RARE KAON DECAYS by JACK L

RARE KAON DECAYS by JACK L. RITCHIE

Rare kaon decay experiments are achieving unprecedented sensitivity to new physics.

HE PARTICLES CALLED KAONS, or K mesons, were ﬁrst observed in the late 1940s in Tcosmic-ray experiments. By today’s standards they are common, easily produced, and well understood. Over the last four decades research into how kaons decay has played a major role in the development of the Standard Model. Yet, after all this time, kaon decays may still prove to be a valuable source of new information on some of the remaining fundamental questions in particle physics. When ﬁrst observed, kaons seemed quite mysterious. Experi- ments showed they were produced in reactions involving the strong force, or strong interaction—the most powerful of the four fundamental forces in nature—but that they did not decay (that is, transform into two or more less massive particles) through the strong interaction. This is because kaons have a property, ultimately labeled “strangeness,” which is conserved in reactions that occur through the strong interaction. Indeed,

28 WINTER 1995 the only fundamental force that does explained electromagnetism and the National Laboratory, using an accel- not conserve strangeness is the weak weak interaction as different mani- erator called the Alternating Gradi- interaction—the force responsible for festations of the same interaction. A ent Synchrotron (AGS). Specifically, nuclear beta decay. Therefore, kaons large body of experimental evidence the experiment observed the decay 0 → π+π− π+ π− can only decay in reactions occurring supports the validity of the elec- KL . The and are pions, through the weak interaction. This troweak theory, and when it is tak- the least massive of the hadrons. The fact has several important conse- en together with quantum chromo- frequency with which this decay oc- 0 quences, one being that kaons are dynamics—the modern theory of the curs compared to all KL decays, a long-lived compared to most other strong interaction—we call the com- quantity called the branching frac- − subatomic particles. One type of bination the Standard Model. How- tion, is only 2×10 3—meaning that 0 0 kaon, the KL (called the “K-long”), ever, in the 1950s and early 1960s only two in 1000 KL’s decay this way. survives without decaying an aver- when the early kaon decay experi- Since this discovery, trying to un- age of 52 nanoseconds (that is, ments were performed, the weak in- derstand the reason for the CP vio- − 52×10 9 seconds). While that may teraction was still not understood. In lation seen in the weak interaction seem like an infinitesimal amount this brief article, it is not possible has been one of the principal prob- of time, on the particle physics scale to review the whole history of kaon lems in particle physics. It remains it is extremely long. Of all the par- physics or to describe all the in- so today, as ever more sophisticat- ticles that are not absolutely stable, stances where studies of kaons made ed tools are brought to bear. The only the neutron and muon are decisive contributions to our current PEP-II B-factory now under con- 0 longer lived than the KL. understanding. Let us consider the struction at Stanford Linear Accel- Today we know that all the par- single instance of CP violation to pro- erator Center has as its goal the study ticles affected by the strong inter- vide a hint of the importance of kaon of CP violation in the decays of B action (particles that we collective- decays. mesons. The B mesons are particles ly call “hadrons”) are made up of Conservation laws are among the which are similar to the K mesons, quarks. There are six types, or “fla- foundations of physics. Much of the except that the more massive bottom vors,” of quarks: down (d), up (u), history of particle physics has been b quark takes the place of the strange strange (s), charm (c), bottom (b), and the struggle to find and to understand s quark (see box on next page). top (t). Kaons, it turns out, are par- the underlying conservation laws ticles consisting of a strange quark that govern the behavior of sub- RESENT KAON decay experi- and an up or down antiquark (or al- atomic particles. Prior to 1964, it was ments are active in two gen- ternatively, a strange antiquark and believed that all fundamental inter- Peral areas: (i) precision studies an up or down quark), which are actions conserved the “charge con- of CP violation that usually focus on 0 bound together by the strong force. jugation-parity,” abbreviated CP, of ever-better measurements of the KL The resulting kaons can have one a physical system. In 1964 a kaon de- decays into two pions, and (ii) search- unit of electric charge, or they can be cay experiment discovered other- es for “rare” kaon decays. In this ar- neutral. Both charged and neutral wise. That experiment found that a ticle, the focus will be on the second kaons have been important in the particular type of kaon decay that category. Decays are rare when they history of particle physics and may should have been forbidden by the are so uncommon that they are hard yet be the source of new discoveries. principle of CP conservation actu- to observe. Over time, and with im- Kaons have some interesting prop- ally takes place, albeit infrequent- provements in accelerators and de- erties because of the way the weak ly. The experiment was performed tectors, our standard of rarity − interaction works. Today we under- by James Christenson, James Cronin, changes. The decay K0 → π+π with L − stand the weak interaction in terms Val Fitch, and Rene Turlay (those its branching fraction of 2×10 3 was of the electroweak theory of Sheldon were the days when particle physics once rare. Now an experiment sen- Glashow, Abdus Salam, and Steven experiments could be carried out by sitive to decays a billion times more Weinberg, which successfully a small team) at the Brookhaven rare is in progress at the AGS. That

BEAM LINE 29 CP VIOLATION It is possible to assign a definite value to the CP of some particles, called CP eigenstates. Also, some combinations of particles have a definite value of CP. For example, consider − YMMETRIES IN PHYSICS refer to the fact that when two charged pions π + and π . Pions are P eigenstates with − certain types of changes are made, often called trans- parity −1. The C transformation changes the π + into a π − Sformations, the behavior of a system is not altered. and the π into a π +, so the full CP transformation returns a These transformations can be of two types: continuous or state with the same particles we started with, but with two discrete. An atomic clock keeps the same time in Chicago factors of −1, which we multiply together to get +1. That is, and New York. The symmetry in this instance is that in dif- the CP of the two-pion state is +1. (For simplicity we have ferent places the same laws of physics apply. Thus, the ignored the orbital angular momentum of the pions, but for transformation of moving the clock from Chicago to New this discussion no harm is done.) So, if CP is conserved, we York, or indeed anywhere in between, does not alter its be- should never see a particle with CP of −1 decay into a π + − havior. This transformation would be called continuous, and π . This is why the observation in 1964 of the decay of since the distance the clock is moved can take on any long-lived neutral kaons into two pions was recognized as value. CP violation. Such CP violation can occur in two ways: i) the A discrete transformation makes a change that cannot parent kaon can be a quantum mechanical mixture of take on a continuous range of values. There are three dis- different CP eigenstates because of a CP-violating interac- crete transformations of special importance: charge conju- tion, or ii) a CP eigenstate may decay directly to a state of 0 → π +π − gation, parity (also called space inversion), and time rever- different CP. The CP violation in the KL decay is sal. Charge conjugation (C) transforms all the particles in a mostly of the first type, but may also include a small system into their associated antiparticles and all the antipar- contribution from the second, which is called “direct” CP ticles into their associated particles. Parity (P) reflects each violation. The amount of CP violation of the first type is point of a system through the origin of coordinates; thus a measured in terms of a quantity usually denoted ε, which is − particle at position (x, y, z) is transformed to the position a complex number whose magnitude is about 2×10 3. The (−x, −y, −z). Time reversal (T) reverses the direction of time. amount of direct CP violation, expressed in terms of an All processes involving both the strong and electromag- analogous parameter ε', is known to be at least five netic interactions are unaffected by C, P, and T transforma- hundred times smaller. tions. The weak interaction was found in the late 1950s to The source of the CP violation observed in kaon decays violate P; that is, weak interaction processes are affected by has not yet been established. A number of theories exist. a parity transformation. The belief at the time was that a According to some of them, direct CP violation should not combination of simultaneous C and P transformations re- occur. Within the Standard Model, direct CP violation is ex- stored the symmetry. So it was surprising in 1964 when an pected, although it may be very small in kaon decays. In the experiment showed that CP was not an exact symmetry of last decade, a tremendous amount of effort has gone into the weak interaction. experiments trying to measure ε'. A non-zero value would A very fundamental symmetry of all interactions is that establish that direct CP violation occurs, thereby eliminating any physical system will behave the same if it simultane- an entire class of theories, and it would be a step toward es- ously experiences all three of these discrete transforma- tablishing the Standard Model picture. Thus far the experi- tions. This is called the CPT theorem. In addition to having a mental results are inconclusive, but new experiments are strong theoretical basis, it has also been tested experimen- being prepared at CERN and Fermilab that should be sensi- tally to great accuracy. Conservation of CPT, but violation of tive to values of ε' as small as one part in 104 of ε. Also, a CP, means that T alone cannot be an exact symmetry of the very elegant approach, described in the following article, is weak interaction. Thus, even on the most microscopic scale planned for an experiment in Frascati, Italy. possible—the interactions of elementary particles—there is In addition to these ever-more precise studies of the two- a difference between going forward and backward in time. pion decays of neutral kaons, some rare kaon decays may 0 → π0νν− CP violation is now recognized as an important ingredi- help provide an answer. For example, the decay KL ent in the evolution of the universe. Immediately after the would be an almost perfect probe of direct CP violation in Big Bang the universe must have consisted of equal quanti- kaon decays. Unfortunately, the branching fraction is ex- ties of matter and antimatter. Over time it evolved toward pected to be very small, roughly in the range between − − the situation we see today, namely an overwhelming excess 1×10 11 and 1×10 10. It will be years before we know of matter over antimatter. Andrei Sakharov pointed out in whether making a measurement is even possible, since 1967 that CP violation was necessary for the matter domi- enormous technical problems must be overcome. Some nance of the universe to come about. This is one of many current experiments are searching for related decays in instances where particle physics has cosmological implica- which charged leptons take the place of the neutrinos. tions. Indeed, many theoretical physicists believe that the Finally, the tremendous excitement surrounding the poten- amount of CP violation we know about so far is insufficient to tial for studying decays of B mesons, where the effects of account fully for the matter dominance in the universe. CP violation should be much more striking, has motivated a Clearly, understanding the origin of CP violation is one of the number of new initiatives, including the construction of the most basic and far-reaching problems in particle physics. PEP-II B-factory and its associated detector BaBar at SLAC.

30 WINTER 1995 LEPTON-FLAVOR VIOLATION

O EXPERIMENT has ever observed a process that failed to conserve addi- Ntively the quantum number associat- experiment is searching for the vio- zero before the decay, and it is also ed with each type of lepton. The underlying lation of another conservation law zero afterwards, since the electron- basis for this conservation law remains called lepton-flavor conservation. type antineutrino cancels with the mysterious. There are other additive con- Leptons are particles that are be- electron. This type of additive conservation laws that are known to hold in lieved to be as fundamental as servation of the number of each type particle interactions. Some, such as the quarks. That is, they are part of the of lepton is sometimes called lepton- conservation of electric charge, are understood on fundamental grounds. minimal set of particles out of which flavor conservation (see box on the In physics there is a deep relationship the entire Universe is constructed. right). between symmetry principles and conser- The electron, familiar as one of the Lepton-flavor violation could vations laws. An additive conservation law building blocks of atoms, is a lepton. show itself in kaon decays if the de- can hold only if there exists a particular 0 ± − The leptons differ from the quarks in cay mode K → µ e+ is ever observed. type of symmetry principle, called a global L − a couple of key respects. For one The notation µ±e+ means the K0 may phase invariance. In the case of electric − − L thing, they are not affected by the decay into either µ+e or µ e+, since charge conservation, the global phase in- strong interaction. For another, they both combinations of electric charge variance arises from a symmetry property have integer values of electric charge are possible. A simpler notation is to of electromagnetism—in particular, the (either −1 or 0), while the quarks have ignore the charges altogether, and property known as gauge invariance. fractional charges (either +2/3 or use K 0 → µe to represent both K 0 Some readers may have encountered L− − L gauge invariance, perhaps in a physics −1/3). The leptons come in three → µ+e and K 0 → µ e+. Notice this L course, in the guise of the electric field not types: electron, muon, and tau. For decay does not include any neutri- changing when a constant is added to the each type, there is a charged lepton nos. If neutrinos (or antineutrinos) electric potential. (A similar property holds and a neutral lepton, called a neu- were present after the decay to can- − for the magnetic field for certain changes of trino. Hence, the electron e has a cel the additive separate lepton num- the vector potential.) When electromagnet- partner neutrino ν . Likewise the bers of the electron and muon, the ism is carried into the quantum mechanical − e − muon µ and tau lepton τ have part- decay would not violate anything. world, this gauge invariance determines ners νµ and ντ , respectively. Searching for such a decay mode of the properties of photons. 0 In the case of lepton-flavor conserva- A mystery is that quarks of one the KL is an interesting gamble. flavor can decay into quarks of an- There is no convincing theoretical tion, the additive conservation laws imply 0 → µ the existence of global phase invariances. other flavor via the weak interac- prediction to suggest KL e should tion—as long as requirements such occur with a branching fraction large But unlike the case of charge conservation, we know of no underlying gauge invari- as electric charge, energy, and mo- enough to observe in today’s exper- ances to cause them. Thus, most theoreti- mentum conservation are satisfied— iments. On the other hand, if an ex- cal physicists expect these conservation 0 → µ resulting in a net change of quark fla- periment observes KL e, then it laws to be inexact—that is, for violations to vor, but leptons of one type never are will be a breakthrough of great im- occur, but at levels too small to have been seen to decay or to transmute in a portance. It is a situation reminis- seen so far. This is the general motivation way that results in a net change of cent of that in 1964 when there was for testing these rules to the most stringent lepton-type. To be more precise, a no particular reason to expect to ob- possible levels. quantum number is associated with serve CP violation. It is fortunate that Many recent theoretical speculations at- each type of lepton and its sum is someone looked anyway. tempt to extend the Standard Model and to conserved in all interactions. For in- address some of its perceived shortcom- stance, a muon decays by emitting NATURAL QUESTION is, ings. These theories go by names such as “supersymmetry” and “technicolor.” These an electron, a muon-type neutrino, however, why kaons? Of all − are topics well outside the scope of this ar- and an electron-type antineutrino (µ the particles in the sub- − − A ticle, but it is interesting that these theories → e ν ν µ e). The number of muon-type atomic zoo, why search for lepton- along with many others predict that lepton- particles is one before the decay, and flavor violation in kaon decays? In flavor conservation is not exact. after the decay it is still one. The fact, such searches are not limited to number of electron-type particles is kaon decays. Some very sensitive

BEAM LINE 31 a third generation, with the highest masses. Some theories exploit this apparent hierarchy. A common result of such theories is that reactions which involve a change of generation number are either forbidden or sup- pressed. Suppose we assign a “generation number” of 1 to members of the first generation (and −1 to its antiparticles), of 2 to the members of the second, and 3 to those of the third generation. Then a muon decay such Brookhaven National LaboratoryBrookhaven − − as µ → e γ involves a net generation Brookhaven National Laboratory on experiments have been and contin- number change of one unit. How- 0 → µ Long Island, New York, is the home of ue to be performed with muons, ever, the kaon decay KL e the Alternating Gradient Synchrotron, a searching for lepton-flavor violating involves no net change in generation − − − − proton accelerator first operated in decays such as µ → e e+e or µ number. Thus, if such theories have 1960. While the energies of AGS beams − → e γ (the symbol γ represents a pho- any validity, kaon decays may be a are low compared to other proton accelerators in use at Fermilab in Illinois ton). Indeed, virtually every experi- more promising place to observe and CERN in Geneva, Switzerland, for ment with a large data sample takes lepton-flavor violation. high-energy physics experiments, the time to look for processes that Other advantages of kaons (over B upgrades over the last three decades would be lepton-flavor violating. For mesons, tau leptons, or the Z, for in- have increased the intensity of available instance, experiments at electron- stance) are the relative ease with beams more than a thousandfold, positron colliders have tried to find which they can be produced (making allowing the AGS to continue forefront decays such as B → µe, B → µτ, it possible to produce them in large research. The AGS currently provides the τ → µγ τ → γ → µ → τ numbers) and their long lifetimes, highest intensity multi-GeV hadron , e , Z e, Z e, and beams in the world, making possible an many others. But indeed there are which make it possible to form kaon ambitious program of rare kaon decay reasons why kaon decays are a par- beams. The result is that kaon decay experiments. The recent commissioning ticularly promising place to look. experiments today can observe de- of the Booster, which feeds bunches of One possible advantage of kaons cays whose branching fractions are protons into the AGS, has increased the (over muons, tau leptons, or the Z, about a million times smaller than available proton flux to a time-averaged for example) has to do with the gen- is possible with B’s, τ’s, or Z’s. While value of about 3 microamperes. Other it is dangerous to generalize, this typ- Brookhaven facilities are also visible in eration structure of the quark and the photograph, including the lepton families. Just as with the lep- ically means that kaon decay search- Relativistic Heavy Ion Collider (RHIC) tons, the quarks fall into a natural es have a greater sensitivity to vari- under construction. grouping of three pairs. The up and ous potential sources of lepton-flavor down quarks along with the electron violation. and electron-type neutrino make up The power of rare kaon decay ex- the first generation. They are the periments to uncover new physical lowest mass members of the hier- processes can be put into quantita- archy. The charm and strange quarks tive terms by making a simple ob- along with the muon and muon-type servation. The force responsible for 0 → µ neutrino make up another genera- a decay such as KL e would be tion, intermediate in mass. Finally, carried by a particle, just as the elec- the top and bottom quarks and the tromagnetic force is carried by pho- tau and tau-type neutrino comprise tons and the weak force by W and

32 WINTER 1995 10–2

Anikina et al. (Dubna)

10–4 Carpenter et al. (BNL) Bott-Bodenhausen et al. (CERN) Fitch et al. (BNL) 10–6

10–8 Upper Limit Clark et al. (LBL) BNL E780

MASS REACH 10–10 KEK E137 BNL E791 ARTICLES INTERACT through the electromagnetic interaction by exchanging a photon. The photon is 10–12 Pa boson, because its spin has an integer value BNL E871 Projection (one). Particles interact through the weak interaction by 1965 1975 1985 1995 2005 exchanging either a W or Z boson. When such interac- Year of Publication tions occur, the bosons which are exchanged are “virtual.” A virtual particle can very brieﬂy exist with a 0 → µ When an experiment searches for a decay such as KL e mass which is larger than that allowed by energy conser- without ﬁnding it, the result of the experiment is an “upper vation because of the principles of quantum mechanics. limit” on the branching fraction—-that is, the largest value + As an example, a charged kaon (K ) can decay to a of the branching fraction consistent with the experiment not muon and neutrino through the exchange of a virtual observing the decay. The graph above shows the history of 0 → µ W boson, as illustrated below. upper limits on KL e. The experiments divide naturally into two groups separated by a hiatus of over a decade, during u µ+ which improvements in both accelerator and detector W+ K+ technology made large gains in sensitivity possible. ν s– µ

The mass of a W boson is about 80 GeV, while the K+ Z bosons. For the branching fraction to be as small as mass is only about 0.5 GeV. The W boson can only ap- we know it must be from experiment, the mass of that pear as a virtual particle, since a real W would violate en- particle must be extremely large. Indeed, based on the ergy conservation. sensitivity of current experiments, the particle would The ﬁrst indication of the existence of the W boson have a mass of at least 90,000 GeV (or 90 TeV since 1 TeV came with the observation of nuclear beta decay, many = 1000 GeV). This mass is so large that it is impossible years before the correct theory of the weak interaction to produce such particles in collisions at any existing, was developed and even more years before the W was or foreseeable, accelerator. Consequently, one can think observed as a real particle in very high energy proton- of rare kaon decay experiments as probing the highest antiproton collisions at CERN in Geneva, Switzerland. A energy scales possible, even though the method is some- similar situation would exist if a rare kaon decay such as 0 → µ what indirect (see box on the left). KL e is ever observed. It would mean that some virtual boson, thus far undiscovered, was being exchanged in the decay process, for example as illustrated below. We ROGRESS IN RARE KAON decay experiments has can relate the branching fraction for this decay to the been rapid in the last decade. It is the result of two mass of the undiscovered boson, subject to a few rea- Psimultaneous developments. The ﬁrst is the avail- sonable assumptions. When we do this, the result is that ability of much higher intensity kaon beams than in the 0 → µ the current upper bound on the KL e branching frac- past, owing to improvements in accelerators. The second −11 tion of 3.3×10 implies the mass of the boson would is progress in particle detector technologies, particu- have to be 90 TeV (1 TeV = 1000 GeV) or more. Thus, we larly those associated with high-speed data handling. can see how a search for rare decays is tantamount to a The experiments that have achieved the highest sensi- search for very massive virtual particles. tivity to rare kaon decays have been performed at the

+ AGS facility at Brookhaven. This is because the AGS can d µ ° ? provide the most kaons per unit time to experiments K L – AGS s– e of any accelerator in the world. The accelerates protons to an energy of typically 24 GeV. The protons are then extracted from the circular accelerator and are

BEAM LINE 33 directed onto external targets, which turn decay very quickly into two are the actual sources of the kaons. photons, so high-quality photon de- With recent upgrades, the AGS can tection is essential in these experi- now extract close to 6×1013 protons ments. The higher Fermilab energy every three seconds. (800 GeV for extracted protons) is an Underway at the AGS are two ex- advantage for the detection of pho- periments searching for rare charged tons, and currently the most promis- Brookhaven National LaboratoryBrookhaven kaon (K+) decays. One of these fo- ing experiment in this area is being An experiment designated E871 is in cuses on lepton-flavor violation and carried out at the Fermilab Tevatron progress at Brookhaven National the other seeks to measure an im- facility. In the future, after con- Laboratory in New York to search for portant Standard Model parameter struction on the Fermilab Main K0 → µe with sensitivity to a branching L − which is related to how the top quark Injector is completed, this experi- fraction as small as 10 12. The detector interacts with other quarks. A third ment should be able to make further is over 30 meters long, much of it surrounded closely by shielding to experiment searches for rare neutral improvements because of the avail- 0 0 → µ protect personnel against the radiation (KL) decays, including KL e. An ablity of a higher intensity kaon 0 generated by the high-intensity beam. earlier version of the KL experiment beam. An experiment with the same The part of the apparatus seen here, reached the best sensitivity ever ob- focus is in progress at the KEK Pro- well removed from the beam region, tained in a kaon decay experiment. ton Synchrotron (PS) in Japan. A rare measures the trajectories of the muons 0 → µ No KL e decays were observed, kaon decay program has been un- from kaon decays. E871 builds on the but the experiment established that derway there for many years, but the experience of a previous experiment, E791, which achieved the greatest the branching fraction must be less experiments have thus far suffered × −11 sensitivity to rare kaon decays of any than 3.3 10 . The newer version from the rather low intensity beams experiment to date. of the experiment will improve upon available there. However, planning the previous sensitivity by an order is underway in Japan for a new of magnitude or more. The progress 50 GeV proton accelerator which in these searches is shown as a func- could, if built, support state-of-the- tion of time in the figure on the pre- art rare kaon decay experiments. ceding page. Progress in particle physics de- Rare kaon decay experiments are pends on experimentation on multi- also underway at other laboratories. ple fronts. Sometimes it is said that These experiments focus on rare there are three experimental fron- kaon decays which can provide more tiers: the high energy frontier, the insight into the phenomenon of CP high precision frontier, and the high violation. Such decays typically in- sensitivity frontier. Most of the pub- clude a neutral pion (π0) as one of the lic attention goes to the high ener- daughter particles. Neutrals pions in gy frontier, because it involves building big and expensive new machines. A Summary of Active Rare K Decay Experiments Some truly basic questions in particle physics require this approach. Even Designation Laboratory Primary Decay Mode Primary Physics Motivation so, experiments at modest energies E787 Brookhaven K+ → π+ννÐ Top quark coupling to other quarks which emphasize high precision or − E865 Brookhaven K+ → π+µ+e Search for lepton-flavor violation high sensitivity, as in the case of rare 0 → µ± −+ kaon decay experiments, may prove E871 Brookhaven KL e Search for lepton-flavor violation 0 → π0 + − E799 Fermilab KL e e Study of CP violation to be the next source of an important 0 → π0 + − E162 KEK (Japan) KL e e Study of CP violation new discovery. The potential is surely there.

34 WINTER 1995