Accelerators, Colliding Beams: Electron-Positron

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ACCELERATORS, COLLIDING BEAMS: ELECTRON-POSITRON

Astronomy, cosmology, and space travel have expanded our frontiers outward to the limits of the universe and to its earliest moments. In the opposite direction, atomic, nuclear, and particle physics have pushed inward toward the ultimate constituents of matter. Both frontiers offer thrilling adventure and great triumphs. Both call for impressively large and expensive machines. And, surprisingly, the discoveries on the innermost scale shed light also on the grandest event of cosmology: the Big Bang—a veritable cauldron of elementary particles.

To explore them deep inside, atoms are bombarded with beams of particles brought to high energy in an accelerator: the higher the projectile's energy, the deeper it can probe into an atom and its nucleus. More spectacularly, as a consequence of relativity, a collision with enough energy can also create new particles. (Conservation laws may call for pair creation, particle plus antiparticle, to balance the books.) The required energy is the equivalent of the total mass created.

The rest energies, E₀ = m₀c², of some interesting particles are given in Table 1. The energy stakes in this game can be high, well above the rest energy of the projectiles themselves—especially if the projectiles are electrons, whose rest energy is only 0.00051 GeV. For example, a 5.1-GeV electron has 10,000 times the energy it had at rest; equivalently, its mass is 10, 000 times its original rest mass. Such an electron is ultrarelativistic.

It is not efficient to shoot a massive particle at a stationary target (as does a fixed-target accelerator).

TABLE 1

Rest Energies of Selected Particles
Particle		Rest Energy
credit: Courtesy of Raphael Littauer.
Electron (e )	Stable	0.00051 GeV
Proton (p )	Stable	0.94 GeV
Muon (μ)		0.11 GeV
pi-zero meson (π⁰)		0.14 GeV
Omega meson (ω)		0.78 GeV
Tau lepton (τ)		1.8 GeV
J/psi meson (J/ψ)	Unstable	3.1 GeV
Upsilon meson (Υ)		9.5 GeV
W boson		79 GeV
Z⁰ boson		91 GeV
Top quark (t )		170 GeV

When a massive projectile strikes a light target, it flies on almost undisturbed, retaining most of its energy—like a truck that has hit a mosquito. A projectile gives up energy only if it is slowed down. That can happen if two beams of particles are aimed at each other: in a head-on collision, both particles may slam to a stop and release all their combined energies. Unfortunately, compared to a slab of stationary matter, an oncoming particle beam makes a frustratingly elusive target. It took single-minded optimism and dedication to overcome this problem. Nevertheless, since the 1960s, colliding beam accelerators have become the dominant tool for particle research.

Event Rate: Cross Section and Luminosity

On the subatomic scale, hitting a target is a matter of chance, rather like shooting into a swarm of mosquitoes. However, large mosquitoes are hit more often than small ones: they present more frontal area. By analogy, the probability of hitting a particle, producing a specified type of outcome, can be represented as an effective frontal area. This is called the production cross section σ(sigma). That is, if a target particle is somewhere within an area A , and one projectile is shot into this area, the chance of obtaining an event of the type specified is σ/A . Shooting N₁ projectiles ƒ times per second at N₂ targets in an area A will produce, on average, ƒN₁N₂(σ/A ) events per second. (For particles, a convenient unit for σ is the nanobarn (nb); 1 nb = 10^-9 barn = 10^-33 cm². Barn is the name jokingly given to a cross section of 10^-24 cm², as easy to hit as the side of a barn!)

The luminosity £ of the collider is defined as the factor that multiplies σ; that is, event rate = £σ. In the situation just described, £ = ƒN₁N₂/A . For example, if a collider produces events of cross section one nb at an average rate of 1 per second, its luminosity is £ = 1/nb/s (or 10³³ cm^-2 s^-1).

Most colliders use storage rings to keep bunches of particles circulating in opposite directions, passing through each other on every turn at one or more interaction points (IP). In principle, the particles continue to circulate until they finally collide; in practice, there are other losses. To increase the luminosity, the bunches are focused into a very small spot at the IP by a low-beta insertion, a set of strong lenses that act like back-to-back burning glasses. (Beta is an optical parameter related to the size of the bunch; its value at the IP also indicates the maximum bunch length that can be accommodated given the diverging bunch profile on either side of the focus.)

A storage ring fulfills two other functions: particles can be accumulated in each bunch from many injection cycles to increase N₁ and N₂ above what is directly available from an injector (particle source plus preaccelerator). Also, when accumulation is complete, the particles can (if necessary) be accelerated to the desired collision energy while they circulate in the ring.

Choice of Particle

Colliders using electrons (e^- ) and their antiparticles, positrons (e⁺ ) represent one of several types of colliding beam accelerators. Electrons—used generically, the term includes both e^- and e⁺ —are distinguished by the type of physics information they reveal and also by the technical aspects of their storage:

Electrons are truly elementary: they have no internal components. Their collisions produce pristine, precisely controllable conditions. (By contrast, the quarks and gluons that make up a proton can lead to very complicated scenarios.) Moreover, an electron and a positron can annihilate each other when they collide, surrendering all their energy to the collision products. The energy of the collider can then be set with almost surgical precision to match a desired final situation. The advantages of this annihilation mode are so compelling that they far outweigh the difficulty of first having to create the positrons. Because of their opposite charges, e^- and e⁺ can circulate in opposite directions in a single ring.
Electrons at collider energies are ultrarelativistic; when forced to circulate in a ring, they emit strong synchrotron radiation. This energy loss is a major burden for electron storage; however, because it damps particle oscillations, it also has beneficial effects. (The "waste" radiation was soon exploited for an impressive range of research and industrial applications. Specialized synchrotron light sources have since proliferated.)

Figure 1 schematically illustrates the main components of a storage-ring collider. Figure 2 is a view inside the tunnel for the Cornell Electron Storage Ring (CESR).

Source of Particles

Electrons are readily emitted from a heated metal, as in a TV picture tube. By contrast, positrons must first be created. This is done by bombarding a converter—a slab of heavy metal—with high-energy electrons from a linear accelerator (linac). Near the heavy nuclei of the converter a cascade of processes develops: electrons radiate some of their energy as photons, and photons, in turn, produce electron- positron pairs. Emerging from the converter is a cloud of electrons, positrons, and photons, from which positrons are directed by magnetic lenses into another linac. For injection into the storage ring, the particles (e⁺ or e^- ) are brought to high energy in one or more boosters (linac or synchrotron).

Injection and Storage

A storage ring is a special-purpose synchrotron. The particles circulate in a vacuum chamber placed in a magnetic guide field, with quadrupoles (magnetic lenses) keeping them close to the desired trajectory. Energy lost by radiation is replaced as the particles traverse one or more radio frequency (rf)

FIGURE 1

cavities—hollow metal structures in which a strong oscillating electric field is maintained. Conveniently, this time-dependent field gathers the particles into

FIGURE 2

short, synchronized bunches by the mechanism of phase stability: particles arriving early or late receive different energy increments that return them toward the bunch center.

Because of the high intensity of the stored bunches and the long storage times, very stringent stability conditions must be met by the components of a synchrotron used in storage mode. Also, to avoid derailing the particles already stored, new ones must be injected on a displaced path that weaves about the central orbit. Fortunately, synchrotron radiation damps these injection oscillations, so the new particles soon coalesce with the older bunch.

When accumulation (and final acceleration, if any) is complete, the circulating bunches are steered to meet head-on at an interaction point (IP), around which the detector is placed. This consists of sophisticated equipment to track and analyze the fragments emerging from a collision, often identifying special patterns in as few as one in a million cases. (In terms of complexity and expense, detectors may rival the collider itself.) After an experimental run is initiated, the bunches may circulate for an hour or more, passing through each other many millions of times. Ultra-high vacuum is maintained in the beam chamber to reduce collisions with residual gas, which would shorten their lifetime and also cause background in the detector.

Synchrotron Radiation (SR)

As they circulate in a ring, continually steered inward, electrons emit synchrotron radiation (SR), a broad spectrum of electromagnetic waves reaching typically into the ultraviolet and X-ray region. The most dramatic feature of SR is its steep rise with beam energy E : the energy radiated per turn is proportional to E⁴. (E ×10 → SR×10,000!) To maintain the beams, the radiated energy must be resupplied continuously by the rf cavities. The required power, sometimes tens of megawatts, can become prohibitive; to lower it, the ring radius is made large (SR power is inversely proportional to the radius squared). At the highest energies, SR ultimately becomes prohibitive for electron storage rings, forcing a retreat to linear colliders (discussed below).

SR is emitted in a narrow forward cone, like light from a car's headlights. A particle traveling at an angle to the ideal trajectory emits SR at that angle; this carries off some of the transverse momentum. Since the rf cavities resupply purely forward momentum, transverse oscillations are gradually damped. (The effect—analogous to friction steadying a pendulum—is used specifically in damping rings to form compact particle bunches.)

SR is not emitted continuously but instead in individual quanta (photons), each of which jolts the electron with a step in energy. This gives the bunch an energy spread; also, because off-energy particles want to travel at different radii, it excites transverse oscillations in the plane of orbit. The ultimate bunch dimensions are governed by equilibrium between quantum excitation and radiation damping; typically, a bunch comprising upward of 10¹¹ particles may be several millimeters wide, a fraction of a millimeter high, and some tens of millimeters long.

Intensity Limitations

Short bunches of many particles represent very large instantaneous beam currents—often several hundreds of amperes—accompanied by strong electromagnetic pulses. These wake fields echo around the vacuum chamber and can react back on the bunch (or subsequent bunches) causing instability. The beam's environment (chamber, rf cavities, and auxiliary apparatus) must be carefully controlled to raise the usable intensity. In addition, feedback devices can detect incipient oscillations and, within limits, act to suppress their growth.

Unfortunately, as the particles pass through the electromagnetic field of the opposing bunch, they are deflected by an amount that varies strongly across the bunch. This unavoidable beam-beam interaction (BBI) dilutes bunch density and limits the maximum usable intensity per bunch. The ensuing ceiling on luminosity is raised by tighter focusing at the IP (lower beta), but here the limit is set by the bunch length. Further increases ultimately result only from raising the number of bunches in each beam.

When B bunches circulate in each of the two beams, they make 2B encounters around the ring, at each of which the BBI must be controlled. With only a few bunches, each crossing point can be configured with a low-beta insertion as a usable IP. Many colliders have done this, but only at the cost of exacerbating the BBI. For more bunches, multiple meeting points must be avoided by separating the bunches with electric fields. Even so, residual BBI makes it progressively harder to raise the number of bunches. CESR represents an extreme case: with up to forty-five bunches each of e⁺ and e^- it produces a luminosity ten times that of other single-ring colliders (Table 2).

The highest luminosities, achieved in colliders ambitiously known as particle factories, are obtained with two separate rings, where the trajectories are separated except near an IP.

Asymmetrical Colliders

Use of equal-energy colliding beams is motivated by the energy yield achieved in head-on collisions. However, the available energy is not much reduced if the two beams have somewhat unequal energy. The collision products are then carried forward in the direction of the higher-energy beam, which makes the decay points of short-lived collision products visible by moving them away from the IP. Knowing how long an unstable particle survived is important in some experiments, such as those looking for particle-antiparticle asymmetry in the decay of B and B̄ mesons. (This information could shed light on how the universe evolved from the Big Bang to a state where matter dominates over antimatter.)

Physics Results from Electron Colliders

Some major electron-positron colliders are listed in Table 2. There has been dramatic progress on both frontiers: energy and luminosity. Because a collider yields peak performance over only a relatively narrow energy span, many different colliders are in service. The largest ring, LEP, about 27 kilometers in circumference, reached an energy (100 + 100 GeV) still far short of the energies possible with proton rings. (Protons, 2,000 times more massive than electrons, are less relativistic for a given energy and emit only an insignificant amount of synchrotron radiation. On the other hand, in comparing effective collision energies, one must consider that the real projectiles and targets—the quarks within the protons—each carry only a fraction of the proton's energy as a whole.)

Energy alone is not enough for a collider; there must also be sufficient luminosity to yield an acceptable event rate. To place this in perspective, Figure 3 shows how the cross section σ varies with total energy E . (Note that, to do justice to the very wide range of values, the scales on this graph are logarithmic.) The dominant feature is the steep decrease of σ—in proportion to 1/E². (Every time E increases tenfold, σ is divided by 100.) This trend underlies all collision processes that start with e⁺ e^- annihilation, which is the dominant mode in the region up to approximately 100 GeV. The cross section for the production of a lepton pair—e , μ , or τ , involving no strong forces, only quantum electrodynamics (QED)—is shown as a broken line. Measurements at successive colliders have checked the theoretical prediction to great accuracy, verifying that leptons are indeed pointlike particles, down to a scale of 10^-16 cm.

In the late 1960s, when ADONE came into operation, it was a pleasant surprise to many how readily e⁺ e^- collisions yielded hadrons (strongly interacting particles). This was interpreted as being initiated by production of a quark pair and helped quarks gain acceptance as likely constituents of matter. The solid curve in Figure 3, with its dotted extension, shows that the cross section for quark-pair processes is a constant multiple of the lepton-pair cross section; the numerical ratio confirms a fundamental tenet of the Standard Model, namely, that quarks come in three "colors."

TABLE 2

Selected Electron-Positron Colliders
Name	Location	Maximum Energy (GeV)	Circumference (m)	Dates	Luminosity (events/nb/s)^*
^*See text for this unit; 1/nb/s = 1×10³³ cm^-2s^-1. Quoted luminosities are values achieved by time of writing (May 2002).
credit: Courtesy of Raphael Littauer.
ACO	Orsay, France	0.6+0.6	22	1967–1974	0.0001
ADONE	Frascati, Italy	1.5+1.5	105	1969–1995	0.0006
SPEAR	Stanford, California, USA	4.1+4.1	234	1972–1990	0.02
VEPP-2M	Novosibirsk, Russia	0.9+0.9	18	1975–2001	0.005
PETRA	Hamburg, Germany	22+22	2,304	1978–1987	0.02
CESR	Ithaca, New York, USA	8+8	768	1979–	1.3
DORIS–II	Hamburg, Germany	5.5+5.5	288	1979–	0.03
VEPP-4M	Novosibirsk, Russia	5.5+5.5	365	1979–	0.006
PEP	Stanford, California, USA	15+15	2,200	1980–1995	0.03
TRISTAN	Tsukuba, Japan	15+15	3,016	1987–1995	0.014
BEPC	Beijing, China	2.5+2.5	240	1988–	0.01
LEP	Geneva, Switzerland	100+100	26,659	1989–2001	0.1
SLC	Stanford, California, USA	50+50	n/a (linear)	1989–1998	0.003
PEP-II	Stanford, California, USA	9×3(10.4)	2,200	1998–	4
DAFNE	Frascati, Italy	0.51+0.51	98	1999–	0.05
KEK-B	Tsukuba, Japan	8×3.5(10.6)	3,016	1999–	7

FIGURE 3

The tall, narrow peaks of Figure 3 superimposed on the sloping curve are resonances that occur when the collision energy matches the rest energy of a specific final-state particle. Finding such a resonance can be dramatic. For example, in 1974 the event rate at SPEAR went up a hundredfold when the energy coincided with the rest energy of the J/ψ meson (consisting of a pair of charmed quarks), but the collider's energy had to be correct to within 0.00005 GeV! Once found, such resonances are a cornucopia of information about the particle, its lifetime and decay patterns, and the properties of the secondary particles in their turn. Studying rare decay modes requires a large number of "raw" events; even with a relatively large resonance production cross section, there is always a call for higher luminosity.

At the energies first reached by PETRA, particles often emerge from the collision clustered in two or three "jets." These trace back to individual collision products, confirming the presence of quarks and providing the first evidence of gluons, the essential carriers of the strong force.

The last peak on the graph, for the Z⁰ intermediate boson, comes from LEP. Measuring the lifetime of the Z⁰ (via the width in energy of its resonance) indicated that there are three, and only three, generations of light neutrinos, an important piece of information for the Standard Model.

The τ lepton—a member of the third generation in the Standard Model—was discovered at SPEAR in1976.

Toward Higher Energy

To reduce the burden of synchrotron radiation, it is tempting to think about colliding leptons more massive than electrons (and thus not so extremely relativistic). Unfortunately, the next best candidate, the muon, is unstable, with a lifetime of only 2.2 microseconds. Relativistic time dilation helps: for example, a 100-GeV muon lives for 2 milliseconds, but this is still very marginal. Creating muons and anti- muons at a sufficient rate to make up for their decay is a major challenge.

Less speculative is the use of a linear collider, avoiding rings entirely—but giving up their advantages, too. In a linear colliders there is no accumulation, ramping up to final energy, or recycling of particles: it is like single-shot injection at full energy. To recoup luminosity, the bunches must be made to cross in an extremely small spot, perhaps a few nanometers in diameter. At such densities, the beam- beam interaction becomes so strong that it is better called disruption. The bunches also radiate energy as they cross, which degrades the energy definition (and will ultimately limit the maximum energy of e⁺e^- colliders).

In a dramatic drive for quick progress, the Stanford Linear Collider (SLC) was built at the Stanford Linear Accelerator Center (SLAC), using just their single linac. Bunches of electrons and positrons were accelerated to 50 GeV in close succession and were then steered into head-on collisions by two guide-field arcs, through which they needed to pass only once. Although the complexities of bending and focusing the very small bunches limited luminosity, both high- energy and accelerator physics results were noteworthy.

Several linear collider projects are currently under development. NLC in the United States and JLC in Japan both use room-temperature copper accelerating rf cavities; TESLA in Germany uses superconducting niobium. These machines would stretch over 30 kilo- meters in total length and likely be deep underground. A facility of this size will, of necessity, be an international project. Several laboratories are conducting research on more potent (higher field) accelerating structures for a second generation of linear colliders.