When the machine runs in collider mode, one should forget the lattice,” said Norbert Siegel. “Where it all happens is at the interaction points.” Siegel is leader of the CERN group responsible for Large Hadron Collider LHC superconducting magnets other than those of the machine’s main lattice. Like other accelerators and colliders, the LHC’s magnets can be divided into two categories. Lattice magnets keep protons on course and are responsible for maintaining stable circulating beams. The rest go by the name of insertion magnets, performing specific tasks such as final focus before collision, beam cleaning, injection and extraction.
Inner triplets
For the LHC, the most complex insertion magnets are the eight so-called inner triplets that will squeeze the proton beams and bring them into collision in the centre of the four LHC experiments. The inner triplets are placed symmetrically at a distance of 23 m on either side of the interaction points, and each forms a cryogenic unit about 30 m long. They consist of four low-beta quadrupole magnets, so-named because their job is to minimize the beta-function, which is proportional to beam size, at the interaction point. Because of the special job they have to do and their proximity to the interaction points, the inner triplet magnets will be subject to unusually high heat loads. This means that a superfluid helium heat exchanger of unprecedented scale is required to keep them at their 1.9 K operating temperature.
The inner triplets are being provided as part of the US and Japanese contributions to the LHC project. They will use two types of quadrupole, along with various corrector magnets that are being supplied by CERN. One type of quadrupole is being developed at Japan’s KEK laboratory, the other at the US Fermilab, which also has the task of integrating all of the components into their cryostats. After a successful development programme using short model magnets, full- size low-beta quadrupoles have been made and were tested in May.
The first piece of hardware built by the US–LHC project, which coordinates the US contribution to the accelerator, arrived at CERN from Fermilab last year (CERN Courier November 2000 p40). A heat exchanger test unit, it had the job of verifying the design of the inner triplet cooling system. Existing data on heat exchangers of this scale being scarce, the final inner triplet design had to wait until the test unit was put through its paces at CERN, one of the few places in the world with the capacity to provide superfluid helium at the necessary flow rate. With the tests reaching a successful conclusion, the design has now been frozen and inner triplet production started at Fermilab in July. The first inner triplet is scheduled to arrive at CERN by the end of 2002.
Dedicated separators
As well as bringing the accelerator’s counter-rotating beams together, LHC insertion magnets also have to separate them after collision. This is the job of dedicated separators, and the US Brookhaven Laboratory is developing superconducting magnets for this purpose. Brookhaven is drawing on its experience of building the Relativistic Heavy Ion Collider (RHIC), which like the LHC is a superconducting machine. Consequently, these magnets will bear a close resemblance to RHIC’s main dipoles. Following a prototyping phase, full-scale manufacture has started at Brookhaven and delivery of the first superconducting separator magnets to CERN is fore seen before the end of the year.
All LHC insertions include dispersion suppressors and matching sections. The dispersion suppressors will limit the variation of beam position at the collision points caused by a spread in particle momenta, while the matching sections tailor the beam size in the insertions to the acceptance of the machine’s lattice. Dedicated insertion quadrupoles of various designs have been developed and optimized by CERN to fulfil the aperture, space and magnetic strength requirements for these tasks. All are now at the production stage in European industry, with the first due for delivery at the beginning of 2002.
Other magnets
All of the magnets discussed above are superconducting. The LHC will, however, make use of room-temperature magnets in several of its insertions. These are being provided as part of the Russian and Canadian contributions to the LHC, and they include special quadrupoles and dipoles for the beam-cleaning insertions, and beam injection and ejection magnet systems that include fast kicker magnets and steel septum magnets. The septa are all being provided by the Russian IHEP laboratory in Protvino near Moscow, where production is well under way. In the cleaning insertions, which remove beam halo particles from the circulating beams, magnets must operate at room temperature due to the harsh radiation environment. Separation dipoles for these insertions are being made by the Russian Budker Institute of Nuclear Physics in Novosibirsk, while double-aperture quadrupoles are being provided by Canada’s TRIUMF laboratory.
Finally, there is one kind of insertion magnet that plays no role in the effective working of the LHC as a collider – the huge magnet systems of the four experiments. Their magnetic fields have an influence on the beams’ trajectories and have to be compensated for by orbit compensation magnets.
Production of all of the LHC insertion magnets is now well under way. Their preparation and installation in the tunnel, along with integration with other LHC systems, such as cryogenics, vacuum and power, provide challenging work for the years ahead. When that is over and the LHC is complete, it will be a phenomenally complex machine. However, as Norbert Siegel points out, once the LHC is running, attention will be diverted from the machine, as all eyes turn to the four main experimental insertions – the key to a better under standing of our universe.
Quantum field theory is the calculus of the microworld. It consists principally of a combination of quantum mechanics and special relativity, and its main physical ingredient – the quantum field – brings together two fundamental notions of classical (and non-relativistic quantum) physics – particles and fields.
For instance, the quantum electromagnetic field, within appropriate limits, can be reduced to particle-like photons (quanta of light), or to a wave process described by a classical Lorentz field. The same is true for the quantum Dirac field.
Quantum field theory (QFT) , as the theory of interacting quantum fields, includes the remarkable phenomenon of virtual particles, which are related to virtual transitions in quantum mechanics. For example, a photon propagating through empty space (the classical vacuum) undergoes a virtual transition into an electron-positron pair. Usually, this pair undergoes the reverse transformation: annihilation back into a photon. This sequence of two transitions is known as the process of vacuum polarization (figure 1(a)). Hence the vacuum in QFT is not an empty space; it is filled by virtual particle-antiparticle pairs.
Another example of vacuum polarization is the electromagnetic interaction between two electric charges (e.g. between two electrons, or between a proton and an electron). In QFT, rather than a Coulomb force described by a potential, the interaction corresponds to an exchange of virtual photons, which, in turn, propagate in space-time accompanied by virtual electron-positron pairs (figure 1(c)). The theory of the interaction of quantum fields of radiation (photons) and of quantum Dirac fields (electrons and positrons) formulated in the early 1930s is known as quantum electrodynamics.
QFT calculation usually results in a series of terms, each of which represents the contribution of different vacuum-polarization mechanisms (illustrated by Feynman diagrams). Unfortunately, most of these terms turn out to be infinite. For example, electron-proton scattering, as well as Feynman diagram 1(b) (Møller scattering), also includes radiative corrections (figure 1(c)). This last contribution is infinite, owing to a divergence of the integral in the low wavelength/high-energy region of possible momentum values of the virtual electron-positron pair. One such infinity is the analogue of the well known infinite self-energy of the electron in classical electrodynamics.
When theorists met this problem in the 1930s, they were puzzled – the first QED approximation (e.g. for Compton scattering) produces a reasonable result (the Klein-Nishina-Tamm formula), while the second, involving more intricate vacuum-polarization effects, yields an infinite contribution.
Renormalization is discovered
The puzzle was resolved in the late 1940s, mainly by Bethe, Feynman, Schwinger and Dyson. These famous theoreticians were able to show that all infinite contributions can be grouped into a few mathematical combinations, Zi (in QED, i = 1,2), that correspond to a change of normalization of quantum fields, ultimately resulting in a redefinition (“renormalization”) of masses and coupling constants. Physically, this effect is a close analogue of a classical “dressing process” for a particle interacting with a surrounding medium.
The most important feature of renormalization is that the calculation of physical quantities gives finite functions of new “renormalized” couplings (such as electron charge) and masses, all infinities being swallowed by the Z factors of the renormalization redefinition. The “bare” values of mass and electric charge do not appear in the physical expression. At the same time the renormalized parameters should be related to the physical ones, measured experimentally.
When suitable renormalized quantum electrodynamics calculations gave results that were in precise agreement with experiment (e.g. the anomalous magnetic moment of the electron, where agreement is of the order of 1 part in 10 billion), it was clear that renormalization is a key prerequisite for a theory to give useful results.
Once the field theory infinities have been suitably excluded, the resultant finite parameters have the arbitrariness that corresponds to the possibility of various experimental measurements. For example, the electric charge of the electron measured at the Z mass (at CERN’s LEP electron-positron collider) yields the fine structure constant a as 1/128.9 (the value used in the theoretical analysis of LEP events), rather than the famous Millikan value 1/137. However, the theoretical expressions for physical quantities, like observed cross-sections, should be the same, invariant with respect to renormalization transformations equivalent to the transition from one a value to the other. In the hands of astute researchers, this invariance with respect to arbitrariness has been developed into one of the most powerful techniques of mathematical physics. (For a more technically detailed historical overview, see Shirkov 1993.)
The impressive story of an elegant mathematical method that is now widely used in various fields of theoretical and mathematical physics started just half a century ago. The first published “signal” – a two-page note by Ernest Stückelberg and André Petermann (1951), entitled “The normalization group in quantum theory” (figure 2) remained unnoticed, even by QFT experts.
However, from the mid-1950s the Renormalization Group Method to improve approximate solutions to QFT equations became a powerful tool for investigating singular behaviour in both the ultraviolet (higher energy) and infrared (lower energy) limits.
Later, this method was transferred from QFT to quantum statistics for the analysis of phase transitions and then to other fields of theoretical and mathematical physics.
In their next major article (Stückelberg & Petermann 1953), the same authors gave a clearer formulation of their discovery. They distinctly stated that, in QFT, finite renormalization transformations form a continuous group – the Lie group – for which differential Lie equations hold. Unfortunately, the paper was published in French, a language not very popular among theorists at that time. In any case, it was not mentioned in Murray Gell-Mann and Francis Low’s important paper of 1954.
A more complete and transparent picture appeared in 1955-1956 with papers by Nicolai Bogoliubov and Dmitry Shirkov. In two short Russian-language notes (Bogoliubov & Shirkov 1955a), these authors established a connection between the work of Stückelberg and Petermann and that of Gell-Mann and Low, and they devised a simple algorithm, the Renormalization Group Method (RGM – using differential group equations and the famous beta-function) for practical analysis of ultraviolet and infrared asymptotics. These results were soon published in English (Bogoliubov & Shirkov 1956a, 1956b) and then included in a special chapter of a monograph (Bogoliubov & Shirkov 1959), and from that time the RGM became an indispensable tool in the QFT analysis of asymptotic behaviour.
It was in these papers that the term “Renormalization Group” was first introduced (figure 3), as well as the central notion of the RGM algorithm – an invariant (or effective, or running) coupling. In QED, this function is just a Fourier transform of the effective electron charge squared, e2(r), first introduced by Dirac (1934).
The physical picture qualitatively corresponds to the classical electric charge, Q, inserted into polarizable media, such as electrolytes. At a distance r from the charge, due to polarization of the medium, its Coulomb field will depend on a function Q(r) – the effective charge – instead of a fixed quantity, Q. In QED, polarization is produced by vacuum quantum fluctuations. Figure 4 shows the momentum transfer evolution of QED effective coupling (a = e2/hc).
Applications in QFT
The very first applications of the RGM included the infrared and ultraviolet asymptotic analysis as well as the resolution (Bogoliubov & Shirkov 1955b) of the “ghost-problem” for renormalizable local QFT models.
The most important physical result obtained via RGM was the theoretical discovery (Gross & Wilczek 1973; Politzer 1973) of the “asymptotic freedom” of non-Abelian vector models. In contradistinction with QED, here the vacuum polarization effect has an opposite sign owing to fluctuations of non-Abelian vector mesons, such as gluons. This explained quantitatively why quarks interacted less at smaller distances, and it became a cornerstone of the theoretical QFT now known as Quantum Chromodynamics (QCD; figure 5).
Another illustration, this time more speculative, is the so-called “chart of interaction” that gave rise to the idea of the Grand Unification of strong and electroweak interactions.
At the beginning of the 1970s, Kenneth Wilson (1971) devised a specific version of the RG formalism for statistical systems. It was based on Kadanoff’s idea of “blocking”; more specifically, averaging over a small part of a big system. Mathematically, the set of blocking operations forms a discrete semigroup, different from that of QFT. The Wilson group was then used for the calculation of critical indices in phase transitions. As well as critical phenomena (in the 1970s and 1980s), it was applied to polymers, percolation, non-coherent radiation transfer, dynamical chaos and some other problems. A rather transparent motivation of Wilson’s RG facilitated this expansion. Kenneth Wilson was awarded the 1982 Nobel Prize for this work.
On the other hand, in the 1980s a more simple and general formulation of the QFT renormalization group was found (Shirkov 1982, 1984). This relates the RG symmetry to a widely known notion of mathematical physics – self-similarity. Here, the RG symmetry appears in the role of symmetry of a particular solution with respect to its reparameterization transformation. It can be treated as a functional generalization of self-similarity – functional similarity.
Later, this formulation was successfully applied to some boundary value problems of mathematical physics, such as to the problem of a self-focusing laser beam in nonlinear media (Kovalev & Shirkov 1997). Here, the RG-type symmetry solution is described by a multiparametric group, and it enables the two-dimensional structure of the solution singularity to be studied.
The Sudbury Neutrino Observatory, which started taking data in 1999, has announced its first results on solar neutrinos, which confirm the suspicion that something happens to these particles on their 150 million kilometre journey from the Sun to the Earth.
Experiments have been monitoring solar neutrinos for some 40 years. To see neutrinos at all demands a major effort, so measurements are difficult and reliable results take time to amass. As the work continued, physicists began to suspect that their experiments were not seeing as many solar neutrinos as expected – there was a “solar neutrino problem”.
Neutrinos are produced in the nuclear reactions in the Sun’s core, which provide the Sun’s energy (the radiant light and heat which make life possible is only a by-product of the Sun’s nuclear furnace). If physicists think that they understand what happens inside the Sun, they should be able to predict the number of neutrinos which arrive at the Earth. When measurements do not agree with the prediction, there is a dilemma – either we do not understand how the Sun works, or neutrinos are perverse particles that do not behave as expected.
In appraising these two alternatives, it is important to remember that, 100 years ago, physicists could not understand where the Sun got its energy from and why it hadn’t yet burned out. Only the advent of nuclear physics in the 1930s showed how nuclear transformations could supply such prodigious and enduring outputs. The neutrino concept was an initially hesitant postscript to this nuclear picture. To understand nuclear beta decay, there had to be a particle that would be very difficult to detect – if it could be detected at all. From the start, neutrinos acquired a reputation for being non conformist.
The new Sudbury results confirm that bizarre neutrino behaviour is the reason for the solar neutrino deficit – the particles are indeed living up to their non conformist reputation.
Neutrinos come in three types – electron, muon and tau – according to their subnuclear parentage. When such distinct neutrino types were first discovered, it was initially believed that each type was immutable – a neutrino born with an electron (as in beta decay or the reactions deep inside the Sun) could continue to show such electron character for ever.
However, the non conformist reputation of these particles led some far-sighted physicists to suspect that perhaps neutrinos were not immutable. Perhaps there was a small chance that a neutrino could change its allegiance in flight. A neutrino that began its journey in electron class could ‘oscillate’ and upgrade to muon class. Such changed seating arrangements en route could explain an observed deficit of electron-type solar neutrinos.
The Sudbury Neutrino Observatory (SNO) is a vessel containing 1000 tonnes of heavy water, 2000 m underground in an active nickel mine in Ontario, Canada. Particles resulting from neutrino collisions produce flashes of light that are picked up by 9500 photomultiplier tubes. The detector is sensitive to those solar neutrinos produced via the beta decay of boron-8.
The heavy water is the key – SNO is the first extraterrestrial neutrino detector to use heavy water. In one heavy water reaction (call it reaction A), an electron-type neutrino can break up a target deuteron, producing two protons and an emergent electron. Electrons can also appear from elastic scattering (reaction B), where an incoming neutrino bounces off an atomic electron, which then recoils. However, reaction B can be produced by any kind of neutrino.
Over 241 days, SNO collected 1169 neutrino events, which were carefully analysed to classify them as being due to reaction A or B.
The apparent flux of solar neutrinos measured via the observed rate for reaction A (1.75 0. ± 07 + 0.12 – 0.11 ± 0.05 x 106 cm-2 s-1, where the three sets of errors are respectively statistical, systematic and theoretical) is slightly lower than the precision measurement (2.32 ± 0.03 + 0.08 – 0.07 x 106 cm-2 s-1,) via reaction B, by the Superkamiokande detector in Japan (CERN Courier September 2000 p8 – SNO’s measurement of the rate for reaction B has not yet attained this precision). The fluxes as measured via the two reactions are different because some of the electron neutrinos produced in the Sun have “oscillated” into other types of neutrino en route, and on arrival at SNO are no longer able to trigger reaction A.
Evidence for neutrino oscillations has been seen in other situations. The SNO result is the first direct evidence for solar neutrinos oscillating on their journey to Earth. When an experiment makes its debut with such important results, its future looks assured.
The problem of obtaining a precise measurement of one of the most elusive effects in particle physics has finally been overcome. After many years of uphill struggle, with sometimes conflicting results from different experiments, the parameter that measures the tiny matter-antimatter asymmetry of quarks has been found to be non-zero with almost complete certainty (six standard deviations).
From 1997 to 1999, the big NA48 experiment at CERN patiently accumulated data from the decays of neutral kaons. A preliminary analysis using only a portion of the data (May 2000 p6) reported that the vital charge/parity (CP) violation parameter was 14 ± 4.4 x 10-4. This was in line with an earlier NA48 measurement of 18.5 ± 7.3 x 10-4, but the same quantity reported in 1998 by the KTeV experiment at Fermilab was higher at 28 ± 4.1 x 10-4. The difference between the CERN and Fermilab results was difficult to reconcile*. However, the new CERN result, 15 ± 2.7 x 10-4, based on 20 million CP-violating decays of neutral kaons, each producing a pair of pions, has far better statistics than all previous measurements.
With CP symmetry, the physics of right-handed particles is the same as that of left-handed antiparticles (and vice versa). CP symmetry was introduced in the late 1950s, when physicists were stunned to discover that weak interactions (nuclear beta decays) are not left-right symmetric. In 1964 an experiment found that CP too was flawed.
The classic stage for such experiments is the neutral kaon – an enigmatic particle-antiparticle pair distinguished only by the obscure quantum number of strangeness. However, strangeness is only conserved in strong interactions, and in weak decays the neutral kaon particle and antiparticle get mixed up.
This mixing produces two clearly distinguishable kinds of neutral kaon – a variety that decays relatively easily into two pions and is therefore short-lived, and another that cannot slip easily into two pions and instead has to struggle to decay into three pions. The latter is therefore longer lived.
The 1964 experiment by Christenson, Cronin, Fitch and Turlay found that a few long-lived kaons in every thousand disobeyed the rules and instead decayed into two pions. CP was violated.
But there could be a deeper form of CP violation at work. Instead of arriving via the quantum mechanical mixing of neutral kaons, CP violation could also happen in the underlying quark transitions that are the cause of weak decays. If so, nature would have a way of distinguishing between quarks and antiquarks.
This “direct” CP violation could have occurred immediately after the Big Bang, when subnuclear particles began to freeze out of the primordial quark-gluon soup. Such an effect could help to explain the mystery of how a universe that appears to consist only of matter could have been produced from a Big Bang, which nevertheless produced equal numbers of particles and antiparticles.
To establish whether direct CP violation occurs and to measure it, physicists must carefully compare two ratios. The first is the rate of long-lived kaons decaying into two charged pions, compared with the decay rate into two neutral kaons. The second ratio is the equivalent pion pair comparison for short-lived kaons. If these two ratios were not exactly the same, then direct CP violation would occur.
Measuring this double ratio, which involves very similar particle signatures, is extremely difficult. NA48 uses simultaneous and collinear beams of short-lived and long-lived kaons and all decays are examined inside the same region. A large magnetic spectrometer analyses the charged pions, while a liquid-krypton calorimeter analyses the production of neutral pions.
The number of neutral kaon decays collected and analysed by NA48 is far greater than in any other experiment so far. The parameter used by physicists to measure this CP violation (e‘/e) is the difference of the double ratio from unity, divided by a numerical factor. The new NA48 result is 15 ± 2.7 x 10-4. Note the small errors, compared with earlier measurements. Combined with previous NA48 data, this gives 15.3 ± 2.6 x 10-4 and contributes to a world average figure of 18 ± 2 x 10-4.
Thus direct CP violation certainly happens. The classic “indirect” CP violation discovered in 1964 happens in a few decays in every thousand, and for every thousand indirect CP violations there are a few direct CP violations. Looking at the decays of the neutral kaon and its antiparticle into two oppositely charged pions, direct CP violation gives an asymmetry of 5 ± 0.9 x 10-6. The universe can discriminate between matter and antimatter, and even the resulting tiny imbalance of a few decays per million is apparently enough to ensure the demise of Big Bang antimatter.
NA48 was brought to a halt by an accident to its high-tech carbon fibre beam pipe in 1999, but this damage has since been repaired and the experiment is set to continue its careful analysis of neutral kaon decays.
*On 8 June, the KTeV experiment at Fermilab announced a reanalysis of their earlier result, giving (23.2 ± 3.0 ± 3.2) x 10-4, and a new result of (19.8 ± 1.7 ± 2.3) x 10-4.
A strong physics case has been made for building and electron-positron linear collider with an energy range from 90 GeV up to about 1 TeV.
It was presented on 23-24 March at the TESLA Colloquium at DESY and is documented – along with a detector design – in the third volume of the TESLA Technical Design Report (the “TDR”; see DESY report 2001-011, ECFA report 2001-209).
That volume, along with the detailed supporting notes that go with it, was produced by members of the Second ECFA/DESY Study of Physics and Detectors for a Future Electron-Positron Collider, drawing on contributions from physicists from throughout Europe and around the world. Now the mandate to the study from the European Committee for Future Accelerators (ECFA) has been extended for another two years, until spring 2003.
The goals of the extended study are:
to continue to build up the active community of experimenters, theorists and machine physicists who prepared the TDR, in order to be ready to make firm proposals by 2003 for a funded programme of linear electron- positron physics up to about 1 TeV, if it is agreed to go ahead;
to complete and extend feasibility studies on important physics channels;
to review the detector’s design in the light of results from the R&D programmes that are now under way;
to interact with the accelerator’s designers on questions relating to the machine-detector interface, including backgrounds, shielding, radiation levels, beam position monitoring, luminosity measurement and energy measurement;
to look at the physics potential and technical possibilities for extensions of the programme to produce real photon-photon, electron-photon and electron-electron collisions;
to extend the work of the “LoopVerein”, developing new tools and techniques for calculating precise rates for Standard Model and supersymmetric processes that match the expected experimental precision;
to continue to make and extend contacts with physicists in the US, Asia and the rest of the world.
Wherever the collider is built, the collaborations carrying out the experiments are likely to be composed of groups from all over the world – as they were at LEP, and are at HERA, the Tevatron and the LHC.
The first workshop of the extended study will be held in Cracow, Poland, on 15-18 September 2001. Details of registration, the programme and the working groups can be found on the study’s Web page at http://www.desy.de/conferences/ecfa-desy-lcext.html. Some of the working groups on physics and detector topics are already holding their own specialized meetings.
There will be a worldwide workshop in Korea in summer 2002 – the fifth of the LCWS series, following Saariselkä, Finland 1991; Waikoloa, Hawaii 1993; Morioka, Japan 1995; Sitges, Spain 1999; and Fermilab, US 2000. An open invitation is offered to interested physicists from anywhere in the world to participate in all of these activities.
Membership of the ECFA/DESY study is likely to overlap strongly with the studies currently being carried out at CERN on the higher-energy CLIC collider. The two studies will also share tools and ideas.
The organizing committee for the extended ECFA/DESY study comprises Mikhail Danilov (ITEP, Moscow), Enrique Fernandez (Barcelona), Rolf Heuer (Hamburg), Leif Jönsson (Lund), Paolo Laurelli (Frascati), Martin Leenen (DESY), David Miller (UCL, London, chair), Walter Majerotto (Vienna), Francois Richard (Orsay), Albert de Roeck (CERN), Ron Settles (MPI, Munich), Janusz Zakrzewski (Warsaw) and Peter Zerwas (DESY).
April and May were exciting months for cosmologists, as new results brought them one step closer to unravelling the mysteries of the early universe. Observations of fluctuations in the microwave background placed important new constraints on the fundamental cosmological parameters; and for the first time, optical observations showed hints of analogous structure in matter distribution.
Cosmic microwave background radiation (CMB) dates from 300 000 years after the Big Bang, when radiation decoupled from matter. Fluctuations in the CMB are evidence for the first clumping of matter particles – the seeds of the galaxies that we see today. Plotting the observed power as a function of the angular size of contributing regions provides a constraint on
cosmological parameters.
It is predicted that this power spectrum will show a number of peaks. The first, corresponding to the largest clumps of matter in the early universe, can be used to give a constraint on W – the ratio of matter in the universe to the critical level needed to halt its expansion. Subsequent peaks give an indication of the amount of ordinary matter and dark matter in the universe.
Last year’s results from the Boomerang and Maxima balloon experiments provided a map of the first peak, and suggest that W is equal to one, which is equivalent to a flat universe. Now a new analysis of the Boomerang data has revealed other peaks that show that the amount of baryonic, or ordinary, matter is about 5%. Results from the Degree Angular Scale Interferometer, which is based at the South Pole, agree with Boomerang, lending strong support to the inflationary model of the early universe.
The two experiments also suggest that the amount of dark matter present in the universe is between 30% (Boomerang) and 65% (Maxima). These results were announced at the American Physical Society meeting in late April.
Meanwhile, astronomers using the Anglo Australian Telescope (AAT) announced observations of ripples in the matter distribution of the universe, in a structure analogous to the fluctuations in the radiation background. The discovery resulted from a survey of 170 000 galaxies carried out using the AAT’s two degree field instrument.
“What we showed was not just that there are ripples in the matter distribution, but that the strength of these ripples is enhanced at certain wavelengths related to the preference for certain angular scales in the CMB,” said John Peacock of Edinburgh. He added: “These are consistent with the effects of acoustic oscillations and allow us to rule out the higher end of the CMB range for dark matter. We prefer 5% baryons and about 30% dark matter.”
It follows from the underlying principles of quantum mechanics that the investigation of the structure of
matter at progressively smaller scales demands ever-increasing effort and ingenuity in constructing new accelerators.
As these updated machines come into operation, it becomes more and more important to as certain whether any deviation from theoretical predictions is the result of new physics or is due to extra (non-perturbative) effects within our current understanding – the Standard Model. Confronted with the difficulties of doing precise calculations, the lattice approach to quantum field theory attempts to provide a decisive test by simulating the continuum of nature with a discrete lattice of space-time points.
While this is necessarily an approximation, it is not as approximate as perturbation theory, which employs only selected terms from a series field theory expansion. Moreover, the lattice approximation can often be removed at the end in a controlled manner. However, despite its space-time economy, the lattice approach still needs the power of the world’s largest supercomputers to perform all of the calculations that are required to solve the complicated equations describing elementary particle interactions.
Berlin workshop
A recent workshop on High Performance Computing in Lattice Field Theory held at DESY Zeuthen, near Berlin, looked at the future of high-performance computing within the European lattice community. The workshop was organized by DESY and the John von Neumann Institute for Computing (NIC).
NIC is a joint enterprise between DESY and the Jülich research centre. Its elementary particle research group moved to Zeuthen on 1 October 2000 and will boost the already existing lattice gauge theory effort in Zeuthen. Although the lattice physics community in Europe is split into several groups, this arrangement fortunately does not prevent subsets of these groups working together on particular problems.
Physics potential
The workshop originated from a recommendation by working panel set up by the European Committee for Future Accelerators (ECFA) to examine the needs of high-performance computing for lattice quantum chromodynamics (QCD, the field theory of quarks and gluons; see Where did the ‘No-go’ theorems go?). It found that the physics potential of lattice field theory is within the reach of multiTeraflop machines, and the panel recommended that such machines should be developed. Another suggestion was to aim to coordinate European activities whenever possible.
Organized locally at Zeuthen by K Jansen (chair), F Jegerlehner, G Schierholz, H Simma and R Sommer, the workshop provided ample time to discuss this report. All members of the panel were present. The ECFA panel’s chairman, C Sachrajda of Southampton, gave an overview of the report, emphasizing again the main results and recommendations. The members of the ECFA panel then presented updated reports on the topics discussed in the ECFA report. These presentations laid the ground for discussions (led by K Jansen and C Sachrajda) that were lively and to some extent controversial. However, the emerging sentiment was a broad overall agreement with the ECFA panel’s conclusions.
Interpreting all of the data that results from experiments is an increasing challenge for the physics community, but lattice methods can make this process considerably easier. During the presentations made by major European lattice groups at the workshop, it became apparent that the lattice community is meeting the challenge head-on.
On behalf of the UK QCD group, R Kenway of Edinburgh dealt with a variety of aspects of QCD, which ranged from the particle spectrum to decay form factors.
Similar questions were addressed by G Schierholz of the QCDSF (QCD structure functions) group, located mainly in Zeuthen, who added a touch of colour by looking at structure functions on the lattice. R Sommer of the ALPHA collaboration, also based at Zeuthen, concentrated on the variation (“running”) of the quark-gluon coupling strength as (hence the collaboration’s name) and quark masses with the energy scale.
The chosen topic of the APE group (named after its computer) was weak decay amplitude, presented by F Rapuano of INFN/Rome. This difficult problem has gained fresh impetus following recent proposals and developments. T Lippert of the GRAL (going realistic and light) collaboration from the University of Wuppertal described the group’s attempts to explore the limit of small quark masses.
The activities of these collaborations are to a large extent coordinated by the recently launched European Network on Hadron Phenomenology from Lattice QCD.
New states of matter
Another interesting subject was explored by the EU Network for Finite Temperature Phase Transitions in Particle Physics, which is now tackling questions concerning new states of matter. These calculations are key to interpreting and guiding present and future experiments at Brookhaven’s RHIC heavy ion collider and at CERN. F Karsch and B Petersson, both from Bielefeld, presented the prospects.
The various presentations had one thing in common – all of the groups are starting to work with fully dynamical quarks and are thus going beyond the popular “quenched” approximation, which neglects internal mechanisms involving quarks.
Although this approximation works well in general, there are small differences between experiment and theory. To clarify whether these differences are signs of new physics or simply an artefact of the quenched approximation, lattice physicists now have to find additional computer power to simulate dynamical quarks – a quantum jump for the lattice community, as dynamical quarks are at least an order of magnitude more complicated.
This means that computers with multiTeraflop capacity will be required. All groups expressed their need for such computer resources in the coming years – only then can the European lattice community remain competitive with groups in Japan and the US.
Two projects that aim to realize this ambitious goal were presented at the workshop: the apeNEXT project (presented by L Tripiccione, Pisa), which is a joint collaboration of INFN in Italy with DESY and NIC in Germany and the University of Paris-sud in France; and the US-based QCDOC (QCD on a chip) project.
Ambitious computer projects
QCDOC and apeNEXT rely to a significant extent on custom-designed chips and networks, with QCDOC using a link to industry (IBM) to build machines with a performance of about 10 Tflop/s. Each of these projects is based on massively parallel architectures involving thousands of processors linked via a fast network. Both are well under way and there is strong optimism that 10 Tflop machines will be built by 2003. Apart from these big machines, the capabilities of lattice gauge theory machines based on PC clusters were discussed by K Schilling of Wuppertal and Z Fodor of Eotvos University, Budapest.
The calculations done using lattice techniques not only provide results that are interesting from a phenomenological point of view, but are also of great importance in the development of our understanding of quantum field theories in general. This aspect of lattice field theory was covered by a discussion on lattice chiral symmetry involving L Lellouch of Marseille, T Blum of Brookhaven and F Niedermayer of Bern. The structure of the QCD vacuum was covered by A DiGiacomo of Pisa.
There is great excitement in the lattice community that the coming years, with the advent of the next generation of massively parallel systems, will certainly bring new and fruitful results.
However, the proposed machines in the multiTeraflop range can only be an interim step. They will not be sufficient for generating higher-precision data for many observables. It is therefore not difficult to predict a future workshop in which lattice physicists will call for the subsequent generation of machines to reach the 100 Tflop range – a truly ambitious enterprise.
A new precision measurement of the muon’s magnetism during an experiment at Brookhaven has shown a tiny unexplained discrepancy.
The experiment is one of the few in particle physics that does not study particle scattering. A team of physicists from Germany, Japan, Russia and the US injects 3.09 GeV polarized (spin-oriented) positively charged muons from Brookhaven’s Alternating Gradient Synchrotron into a superconducting storage ring with a circumference of 14.2 m. As they circulate round the ring, the stored muons decay into positrons, which can be detected, and neutrinos, which cannot, over periods measured in microseconds.
A muon spins round an internal axis. A spinning charged particle acts like a tiny magnet, and the positrons emitted as the muons decay inside the ring reflect the magnetic behaviour of the parent particle.
Classical Dirac quantum theory of spin 1/2 particles shows that the “gyromagnetic ratio” (g) of the magnetic moment of a charged particle, such as the muon, to its spin angular momentum is exactly two. However, additional small effects can creep in to change this value, so that g-2 is not zero. Such precision magnetism measurements are collectively known as “g-2” experiments.
The additional effects mean that the muon magnets do not line up inexactly the direction of the magnetic field in the storage ring. Instead, each muon wobbles (precesses) as it circulates round the ring, and the observed positron pattern reflects these wobbles.
What are these additional magnetic effects? First, the muon’s magnetism is affected by its attendant electromagnetic cloud. The muon behaves like a heavy cousin of the electron, and the discovery in 1947 by Polycarp Kusch and Henry Foley that the electron’s g-2 is not zero provided some of the first experimental evidence for the then new theory of quantum electrodynamics. This describes the way in which charged particles like electrons and muons are surrounded by tiny clouds of additional electromagnetic effects. Quantum electrodynamics predicted exactly what the electron’s g-2 should be, and the agreement with experimental results was an impressive confirmation of the new theory.
In the 1960s and 1970s a series of precision experiments at CERN measured g-2, this time for muons, to a few parts per million. These were among the most precise particle physics results ever obtained at that time. This pioneered the idea of a storage ring in which the muons could decay.
Unlike the earlier experiments at CERN, the Brookhaven g-2 experiment injects muons into the ring. The CERN studies injected pions, which then decayed in orbit. Muon injection was suggested by the late g-2 pioneer Fred Combley.
As well as interacting electromagnetically, the muon is also affected by weak interactions. In addition, the photon – the carrier of the electromagnetic force – has a minute quark-gluon component, which is affected by the strong nuclear force. This has a further effect on the muon’s g-2.
Taking all of these effects into account, the experimental measurement at Brookhaven (to a precision of about one part per million) and the theoretical prediction differ by 2.6 times the estimated error of the measurement.
This result from Brookhaven is based on 2.9 billion muon decays carefully accumulated during 1999. Analysis of the experiment’s 2000 data sample has not yet been completed.
With such a precise result apparently differing from the theoretical prediction, those involved in the experiment may indulge in the luxury of speculation. Is additional physics being seen for the first time? Only with more g-2 information will we know.
Two major new experiments have provided the first strong indications of the delicate CP violation effect in a totally new domain – the decays of B mesons (containing the fifth or “b” quark). Exploring this still unexplained phenomenon under these conditions could provide fresh insights.
The phenomenon that physicists call CP violation ultimately distinguishes matter from antimatter. In CP (charge/parity) symmetry, the physics of left-handed particles is the same as that of right-handed antiparticles – a natural enough assumption after physicists had been shocked in 1956 to discover that nuclear beta decay is spectacularly left-right asymmetric (P-violating). However, in 1964 new experiments found that CP symmetry is also flawed. Until recently, the only way to explore CP violation was via the study of the neutral kaon, where CP violation was originally discovered in 1964. However, a new generation of experiments at the PEP-II and KEKB electron-positron colliders at SLAC, Stanford, and Tsukuba, Japan, tuned to produce copious supplies of B-mesons, has opened up a new phase of CP violation research.
These “B-factory” machines achieve unprecedented collision rates for electron-positron machines (luminosities well over 1033/cm2/s). At SLAC, the BaBar detector has studied 23 million B pairs produced by PEP-II tuned to the upsilon 4S resonance. At KEK, with KEKB tuned to the same energy, the Belle detector has investigated 11.1 million B pairs. The experiments look for CP-violating B decays, mainly into a J/psi particle and a short-lived kaon. When comparing the decays of the neutral B meson and its antiparticle, CP appears as a time-dependent asymmetry in the decays to a specific CP state.
The quark transitions responsible for CP violation are conventionally described by a 3 x 3 matrix – the Cabibbo/Kobayashi/Maskawa (CKM) matrix – the rows and columns of which correspond to the six types of quark. For the B meson system, the relevant parts of this matrix are conveniently represented by a triangle, the angles of which can be measured via CP violation effects.
One of these angles, ß, or rather sin2 ß, has been measured by the new experiments. The BaBar result is sin2 ß = 0.34 ±0.20 ±0.05, while that of Belle is 0.58 + 0.32 – 0.34 + 0.09 – 0.10. (For historical reasons, the Japanese prefer to label the angle as F1.) Combined with results from other experiments, including a measurement by the CDF detector at Fermilab’s Tevatron, the world average sin2 ß = 0.49 ±0.16, which pretty much rules out (3 standard deviations) the possibility of no CP violation at all.
In reporting this development, CERN Courier has an apology to make. First indications of these B-decay CP violation measurements were announced at last year’s International High Energy Physics Conference in Osaka. These initial measurements still had rather large errors, which meant that the provisional result was still compatible (just) with no CP violation at all. CERN Courier’s report of this meeting jumped the gun when it alleged that CP violation had been “seen” in B decays.
“It is only a 1-sigma effect,” objected the physicists, who are still stopping short of announcing a discovery. For an appraisal of these latest results, see B factories measure an eternal triangle.
The CERN Solar Axion Telescope, CAST, aims to shed light on a 30-year-old riddle of particle physics by detecting axions originating from the 15 million degree plasma in the Sun’s core. Axions were proposed as an extension to the Standard Model of particle physics to explain why CP violation – a phenomenon linked to the dominance of matter over antimatter in the universe – is observed in weak but not strong interactions – the so-called strong-CP problem.
One of the most striking consequences of this is the neutron electric dipole moment, which, due to a CP-violating term in the standard equations, is calculated to be ten orders of magnitude larger than its measured upper limit. This can be overcome by introducing a further symmetry, the spontaneous breaking of which yields the axion – a neutral pion-like particle that interacts very feebly. Owing to their potential abundance in the early universe, axions are also leading candidates for the invisible dark matter of the universe.
Searches for solar axions began a decade ago when the US Brookhaven Laboratory first pointed an axion telescope at the Sun – a highly useful source of weakly interacting particles for fundamental research, as the solar neutrino anomaly amply demonstrates. Axions would be produced in the Sun through the scattering of photons from electric charges – the Primakoff effect – and their numbers could equal those of solar neutrinos. The idea behind the Brookhaven experiment, first proposed by Pierre Sikivie, was to put the Primakoff effect to work in reverse, using a magnetic field to catalyse the conversion of solar axions back into X-ray photons of a few kilo-electronvolts.
The Brookhaven telescope was later joined by another in Tokyo, while other experiments continued the search in different ways. Experiments at Brookhaven, the Lawrence Livermore Laboratory and Kyoto, for example, search for relic axions from the early universe. CERN’s NOMAD experiment joined the hunt, looking for axion production in a neutrino beam. Searches based on axion Bragg scattering have been performed by the SOLAX collaboration using a 1 kg single crystal of germanium in an underground laboratory in Argentina, while optical detection techniques are employed by Italy’s INFN experiment, PVLAS.
This list is not complete, but, taken together, earlier experiments have scanned the kinetic energy range from 10-11 eV up to 1011 eV, so far without success. CAST, however, could make a difference because of the length and strength of the magnetic field that it will have available by using a prototype magnet for CERN’s LHC collider.
The conversion efficiency for axions increases as the square of the product of the transverse magnetic field component and its length. This makes a 9 tesla, 10 m LHC prototype dipole magnet with straight beam pipes ideal for the task, giving a conversion efficiency exceeding that of the two earlier telescopes by a factor of almost 100.
CAST’s LHC magnet will be mounted on a moving platform with X-ray detectors on either end, allowing it to observe the Sun for half an hour at sunrise and half an hour at sunset. The rest of the day will be devoted to background measurements and, through the Earth’s motion, observations of a large portion of the sky. CAST’s X-ray detectors are under development, with the collaboration looking at gas-filled and solid-state options. A chamber using the “micromegas” principle has been tested.
The aperture of the LHC magnet’s beam pipes is around five times the predicted solar axion source size, so its X-ray detectors must be correspondingly large, implying a high level of noise. To overcome this problem, the CAST collaboration is considering using X-ray lenses to focus the converted X-rays emerging parallel from the 50 mm magnet aperture to a submillimetre spot. This will bring a vast signal-to-noise improvement over the original CAST proposal and the earlier solar axion telescopes. An option to recover mirrors constructed for the German orbiting X-ray telescope ABRIXAS is being pursued.
CAST is a new departure for CERN, relying not on the lab’s expertise in accelerators but on its know-how in X-ray detection, magnets and cryogenics. With a discovery potential for axions extending beyond that dictated by astrophysical considerations, the experiment leaves room for surprises and could open up a new field of terrestrial axion astrophysics. CAST should be ready to begin its search this autumn.
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