle. Interestingly, Zweig is now combining Los Alamos computer re- ly many subtleties need to be care- a theoretical biophysicist at Los sources and expertise with that of fully considered in these calcula- Alamos doing pioneering work on the Russians, we hope to make reli- tions, and it is not at all clear that the physics of the ear and Gell- able predictions long before the SSC this naive prediction will, in fact, be Mann is spending his sabbatical year turns on in the next century. borne out. As stated above, this at the Laboratory mostly involved in The possibility of performing a subject is under intense investiga- exploring new ideas concerning the controlled experiment at the SSC tion at Los Alamos and elsewhere at concept of complexity. that would detect baryon-number vi- the present time. If the predictions At first the existence of these olation experimentally is truly fan- are true, the results would be quite “quarks’’ was not taken very serious- tastic. Thus far, all experimental at- spectacular. ly, since no one had ever observed a tempts to observe a violation of free quark (or fractional charge) in a baryon-number conservation by de- particle detector of any kind. How- tecting the decay of the proton have Quantum Chromodynamics— ever, the unmistakable presence of failed, implying that the proton life- The Theory of the point scattering centers within pro- time must be greater than approxi- Strong Interactions tons discovered by the now famous mately 1032 years! (Recall that the deep-inelastic-scattering experiments age of the universe is only (sic!) on Even as gauge symmetry was at the Stanford Linear Accelerator the order of 1010 years). Further, being recognized as essential to unifi- Center (SLAC) in the early 1970s, as observing violation of baryon-num- cation of the electromagnetic and well as other indirect checks of the ber conservation in a proton-proton weak forces, it was simultaneously theory, finally led to the acceptance collision at energies below 10 TeV playing a no less central role in un- of quarks as the genuine building (in the center-of-mass system) is im- derstanding the strong force that blocks of all the strongly interacting possible because quantum tunneling binds protons and neutrons together particles (known collectively as through the 10-TeV barrier of the in atomic nuclei. Our present under- hadrons). Thus, in analogy with periodic vacuum is exponentially standing of the strong force is that it QED, quarks play the role of elec- suppressed (just as the universe is too arises from a force-carrier with trons and gluons that of photons. suppressed from doing so at temper- spin angular momentum equal to one The analog to the electric charge— atures below 10 TeV). that is analogous to the photon of the “strong charge,’’ so to speak— Thus baryon number will always QED. The carrier of the strong force was whimsically dubbed color, and be exactly conserved in a high-ener- is called a “gluon.’’ so the theory of the strong interac- gy proton-proton collision below 10 The present theory of the strong tions became known as quantum TeV. Recall, however, that the total interactions was developed during chromodynamics’ (QCD). A crucial- center-of-mass energy available in a the 1970s and is based on the idea ly new feature of QCD is that color collision at the SSC will be 40 TeV, that all baryons and mesons are comes in three varieties and that the which is fortuitously in excess of made of spin-1/2 particles called gluon itself carries this color. In that the barrier height. A naive calcula- quarks that interact via the exchange respect the gluon resembles more the tion indicates that at these energies of gluons. Quarks themselves were Ws and Z of the weak interactions the colliding protons could jump first postulated in the early 1960s than the photon of QED in that it can over the barrier and baryon-number independently by Murray Gell-Mann now self-interact. On the other hand, conservation would be violated. In and George Zweig. They are indeed the gauge symmetry of the vacuum of

148 Los Alamos Science Number 21 1993 Unification of Nature’s Fundamental Forces

West fig2 4/5/93

QCD is not spontaneously broken, so the gluons, at least naively, remain massless like photons. The strength of the gluon self-interaction is, how- 7 antiquarks ever, so large that it is believed to "Fireball" of ~100 forbid color and, in particular, quarks Quark +,− 0 W , Z , and Higgs particles from ever being liberated and ob- . served directly in an experiment. .. Nevertheless, the theory dictates that SSC at high energies quarks and gluons collision inside the proton should behave es- 3 antileptons sentially as if they were free particles. In other words, in a high-ener- Quark gy collision between two protons, the quarks that make up the protons should briefly act as if they were not bound. The precise predictions of QCD were, in fact, brilliantly confirmed by the SLAC experiments for Figure 2. Baryon-Number Violation in a Collision at the SSC which the originators received the The figure illustrates a collision at the SSC that violates baryon-number (B) conserva- Nobel Prize. It should be recognized tion and lepton-number (L) conservation. (Muons, electrons, and neutrinos are lep- that truly free quarks and gluons tons and have L = 1; their antiparticles have L = °1). In this collision B and L each have never been observed directly in change by three units. The prominent signature of such an event would be the pro- any experiment. The situation recalls duction of an extraordinarily large number of Ws, Zs, and Higgs particles. Currently one encountered in an earlier period theorists are sharply divided on whether B-violating events can occur at the SSC at of the history of science. By the end an observable rate. Estimates of the rate published by prominent scientists differ by of the last century, most working as much as a hundred orders of magnitude! For a review of the controversy see the physicists and chemists tacitly as- article by Michael Mattis listed in Further Reading. sumed the existence of atoms in order to interpret a wide variety of coworkers to obtain a “solution’’ to ons can never get completely free of experimental data. But not one of full QCD at an accuracy of about 10 each other, when the temperature those scientists had ever seen a sin- to 20 percent (see “Testing the Stan- gets high enough (around 150 MeV, gle atom, so that as late as 1916 no dard Model Using State-of-the-Art or more than 100,000 times hotter less a figure than Ernst Mach still Supercomputers). These calcula- than the center of the sun), the be- doubted their existence. tions are based on Monte Carlo al- havior of matter changes and a The theoretical aspects of QCD gorithms invented at Los Alamos phase transition takes place (like the have been studied most intensively forty years ago by Nick Metropolis transition from water to steam). In in recent years by the technique of and first used by Stanislaw Ulam this new high-temperature phase “lattice gauge theory” calculations, and Enrico Fermi in now classic quarks and gluons interact more performed on state-of-the-art super- work. weakly than they do in normal nu- computers. Rajan Gupta heads the clear matter, somewhat like electri- Los Alamos effort in this area, cally charged particles in a plasma. which is recognized as one of the Time-dependent Calculations For that reason this new phase of leading groups worldwide. In this of Heavy-Ion Collisions and matter is called the quark-gluon- decade the appearance of the Tera- the Quark-Gluon Plasma plasma phase. flop machine (capable of executing The question naturally arises of 1 trillion basic mathematical opera- Present lattice Monte Carlo simu- how one could detect the presence tions per second) is expected to lations of QCD at finite temperature of such a phase. The requisite high make it possible for Gupta and his predict that although quarks and glu- temperatures and densities occurred

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in the early universe, but it was soon signal that could be produced only and antiquarks as a function of time discovered that even if this phase by such a phase. since quark-antiquark pairs would existed in the early universe, it It will not be easy. One of the fun- be the source of the lepton pairs. would not have affected very much damental and most tantalizing prob- Although one can make estimates of the standard nucleosynthesis lems in this field is, in fact, what con- these pair-production rates based on processes that create helium from stitutes a “smoking gun.” Thus far no equilibrium QCD or perturbation hydrogen because those processes one has devised a clear unambiguous theory, such estimates are neither re- mainly take place later in the evolu- methodology for isolating the signal liable nor accurate enough to serve tion of the big bang. Thus, we for the elusive quark-gluon plasma. as a quantitative test of the presence would not be able to tell from look- Although lattice calculations predict of quark-gluon plasma. ing at the relative abundances of hy- the existence of the quark-gluon This problem presents a new chal- drogen and helium in the present phase, those calculations predict only lenge for quantum field theorists. universe whether or not the quark- static equilibrium properties of the Previously theorists treated the in- gluon plasma ever actually existed. plasma. The situation in a high-ener- teraction region of a collision as a If the universe won’t cooperate gy heavy-ion collision is very far “black box.’’ They would calculate and provide us with a suitable labo- from equilibrium, at least initially, only the final state resulting from a ratory for the quark-gluon plasma, and the quark-gluon plasma is expect- collision based on the initial state then we have to build one ourselves. ed to persist for no more than 10−22 preceding the collision. For exam- About ten years ago, it was realized second before the nuclear fireball ple, they might predict how many that relativistic heavy-ion colli- cools and begins to fragment into or- particles of a certain type and with a sions—those in which each nucleon dinary pions, protons, neutrons, and certain amount of energy should in the heavy-ion projectiles has an other hadrons. Hence any signal of reach a particular detector following energy between 10 and 200 GeV (1 the quark-gluon plasma could easily a collision between two protons GeV = 109 eV)—could conceivably be masked by strong interactions tak- whose initial energies and momenta produce energy densities as high as ing place in the ordinary hadronic- are known. This prediction does not 2Ð20 Gev/fermi3 and temperatures matter phase. Thus it becomes imper- require a calculation of the space- on the order of a few Gev (or ten ative to understand in great detail the time evolution of the interacting times larger than the quark-gluon- non-equilibrium processes taking particles: one doesn’t have to solve plasma phase-transition tempera- place in the plasma. the full time-dependent Schrödinger ture). At CERN collisions of light- In particular, we want to calculate equation to answer questions about ion beams (typically consisting of the rate at which lepton particle-an- the asymptotic, or final, states of carbon or sulphur nuclei) with other tiparticle pairs (such as muon-an- particles reaching the detectors. For nuclei have produced conditions that timuon pairs) would be produced by the quark-gluon plasma, however, approach these extreme temperatures electromagnetic interactions in the one needs to track the space-time and densities, but as yet they have plasma. Leptons interact only evolution of the system in detail in not provided unmistakable evidence through the electroweak interaction, order to make quantitative predic- of a quark-gluon plasma. By 1996 and so, once produced, they would tions that can be tested by experi- the Relativistic Heavy Ion Collider be unaffected by the strong forces menters. Remarkably, the need for a (RHIC) at Brookhaven National and propagate straight through the new formulation of quantum field Laboratory will be smashing gold plasma in the collision region to the theory had already arisen in connec- and even heavier nuclei together at particle detectors. In order to deter- tion with the time evolution of the even higher energies, well above mine whether the rate and the energy early universe. In that case one those required to produce the new spectrum of lepton-pair production needed to follow in detail the time phase of quark-gluon plasma in the in the quark-gluon-plasma phase evolution of quantum fields in a laboratory. Then the real problem would be different from those in or- time-evolving gravitational field. will be to sift through the particle dinary matter, one needs to know the The formulation required for that debris of such collisions and to rec- time evolution of the quark-gluon problem in early-universe cosmolo- ognize the “smoking gun” of the plasma. In particular, one needs to gy turns out to be directly applicable quark-gluon-plasma phase; that is, a calculate the distribution of quarks to the time evolution of the quark-

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West fig3 4/8/93 gluon plasma in a relativistic heavy- ion collision—a beautiful illustra- Figure 3. Creation of Quark-Gluon Plasma in Relativistic Heavy-Ion tion of the underlying unity and in- Collisions terconnectedness of physics. (a) Electron-Positron Pair Production by an What then does a relativistic Electromagnetic Field Battery heavy-ion collision look like? The + – + – strong forces between hadrons in the A battery maintains a high voltage + – colliding nuclei are mediated by the + Positron Electron – difference between two parallel + + Ð – exchange of colored gluons. As a conducting plates. The electric field result of these exchanges, the initial- + – between the plates is sufficiently high that + – ly colorless hadrons become charged electron-positron (eÐe+) pairs are created Pair + production – with opposite colors and quickly spontaneously from the vacuum. + – separate since the hadrons are mov- + – + Ð ing away from each other at veloci- (b) Formation of Quark-Gluon Plasma in Electric field lines ties near the speed of light. As Relativistic Heavy-Ion Collision shown in Figure 3, this situation is analogous to two color-charged plates moving away from each other Initial State: Two heavy nuclei approach each other at velocities near the speed of with a constant color electric field light. At these speeds they appear between them. When the energy flattened because of Lorentz contraction. density in the color field is large enough to produce quark-antiquark Color field pairs, then the “vacuum’’ between the hadrons becomes unstable and Immediately Following Collision: The two quark-antiquark pairs begin to pop nuclei have collided and produced a hot out of the vacuum, just as electron- region between them. positron pairs can be created in a very strong electric field. These quarks then produce more color field Creation of Quark-Gluon Plasma: Blobs that tends to reduce the original one. of nuclear material move away from each Quark-gluon plasma phase Thus the resulting quarks and gluons other. In the color field between them, move through and interact with the pair-production processes analogous to Lepton Antilepton original time-varying color electric those shown in (a) produce quark- antiquark pairs. The quarks and field. The quarks in the quark-gluon antiquarks can interact with the plasma also emit pairs of leptons via electroweak field to produce lepton pairs electromagnetic processes. The lep- such as a muon-antimuon (µ+µÐ) pair. ton pairs leave the collision region The leptons are not affected by the strong Photon and can be seen in standard particle force as they escape from the quark- Quark Antiquark gluon plasma. detectors. As the system expands, the energy density decreases and the hadronic phase become energetically favorable so that the quark-gluon- plasma phase changes back into the Final State: Following the collision the quark-gluon-plasma phase has Hadrons ordinary hadronic phase. changed back to the hadronic phase Leptons Even five years ago, calculating and a large number of hadrons γ the time evolution of this semi-clas- (baryons and mesons), leptons, and rays sical model of heavy-ion collisions γ rays emerge from the collision. would not have been possible. Only now that supercomputers have be-

1993 Number 21 Los Alamos Science 151 Unification of Nature’s Fundamental Forces

come readily available, particularly at the Advanced Computing Labora- tory at Los Alamos, is the problem beginning to become tractable nu- merically. Our calculations of this semi-classical model have already led to some interesting results. We have been able to check many assumptions of more phenomenological pictures of the time evolution of the quark-gluon plasma, such as the classical transport, or hydrodynamic, models. Such models typically do not start from the basic equations of QCD, but rather postulate some ef- fective, essentially classical model. The importance of avoiding such ad Left to right: Rajan Gupta, Emil Mottola, Geof- Geoffrey B. West received his B.A. in natural sci- frey West, Fred Cooper, and Michael Mattis ences (physics) from the University of Cambridge hoc assumptions by calculating the in 1961 and his Ph.D. in Physics at Stanford Uni- evolution of the plasma directly from versity in 1966. He came to the Laboratory in 1974 first principles of QCD (even in sim- see around us; they underlie not as the first leader of what is now the Elementary Particles and Field Theory Group (T-8). In 1981 he plified approximations) cannot be only the complex structures that was made a Laboratory Fellow and in 1988 re- overestimated. To our knowledge, constitute our macroscopic world sumed the leadership of T-8. His present interests no other group of researchers any- but also the beginnings of the uni- revolve around the structure and consistency of quantum field theory and, in particular, its rele- where in the world has attempted to verse and the evolution of the heav- vance to quantum chromodynamics and unified carry out this program. Yet, as we ens. From its earliest history Los field theory. have already discussed, any hope of Alamos has played its part in eluci- Frederick M. Cooper received his Ph.D. from recognizing the quark-gluon-plasma dating this structure. It continues to Harvard University in 1968 and came to the Labo- phase in heavy-ion collisions at do so and in so doing provides a ratory seven years later. His research interests in- RHIC depends ultimately upon the unique link between some of the clude hydrodynamical and transport-theory ap- proaches to problems of multiparticle production, detailed theoretical predictions of most fundamental questions in sci- analytical methods for studying field theories and the signature of the plasma. These, ence and their integration into a nonlinear dynamical systems, and understanding in turn, can come only from such a broader spectrum of problems facing the masses of the heavy quarks. His long-standing interest in the time evolution of relativistic quantum first-principles QCD attack on the society as we approach the twenty- systems led to the work presented here on the evo- problem with the formidable compu- first century. lution of the quark-gluon plasma. tational resources available almost Emil Mottola received his undergraduate degree in uniquely at Los Alamos. As in the Further Reading astrophysics and, in 1979, his Ph.D. in physics, SSC effort, our theoretical group is both from Columbia University. He joined the keeping in close contact with the ex- Los Alamos Science, Number 11. 1984. The en- staff of the Elementary Particles and Field Theory tire issue is devoted to particle physics. Group at the Laboratory in 1986. His research fo- perimenters in the Physics Division cuses on quantum fields, quantum gravity, and the who are major participants in plan- Michael P. Mattis. 1992. The riddle of high-en- early universe and includes studies of baryon-num- ning the search at RHIC for the ergy baryon number violation. Physics Reports ber nonconservation and the evolution of the quark- 214: 159Ð221. gluon plasma. quark-gluon plasma. In conclusion, the long quest for a Michael P. Mattis and Emil Mottola, editors. Michael P. Mattis received his A.B. in physics deep and unified understanding of 1990. Baryon Number Violation at the SSC? from Harvard University in 1981 and his Ph.D. Proceedings of the Santa Fe Workshop. Singa- from Stanford University in 1986. After three the most basic laws of nature that pore: World Scientific. years as Enrico Fermi Fellow at the University of govern fundamental processes has Chicago, he came to the Laboratory first as a J. seen remarkable progress in the last Y. Kluger, J. M. Eisenberg, B. Svetitsky, F. Robert Oppenheimer Fellow and then as a Staff Cooper, and E. Mottola. 1992. Fermion pair Member. His recent work on baryon-number vi- twenty years. These basic laws production in a strong electric field. Physical Re- olation in electroweak theory has earned him a fashion the incredible structure we view D 45: 4659. Superconducting Super Collider Fellowship.

152 Los Alamos Science Number 21 1993 Unification of Nature’s Fundamental Forces/Testing the Standard Model

Testing the Standard Model of Particle Interactions Using State-of-the-Art Supercomputers

Rajan Gupta

he successes of the standard QCD has all the right properties, but sample of possible states of a sys- model of electromagnetic, so far theoretical physicists have not tem. Monte Carlo methods are an Tweak, and strong interactions been able to extract accurate predic- efficient way of sampling the im- have been remarkable. Neverthe- tions from this precise mathematical portant states, that is, states that less, this model contains many as- model with the traditional tools of give the dominant contributions to sumptions and undetermined para- the theoretical physicist—pencil and the process. The best Monte Carlo meters that are displeasing aesthet- paper. To obtain reliable self-con- calculations to date have used lat- ically. Also, the model has not yet sistent results when dealing with the tices of size up to 323 × 48 and produced a satisfying route to uni- strong force between, say, two pro- generated only a small statistical fying gravity with the other three tons requires calculating many sub- sample (twenty to fifty of the pos- fundamental forces. processes involving quarks and glu- sible states). The three sources of The goal of particle physicists ons. In fact, the number of sub- errors in such simulations are the now is to discover where the stan- processes is so large that the lattice size, the lattice spacing, and dard model fails and so to find clues calculation far exceeds the scope of the limited statistical sample. to a better theory, perhaps ultimately analytical techniques. These errors can be systematically achieving Einstein’s dream of unify- The solution is to turn to a new reduced by making the lattice size ing all forces including gravity. It is tool: the supercomputer. Large- larger, the statistical sample larger, hoped that the clues will emerge scale numerical simulations of and the lattice spacing smaller. from highly sophisticated experi- QCD are the most promising tech- To reduce statistical and system- ments in which particles are acceler- nique for analyzing the strong in- atic errors to the level of a few per- ated and smashed together at very teractions. In order to solve QCD cent requires a computer with a high energies. To date, however, no on a computer one has to approxi- very large memory and a very high deviations from the standard model mate space and time by a four-di- operating speed, over 1000 billions have been found, and so the search mensional grid, or lattice, of of arithmetic operations per second. for new clues must be performed at points. The discretized version of For comparison, a typical state-of- even higher energies—such as those the theory is called lattice QCD. the-art home computer has a few that will be achieved at the Super- Experimentally measurable quanti- million bytes of memory and runs conducting Super Collider (SSC) ties (such as the particle masses at a few million operations per sec- now under construction in Texas. and the probabilities of specific ond. The required technology is Much theoretical analysis is still transitions) are determined from a just beginning to appear in the form needed to interpret the results of statistical average over quantum of the parallel supercomputer. In these extraordinary and expensive fluctuations in the quark and gluon fact, scientists interested in solving experiments. The strong-interaction fields. The fluctuations at each po- the riddle of QCD have played a part of the standard model—quan- sition in the lattice are simulated significant role in the development tum chromodynamics, or QCD— by a Monte Carlo procedure, so of parallel supercomputers. The presents the major computational each Monte Carlo calculation de- basic principle of these new ma- stumbling block. Qualitatively, termines one state in a statistical chines is simple—thousands of

1993 Number 21 Los Alamos Science 153 Unification of Nature’s Fundamental Forces/Testing the Standard Model

The Pion Propagator The event depicted here was generated using Monte Carlo simulations of lattice QCD and shows the creation of a pion near the center of the box and its propagation through space both forward and backward in time. The pion propagator, which de- scribes this event, is the correlation function defining the probability amplitude for finding a pion at x at time t given that it start- ed at the origin at time t=0. The propagator is a function of the three spatial coordinates and the time coordinate, but for the purposes of visualization, the data have been averaged over the z coordinate and displayed as a function of x and y (the short axes of the box) and time (the long axis). The size of the green “bubbles” at each point represents the magnitude of the propagator at that point in space-time. Note that the “bubbles” decrease in size with distance from the origin, indicating that the magnitude of the propagator decreases. The white surfaces at the ends of the box represent surfaces on which the probability amplitude of the propagator is a constant. The mass of the pion can be calculated from the rate at which the propagator dies out as a function of time. Since the mass of the pion is known from experiment, such calculations of the pion mass can be used to calibrate Monte Carlo simulations of more complicated processes. The data for this Monte Carlo lattice-QCD event were generated on the CM-200, a Connection Machine with 16,000 processors. Many such Monte Carlo events must be calculated to generate a statistically reliable sample for estimating the pion mass. This numerical calculation of the pion propagator exemplifies the first-principles approach to solving strong interactions using lattice QCD.

small but powerful computers work To overcome this limitation, physi- Thinking Machines Corporation in- simultaneously to solve one big cists turned to parallel computers, troduced the first commercial par- problem. often building them themselves. allel supercomputer, the Connec- The first large-scale simulations Though the capabilities of the earli- tion Machine 2 (CM-2), and DOE of lattice QCD were performed er versions of such computers were announced its first “Grand Chal- around 1980. Because in those days quite limited, a start had been made, lenges” program, which allocated the fastest computer generally avail- and scientists in other fields became large grants of supercomputer time able had the same power as today’s excited by the potential of parallel to scientists working on key com- desktop workstation, the simulations computation. putationally intensive problems. involved so many approximations A watershed for parallel com- The Los Alamos QCD collabora- that the results were not realistic. puting came in 1988. In that year tion was one such recipient. Build-

154 Los Alamos Science Number 21 1993 Unification of Nature’s Fundamental Forces/Testing the Standard Model

ing on the cruder calculations of be more than an order of magnitude more precisely we can probe the 1980Ð88, we demonstrated, using greater, and the available computer validity of the standard model. the most powerful Crays and the speed will be at least two orders of Prior to numerical calculations, the CM-2, the viability of numerical magnitude greater. We plan to use uncertainty in BK was at least 50 methods for QCD. We obtained these improvements in computer percent. Our present Grand Chal- many new results with an accuracy hardware in three ways. First, we lenge calculation has reduced this comparing favorably with the best will exploit the increased speed to error to about 15 percent. We ex- analytical estimates, though the generate much larger statistical pect that the planned calculation computational power was still too samples for the processes we have will further reduce the level of un- limited to make definitive predic- already calculated. These simula- certainty to a few percent. tions. The Los Alamos QCD col- tions will be done on lattices of the To search for physics beyond or laboration also played a key role in size we used previously, 323 × 64. in contradiction to the standard technology transfer by pioneering Second, once the new computers model, one must combine experi- the use of the CM-2 and showing become stable and the proposed mental and theoretical knowledge other scientists at the Laboratory hardware upgrades are in place, we of many quantities. Our calcula- and around the world how to use will begin simulations on much tions will provide theoretical re- this machine as a production super- larger lattices of size 643 × 128. sults for a number of the standard- computer. Finally, we will exploit the larger model observables with an accura- The revolutionary nature of par- memory to undertake more complex cy of 10 to 25 percent, small allel computing poses new chal- calculations than have been feasible enough to put meaningful con- lenges beyond the design of faster so far. straints on the unknown parameters hardware: We also need to develop Our calculations will yield pre- of the model. Thus, over the next software paradigms for parallel su- dictions for a large number of ob- few years, theoretical predictions percomputers that simplify their servables affected by strong inter- combined with new experimental use for a wider variety of problems actions. The theoretical uncertain- results will provide stringent tests and fully exploit the advantages of ties in these quantities will be as of the standard model. parallelism. Progress requires low as a few percent. An illustra- close collaboration between scien- tive and important example con- tists, computer engineers, and ap- cerns the violation of “CP” symme- Further Reading plied mathematicians. A success- try. All interactions except the Michael Creutz, editor. 1992. Quantum Fields ful collaboration of this type has weak are unaffected if one simulta- on the Computer. Singapore: World Scientific. begun between our Los Alamos neously interchanges particles and QCD group, the Advanced Com- antiparticles (charge conjugation, M. Fukugita, Y. Iwasaki, M. Okawa, and A. Ukawa, editors. 1992. Lattice 91: Proceedings puting Laboratory (a DOE High or C) and takes the mirror image of of the International Symposium on Lattice Field Performance Computing and Re- space (parity transformation, or P). Theory, Tsukuba, Japan, 5Ð9 November 1991. search Center at Los Alamos), and The only experimentally estab- Amsterdam: North-Holland. Thinking Machines Corporation. lished violation of CP symmetry This collaboration has received a occurs in the transmutation of a Grand Challenge grant from the neutral strange meson (K0) into its Ð DOE to perform the next genera- antiparticle (K0). This discovery Rajan Gupta was awarded an M.S. by the Uni- versity of Delhi, India, and a Ph.D. by the Cali- tion of QCD calculations on the was made more than twenty-five fornia Institute of Technology in 1982. In 1985 1024-node CM-5 located at Los years ago and was rewarded with he became an Oppenheimer Fellow at the Labo- Alamos National Laboratory. the 1980 Nobel Prize. To test the ratory and three years later joined the staff of the Elementary Particles and Field Theory Compared with the computing standard model against this long- Group. Among his scientific interests are the power of the Cray computers and standing experimental result re- development of non-perturbative methods to the CM-2 used in our previous quires calculating a parameter solve QCD, using lattice QCD to constrain the standard model, and studying the critical behav- Grand Challenge calculation, the called BK. The more accurately we ior of statistical-mechanics models by means of available memory in the CM-5 will can determine this quantity, the Monte Carlo renormalization-group methods.

1993 Number 21 Los Alamos Science 155