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Muons: Particles of the Moment

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Muons: Particles of the Moment FEATURES Measurements of the anomalous magnetic moment of the muon provide strong hints that the Standard Model of particle physics might be incomplete Muons: particles of the moment David W Hertzog WHEN asked what the most important strange, bottom and top; and six leptons, issue in particle physics is today, my ABORATORY namely the electron, muon and tau- colleagues offer three burning ques- L lepton plus their associated neutrinos. ATIONAL tions: What is the origin of mass? Why N A different set of particles is respon- is the universe made of matter and not sible for the interactions between these equal parts of matter and antimatter? ROOKHAVEN matter particles in the model. The elec- And is there any physics beyond the B tromagnetic interaction that binds elec- Standard Model? trons to nuclei results from the exchange The first question is being addressed of photons, whereas the strong force by a feverish quest to find the Higgs that binds quarks together inside neut- boson, which is believed to be respon- rons, protons and other hadrons is car- sible for the mass of fundamental par- ried by particles called gluons. The ticles. The Tevatron at Fermilab, which third force in the Standard Model – the is currently running, or the Large Had- weak nuclear interaction, which is re- ron Collider at CERN, which is due sponsible for radioactive decay – is car- to start experiments in 2007, should OWMAN ried by the W and Z bosons. B IPP eventually provide the answer to this R Physicists love the Standard Model, question by detecting the Higgs and but they do not like it. Although just measuring its properties – or showing about every conceivable prediction of that it does not exist. the model has turned out to be correct, The fact that the universe is domin- it seems unnatural and messy. Many ated by matter is also a mystery. It is physical parameters, such as the masses thought that equal amounts of matter of the particles, cannot be predicted and antimatter were produced in the by any rules in the model and must, Big Bang, so there must be some fun- instead, be put in “by hand”. The top damental process that led to the virtual quark, for example, is 35 000 times disappearance of antimatter. A viol- heavier than the up quark, and the ation of charge conjugation and parity other quarks have masses that lie some- (CP) symmetry is thought to be part of where in between these values with no Blueprint for new physics – muons orbiting the g–2 the answer to this question, and is being storage ring at the Brookhaven National Laboratory discernable pattern. investigated in detail at the BABAR ex- do not behave as theory predicts they should. Researchers call the model “robust” periment at Stanford in the US and the and wonder if it will ever really fail. If BELLE experiment at the KEK laboratory in Japan (see physics beyond the Standard Model is discovered, exploring Physics World July 2003 pp27–31). it will be like tapping a rich new vein in an otherwise well But it is the third question – is there new physics beyond explored mine. This will require new particle accelerators the Standard Model? – that could rock the very foundations and armies of physicists, and the cost will be significant. How of modern physics. can we test the Standard Model in such a way that these veins are revealed? One technique is to identify predictions Playing cat and mouse of the model that can be tested with extremely high preci- The Standard Model represents our current understanding of sion. If the experimental results differ from those predicted the fundamental building blocks of the universe. It identifies by the theory,it may be because the theory is incomplete. a basic set of 12 particles: six quarks called up, down, charm, The muon g – 2 experiment at the Brookhaven National P HYSICS W ORLD M ARCH 2004 physicsweb.org 29 Feynman diagrams completes a circular orbit in a magnetic field. This is precisely what the Dirac abcπ dequation predicts. In Dirac’s theory γ π the ratio of the angular momentum Z of a particle to its magnetic moment – µ µ which is called the gyromagnetic ratio, or “g-factor” – is exactly equal to two. B However, experiments in the 1940s revealed that g is slightly greater than Quantum fluctuations give rise to a change in the magnetic moment of the muon, and they two for electrons. Julian Schwinger ex- are usually represented by “Feynman diagrams”. Time flows horizontally and space is plained such deviations with an elegant represented vertically in these diagrams; the muon path is shown in blue and the theory now known as quantum electro- “fluctuation” particles are shown in green. (a) A muon emits a photon before interacting with dynamics (QED), which is widely con- a photon of the magnetic field (red), after which the muon re-absorbs the photon. The sidered to be the most precise theory in contribution of this “photon exchange” diagram can be calculated exactly using QED, and is all of physics. the dominant contribution to the muon anomaly. However, QED permits hundreds of QED permits particles to emit and re- additional diagrams involving photon and electron–positron loops, which must all be absorb “virtual photons” as they move. computed to obtain the full QED effect. This enormous task has been completed, and we This process – which is allowed by the now know the QED part of the muon anomaly to a far greater precision than our uncertainty principle – temporarily vi- experimental measurement. (b) A muon can exchange a Z boson in the same way as (a), olates the conservation of energy and although this Z exchange process is very rare because the Z is extremely massive (whereas momentum (see box). Moreover, it af- the photon is massless). This process reduces the muon anomaly by about 1.6 parts per fects how the spin of the muon changes million. Other weak-interaction diagrams are important too, such as the creation of a virtual direction, and causes the g-factor to W boson. (c) Things start to get messy when the exchanged photon momentarily produces a increase by about 1 part in 800 above pair of strongly interacting pions. This process is called hadronic vacuum polarization, and it its semiclassical value. The results of cannot be calculated using trustworthy QED. It contributes about 60 parts per million to the muon experiments tend to be given in muon anomaly, so we need to know its value with a precision of more than 1% to stay below terms of the anomalous magnetic mo- the experimental uncertainty. Fortunately, this diagram is related to reliable data from ment of the muon, which is defined as independent experiments. (d) The hadronic light-by-light scattering process is even more aµ =(g – 2)/2. complicated than the hadronic vacuum polarization, and can only be described by models. But this is only part of the story. The Although the contribution of this diagram to the muon anomaly is believed to be quite small, full extent of the muon anomaly de- its uncertainty is about half that of the measurement uncertainty. It is therefore important pends on all the different ways that a to improve this calculation. These hadronic diagrams have recently been the subject of muon can emit and re-absorb a photon. intense debate. These more complex quantum fluctu- ations correspond to higher-order “Feyn- man diagrams”. Fortunately, QED is Laboratory in Upton, New York, is an example of this ap- a rigorous theory, and with formidable effort these contri- proach. The experiment measures the motion of the spin butions to the magnetic moment of the muon can be cal- angular momentum of a muon in a magnetic field with great culated. Indeed, the anomalous magnetic moment of the precision. Meanwhile, theorists have calculated the expected electron is believed to be one of the most precisely known motion of this spin within the context of the Standard Model, quantities in physics, with theory and experiment agreeing to and also from creative extensions to the model. eight decimal places. In January this year the final result from the g – 2 experi- The fact that muons are so much heavier than electrons ment was announced, and it is tantalizingly different from means that they are far more likely to emit a heavy particle theory.It seems that the Standard Model might just be start- in one of their quantum fluctuations. The Feynman diagram ing to crack – a conclusion that has taken four years of play- in which a muon emits and re-absorbs a Z boson, for exam- ing cat and mouse with theory and experiment to reach. ple, reduces aµ by about 1.6 parts per million, which is some 40 000 times greater than the effect of the same process for A sensitive magnet an electron. This is because the contribution to the anomaly The muon is a close cousin of the electron. Both particles depends on the square of the mass ratio between a muon and have the same electric charge and both are governed by the an electron. laws of electromagnetism and the weak force. The muon is This brings us to the discovery potential for a high-precision about 200 times heavier than the electron but otherwise it muon experiment. If there exists some undiscovered family of behaves identically. When a muon – or an electron – moves massive fundamental particles that interact with muons, a in a uniform magnetic field that is perpendicular to its direc- Feynman-like diagram can be devised to account for their tion of motion, it follows a precise circular orbit.
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