The Mystery of the Matter Asymmetry by ERIC SATHER

Why is our Universe made of matter and not antimatter? The answer might be found in the laws that govern elementary particles.

E’VE DISCOVERED a lot about our Universe by asking questions and then looking for answers. For example, we asked how stars are powered and found the answer in the Wtransformations of atomic nuclei. But there are still simple questions that we can ask. And one is: Why is our Universe full of things like us and stars, and not empty? It doesn’t seem remarkable that there are things in our Universe. But if we look back toward the beginning of the Universe we can see that having it turn out not empty was a close thing. The Universe has cooled over its long history, but was extremely hot just after it was born in a Big Bang: so hot that there was lots of energy for making particles and antiparticles in pairs. As the Universe cooled, these particles and antiparticles annihilated in pairs. Had the amounts of matter and antimatter been equal, everything would have annihilated and the Universe would be empty. So when the Universe was hot there must have been more matter than antimatter, so that after it cooled we and stars would be left over.

BEAM LINE 31 10–10 s 1015 K Electroweak Era If we work out However the population of the more what the Universe general class of particles called –6 13 10 s 10 K Baryon Pair Annihilation was like one billionth baryons, which includes protons and of a second after it neutrons, doesn’t change. Baryons began, it turns out and antibaryons can be created and 1 Minute 109 K Nucleosynthesis that for every billion annihilated in pairs, but the excess particle-antiparticle of baryons over antibaryons, known pairs there was just as baryon number, is constant. In one extra particle. To fact, baryon number is conserved in that particle we and all reactions that have been observed. 300,000 Years 4000 K Recombination stars owe our exis- Hence the baryon number has re-

1 Billion Years 20 K Galaxies Form tence. If we can ex- mained constant for as far back into plain why for every the history of the Universe as we can 15 Billion Years 3 K Today billion pairs there was one spare par- describe it using the physics we have ticle, we’ll understand why the Uni- observed and understand. verse isn’t empty. And if we can say The above reaction also preserves why the spare was a particle and not a similar quantity called lepton num- an antiparticle, we’ll know why the ber, because a neutrino is an exam- Universe is made of matter and not ple of a lepton, and a positron (anti- antimatter. electron) is an antilepton. And all So why, ultimately, is the world observed reactions conserve lepton made of matter and not antimatter number. However, to determine the Important events in the known history of or nothing at all? Perhaps it is just lepton number we’d have to count the Universe (times and temperatures how the Universe was composed at neutrinos, and neutrinos are hard to are approximate). The Universe has cooled since its formation in a hot Big the instant of the Big Bang or an ac- detect. Baryons meanwhile make up Bang, so the earliest times correspond cident of subsequent history. But it most of the mass of the things we can to the highest temperatures. As could be the result of laws of nature see. Therefore the matter excess that indicated by the level of the mercury, which we can discover. While we’re we can observe, that dates back to this article concerns the electroweak still looking for the answer, in recent the first moments of the Universe, era. Subsequent events shown are years we’ve come to realize that we and that we need to explain is an ex- baryon-antibaryon annihilation, which might find it if we can penetrate the cess of baryons. left the residual baryon asymmetry; the synthesis of light nuclei; recombination, next layer of microscopic physics. High-energy experiments have when electrons and nuclei combined revealed that each baryon, such as into neutral atoms, leaving the Universe BARYOGENESIS a proton or neutron, is actually a transparent to light; galaxy formation; composite of three more fundamen- and today, when the Universe is filled Before looking for the origin of the tal objects, called quarks. To date six with 3-degree-Kelvin microwave excess of matter over antimatter, we kinds, or flavors, of quarks have been background radiation, which is the light first need to understand a little about discovered. Similarly each antibary- released at the time of recombination the excess itself. The matter in our on consists of three antiquarks. The redshifted by the subsequent expansion of the Universe. Universe is not static but is trans- baryon number of the Universe is formed in stars. Nuclear transfor- then one-third the quark number. mations such as the reaction proton The composite nature of baryons im- → neutron + positron + neutrino plies that the ultimate explanation change the populations of particle of the matter-antimatter asymmetry species. Here protons decrease in must be framed in the language of number while neutrons increase. quarks. Nevertheless, for historical

32 SPRING/SUMMER 1996 If we work out what the Universe was like one billionth of a second reasons, the matter excess of the Uni- after it began, it turns years, experiments have observed verse is referred to as the baryon many of these phenomena and shown asymmetry. And the production of out that for every billion that the predictions of the theory hold the matter excess is called baryoge- to remarkable accuracy. nesis. particle-antiparticle Our understanding of the elec- troweak interactions, and indeed all SAKHAROV CONDITIONS pairs there was just one the physics of elementary particles, relies heavily on the ideas of sym- The birth of the field of baryogene- extra particle. To that metry and broken symmetry. To il- sis and the idea that the matter ex- lustrate these ideas, consider the ex- particle we and stars cess could be explained by micro- ample of a ferromagnetic material scopic physics came in 1967. In that owe our existence. like iron. In hot iron, the spins of the year Andrei Sakharov listed three electrons point randomly, oriented conditions necessary for an explana- in all directions with equal proba- tion of the baryon asymmetry. In so bility. There is no net magnetization, doing, he laid the foundation for all and the iron exhibits rotational sym- future attempts to explain the mat- of experiment. Current experiments metry, appearing the same from all ter excess of the Universe. try to test the long-prevailing theory directions (see the illustration on the Sakharov pointed out that in or- of elementary-particle physics, the next page). The energy of a ferro- der to produce a baryon excess where very successful electroweak theory. magnet is least when the electron none existed before there first must After these early investigations of spins all point in the same direction. be processes that change the bary- baryogenesis, it was discovered that So in cold iron the spins align, the on number. Such baryon-number- the electroweak theory itself could iron is magnetized, and the overall violating processes have not yet been provide the necessary baryon-num- rotational symmetry is broken. Some observed. Second, the laws of nature ber violation. With this realization, rotational symmetry persists, how- must be biased so that a matter that the origin of the matter asym- ever. The iron still appears the same excess results and not an antimatter metry might be found in the layer of when rotated about the direction of excess. Third, and less obvious, the physics now being revealed by ex- magnetization (see the illustration baryon-number-violating processes periment, the focus of the baryogen- on page 35). must be out of thermal equilibrium. esis quest shifted. The most important symmetries Otherwise, in equilibrium, these in nature are the so-called gauge sym- processes would even the amounts ELECTROWEAK BARYOGENESIS metries, which give rise to the of baryons and antibaryons and nul- known forces. Gauge symmetry lies lify the baryon number. Providing To see how the baryon asymmetry at the heart of the electroweak the- these three ingredients—baryon- could be produced by electroweak ory, producing the electromagnetic number violation, matter-biased baryogenesis, we need to know some and weak forces. These forces are laws, and thermal nonequilibrium— of the basics of electroweak physics. transmitted by messenger particles is the starting point for any attempt The electroweak theory summarizes called gauge bosons: the photon to explain the matter-antimatter our deepest insights into the ultimate transmits electromagnetism, while asymmetry of the Universe. laws of nature. It synthesizes the W and Z bosons transmit weak in- The earliest ideas about baryoge- electromagnetic theory of charges teractions. nesis centered on speculative theo- and light and the weak theory of nu- We can understand the basics of ries that provide the desired baryon- clear β-decay. In embracing these dis- electroweak gauge symmetry by number violation. Unfortunately, parate theories, the electroweak the- analogy with a ferromagnet. Like these theories describe physics at ory predicts a wealth of new phe- the rotational symmetry of cold, energies far beyond the current reach nomena. Over the last twenty-five magnetized iron, the electroweak

BEAM LINE 33 Higgs mechanism using an analogy with superconductivity.)

ELECTROWEAK PHASE TRANSITION

Returning to the example of a fer- romagnet, hot iron occupies a state, or phase, of symmetry, while cold iron lies in a phase of broken sym- metry. When hot iron is cooled below a critical temperature, magnetization develops and rotational symmetry breaks. At this Curie temperature, the iron suffers a phase transition from the symmetric phase to the bro- ken phase. In direct analogy with the ferro- magnet, which loses its magnetiza- tion and exhibits maximum sym- metry at high temperature, the Schematic showing the electron spins electroweak symmetry was unbro- in a portion of a ferromagnet. Above: At symmetry is broken, but not com- ken when the Universe was born in high temperature the spins point pletely. The weak symmetry breaks a hot Big Bang. The critical temper- in random directions, and the but the electromagnetic symmetry ature for electroweak symmetry ferromagnet is rotationally symmetric. survives. Because electromagnetic breaking is, however, enormously symmetry survives, the photon is higher than the Curie temperature of massless, and electromagnetic forces iron. The Universe had cooled to this carry over large distances. In contrast, temperature and experienced an elec- because weak symmetry breaks, the troweak phase transition only one W and Z are massive, and weak ten-billionth of a second after its interactions act only over a very birth. short range and thus appear weak. During this transition, just as bub- We don’t yet know what breaks bles of steam form in boiling water, the electroweak symmetry. The sim- bubbles of broken phase formed. plest explanation is that there is a These bubbles expanded until they field called the Higgs which, just like filled the Universe, leaving it in its a ferromagnet, breaks symmetry current phase of broken symmetry. when it falls into its state of lowest Throughout the transition, the Uni- energy. All we really know is that verse was out of equilibrium, thus there is some mechanism that breaks satisfying one of Sakharov’s condi- the electroweak symmetry and there- tions. Therefore, if the origin of the by gives mass to the W, Z, and all oth- baryon asymmetry lies in electro- er massive particles. (See the previ- weak physics, the asymmetry must ous article in this issue by Lance have formed during the electroweak Dixon in which he illuminates the phase transition.

34 SPRING/SUMMER 1996 ELECTROWEAK BARYON NUMBER VIOLATION

What about the other Sakharov con- ditions, for instance baryon-number violation? At first glance, the elec- troweak theory appears to conserve baryon number; there are no explicit interactions that change it. However, due to quantum-mechanical sub- tleties, there are baryon-number vio- lating processes. Then why has baryon-number violation escaped detection? Because today, in the broken phase, such violation requires quantum- mechanical tunneling through a large energy barrier and is in consequence suppressed. But in the symmetric phase, both before and during the operation CP turns a particle into an At low temperature the spins align, the electroweak phase transition, this antiparticle with reversed momen- ferromagnet is magnetized, and the barrier was absent and baryon num- tum but identical spin. Since both C overall rotational symmetry is broken. ber could fluctuate. This insight led and CP relate particles to antiparti- The ferromagnet is still symmetric under rotations about the direction to the study of electroweak baryo- cles, if either were a symmetry of the of magnetization. genesis. laws of nature, particle production would always be countered by equal C AND CP antiparticle production, and no baryon asymmetry could result. So the electroweak theory can pro- Are C and CP symmetries of na- vide both baryon-number noncon- ture? C and P are symmetries of the servation and thermal nonequilib- electromagnetic interactions and also rium. What about the remaining of the strong interactions which bind Sakharov condition? Does the elec- quarks into protons and neutrons, troweak theory distinguish between and bind these, in turn, into nuclei. matter and antimatter? These transformations were assumed To answer this question, we need to be exact symmetries of all laws of to consider two transformations nature. But in 1956 Lee and Yang which relate matter to antimatter. realized that C and P are only ap- The first, called charge conjugation proximate symmetries: weak inter- and denoted C, simply interchanges actions violate them. Soon after, par- particles with antiparticles. The sec- ity violation was observed in nuclear ond, denoted CP, is a composite of β-decay. The composite operation CP C and the parity transformation P. still appeared to be an exact sym- Parity, like a mirror, reverses the metry, but in 1964 a group led by direction of particle motion but pre- Cronin and Fitch discovered CP serves spins. Hence the combined violation in the weak decays of

BEAM LINE 35 particles called kaons. The quark THE FAILURE OF STANDARD CP Generation constituents of these kaons must VIOLATION therefore have CP-violating weak in- 123teractions. Hence the weak interac- Thus we have the ingredients and a tions violate both C and CP. recipe for producing a baryon excess. 2 But can they reproduce the baryon – up charm top 3 A RECIPE FOR BARYOGENESIS asymmetry that we observe? Unfor- tunately, the standard electroweak

Charge 1 So the electroweak theory contains theory fails. The reason lies in the – – down strange bottom 3 all three ingredients for baryogene- origin of CP violation. In the standard sis required by Sakharov. Now we electroweak theory, CP violation just need a recipe for how to combine originates from charge-changing them to make a baryon asymmetry. weak interactions that change the 100 W Let us assemble the ingredients at charge and flavor of quarks. The six the time of the electroweak phase known quark flavors divide evenly 10 transition: Initially, the Universe is between two charge states. There are 1 filled with the symmetric phase, but three “up-type” quarks with charge bubbles of broken phase form and ex- 2/3: up, charm, and top; and three 0.1 pand, supplanting the symmetric “down-type” quarks with charge Mass (GeV) phase. Baryon-number-violating pro- −1/3: down, strange, and bottom. The 0.01 cesses are rapid in the symmetric up-type and down-type flavors can

up down strange charm bottom top phase but shut off—out of equilib- be thought of as coming in pairs: up- rium—inside the bubbles. Finally, a down, charm-strange, and top- Flavor plasma of quarks and antiquarks bottom (see top figure on the left). To The six known quark flavors. Top: The with C- and CP-violating interactions a good approximation, the charge- known quarks and leptons occur in three permeates the Universe. changing interactions only operate sets called generations. Each genera- Now suppose that as the surfaces within a pair, for example turning up tion consists of a pair of quarks, with of expanding bubbles sweep through into down or vice versa. But more charges 2/3 and −1/3, and a pair of the plasma, antiquarks are less likely precisely, these interactions turn an leptons. This illustration shows how the to enter the bubbles than quarks be- up quark into a quantum mixture six quark flavors pair to fit into genera- C CP tions. To a first approximation, charge- cause of and violation. The ex- of down-type quarks which is most- changing weak interactions only inter- cess of antiquarks left outside the ly down but is partly strange and bot- convert quarks within a generation. bubbles is simply erased by the tom. The charm and top quarks turn Bottom: Illustration showing quark mass- baryon-number changing processes into similar, but orthogonal, mix- es, together with a dashed line indicat- active in the symmetric phase. How- tures, which are mostly strange and ing the mass of the W boson, that char- ever, an opposite excess of quarks bottom respectively. acterize the mass scale of the weak is deposited inside the bubbles, By considering the most general interactions. All quark flavors other than where baryon-number is conserved. mixing of this kind, Kobayashi and the top are very light compared to the W. This suppresses baryogenesis that This excess would survive to the Maskawa discovered that these relies on Kobayashi-Maskawa CP present day as the baryon asymme- charge-changing interactions can violation. try of the Universe. violate CP. Because the mixing is

36 SPRING/SUMMER 1996 A definitive answer to the mystery of the baryon asymmetry thus awaits the next observed to be small, the CP viola- generation of potentially a high-energy electron tion is a small effect. This Kobayashi- collider (NLC) will all attempt to Maskawa CP violation vanishes if high-energy probe the symmetry-breaking mech- any two quark flavors with the same experiments, which anism directly. Meanwhile B-meson charge have the same mass. In real- factories at SLAC, KEK, and else- ity, no two flavors have the same hope to shed light on where will look for the origin of CP mass. However, setting aside the top, violation. the other five flavors are very light the far-reaching As these facilities begin to reveal compared to the typical mass scale phenomenon the foundations of electroweak phys- of the weak interactions, for exam- ics, we’ll learn why weak forces are ple the mass of the W (see bottom of electroweak- weak, what gives particles mass, and illustration on the previous page). symmetry breaking. how nature distinguishes matter Compared to the typical weak scale, from antimatter. Our knowledge of these five flavors all have nearly the history will then reach back a little same mass, namely zero mass. further, to a time of baryon-number Therefore, in any process character- violation and symmetry breaking, ized by the weak scale, the CP vio- our understanding of physical laws, when perhaps the baryon asymmetry lation will be tiny because of these either at the electroweak scale or else was forged. At last we might under- small quark masses and also the at an even deeper level. stand why our Universe is made of small quark mixing. From the beginning, work on elec- matter and not antimatter. And we’d Electroweak baryogenesis, a CP- troweak baryogenesis has considered know why it isn’t empty. violating, weak-scale process, would generalizations of the standard elec- thus have been ineffectual. Of course, troweak theory which include new, as mentioned at the outset, the ex- nonproblematic sources of CP viola- cess of matter over antimatter was tion. Usually the mechanism of sym- only one part per billion at this ear- metry breaking is modified, which is ly epoch. Nevertheless, baryogene- allowed since so little is known sis using Kobayashi-Maskawa CP about this mechanism. Several vari- violation falls far short of even this ants of the electroweak theory ap- tiny number. pear capable of producing the ob- served baryon asymmetry. OUTLOOK FOR ELECTROWEAK A definitive answer to the mys- BARYOGENESIS tery of the baryon asymmetry thus awaits the next generation of high- Is electroweak baryogenesis a failure energy experiments, which hope to then? Actually, the inadequacy of at last shed light on the far-reaching Kobayashi-Maskawa CP violation for phenomenon of electroweak- baryogenesis was recognized imme- symmetry breaking. The Fermi- diately. From this we learn that lab Tevatron, the Large Electron before we can explain the baryon Positron (LEP) collider and Large asymmetry, we must first improve Hadron Collider (LHC) at CERN, and

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