Jobs – Page 152 of 527

Search for WISPs gains momentum

Test setup of the MADMAX experiment with sapphire plates to allow the detection of axion–photon conversion. Credit: S Knirck/MPI

Understanding the nature of dark matter is one of the most pressing problems in physics. This strangely nonreactive material is estimated, from astronomical observations, to make up 85% of all matter in the universe. The known particles of the Standard Model (SM) of particle physics, on the other hand, account for a paltry 15%.

Physicists have proposed many dark-matter candidates. Two in particular stand out because they arise in extensions of the SM that solve other fundamental puzzles, and because there are a variety of experimental opportunities to search for them. The first is the neutralino, which is the lightest supersymmetric partner of the SM neutral bosons. The second is the axion, postulated 40 years ago to solve the strong CP problem in quantum chromodynamics (QCD). While the neutralino belongs to the category of weakly interacting massive particles (WIMPs), the axion is the prime example of a very weakly interacting sub-eV particle (WISP).

Neutralinos as WIMPs have dominated the search for cold dark matter since the mid-1980s, when it was realised that massive particles with a cross section of the order of the weak interaction would result in precisely the right density to explain dark matter. There have been tremendous efforts to hunt for WIMPs both at hadron colliders, especially now at CERN’s Large Hadron Collider (LHC), and in large underground detectors, such as CDMS, CRESST, DARKSIDE, LUX, PandaX and XENON. However, up to now, no WIMP has been observed (CERN Courier July/August 2018 p9).

Fig. 1. The potential of a complex scalar field in primordial plasma in the very early universe (left) takes the form of a Sombrero (right) once the temperature drops below the symmetry- breaking scale. The energy-breaking scale corresponds to the radius of the valley from the centre, while the axion represents oscillations around one of the minima, which arise due to QCD gluon-field fluctuations.

Very light bosons as WISPs are a firm prediction of models that solve problems of the SM by the postulation of a new symmetry which is broken spontaneously in the vacuum. Such extensions contain an additional scalar field with a potential shaped like a Mexican hat – similar to the Higgs potential in the SM (figure 1). This leads to spontaneous breaking of symmetry at a scale corresponding to the radius of the trough of the hat: excitations in the direction along the trough correspond to a light Nambu–Goldstone (NG) boson, while the excitation in the radial direction perpendicular to the trough corresponds to a heavy particle with a mass determined by the symmetry-breaking scale. The strengths of the interactions between such light bosons and regular SM particles are inversely proportional to the symmetry-breaking energy scale and are therefore very weak. Being light, very weakly interacting and cold due to their non-thermal production history, these particles qualify as natural WISP cold dark-matter candidates.

Primordial production

In fact, WISP dark matter is inevitably produced in the early universe. When the temperature in the primordial plasma drops below the symmetry-breaking scale, the boson fields are frozen at a random initial value in each causally-connected region. Later, they relax towards the minimum of their potential at zero fields and oscillate around it. Since there is no significant damping of these field oscillations via decays or interactions, the bosons behave as a very cold dark-matter fluid. If symmetry breaking occurs after the likely inflationary-expansion epoch of the universe (corresponding to a post-inflationary symmetry-breaking scenario), WISP dark matter would also be produced by the decay of topological defects from the realignment of patches of the universe with random initial conditions. A huge region in parameter space spanned by WISP masses and their symmetry-breaking scales can give rise to the observed dark-matter distribution.

The axion is a particularly well-motivated example of a WISP. It was proposed to explain the results of searches for a static electric dipole moment of the neutron, which would constitute a CP-violating effect of QCD. The size of this CP-violation, parameterised by the angle θ, is predicted to have an arbitrary value between –π and π, yet experiments show its absolute value to be less than 10^–10. If θ is replaced by a dynamical field, θ(x), as proposed by Peccei and Quinn in 1977, QCD dynamics ensures that the low-energy effective potential of the axion field has an absolute minimum at θ = 0. Therefore, in vacuum, the CP violating effects due to the θ angle in QCD disappear – providing an elegant solution to the strong CP problem. The axion is the inevitable particle excitation of θ(x), and its mass is determined by the unknown breaking scale of the global symmetry.

Fig. 2. Left: diagram showing axion–photon coupling via axion–pion oscillation. Right: via the Primakoff effect, a virtual photon can be borrowed from a static magnetic field (denoted by the cross) to induce photons to convert into axions or vice versa, as first suggested by P Sikivie.

Lattice-QCD calculations performed last year precisely determined the temperature and corresponding time after the Big Bang when axion cold dark-matter could have formed as a function of the axion mass. It was found that, in the post-inflationary symmetry breaking scenario, the axion mass has to exceed 28 μeV; otherwise, the predicted amount of dark matter overshoots the observed amount. Taking into account the additional production of axion dark-matter from the decay of topological defects, an axion with a mass between 30 μeV and 10 meV may account for all of the dark matter in the universe. In the pre-inflationary symmetry breaking scenario, smaller masses are also possible.

Axions are not the only WISP species that could account for dark matter. There could be axion-like particles (ALPs), which are very similar to axions but do not solve the CP problem of QCD, or lightweight, weakly interacting, so-called hidden photons, for example. String theory suggests a plenitude of ALPs, which could have couplings to photons, leptons or light quarks.

Due to their tiny masses, WISPs might also be produced inside stars or alter the propagation of photons in the universe. Observations of stellar evolutions hint at such signals: red giants, helium-burning stars and white dwarfs seem to be experiencing unseen energy losses exceeding those expected from neutrino emission. Intriguingly, these anomalies can be explained in a unified manner by the existence of a sub-keV-mass axion or ALP with a coupling both to electrons and photons. Additionally, observations suggest that the propagation of TeV photons in the universe suffers less than expected from interactions with the extragalactic background light. This, in turn, could be explained by the conversion of photons into ALPs and back in astrophysical magnetic fields, interestingly with about the same axion–photon coupling strength as indicated by the observed stellar anomalies. Both effects have been known for almost 10 years. They are scientifically disputed, but a WISP explanation has not yet been excluded.

Experimental landscape

Most experiments searching for WISPs exploit their possible mixing with photons. Given the small masses and feeble interactions of axions and ALPs, however, building experiments that are sensitive enough to detect them is a considerable challenge. In the 1980s, Pierre Sikivie of the University of Florida in the US suggested a way forward based on the conversion of axions to photons: in a static magnetic field, the axion can “borrow” a virtual photon from the field and turn into a real photon (figure 2). Most experiments search for axions and ALPs in this way, with three main approaches being pursued: haloscopes, which look directly for dark-matter WISPs in the galactic halo of our Milky Way; helioscopes, which search for ALPs or axions emitted by the Sun; and laboratory experiments, which aim to generate and detect ALPs in a single setup.

Fig. 3. The principle of a dielectric haloscope (left) and a schematic of the proposed MADMAX setup (right). Credits: (left) Taken from PRL 118 091801; (right) MADMAX collaboration

Direct axion dark-matter searches differ in two aspects from WIMP dark-matter searches. First, axion dark matter would convert to photons, while WIMPs are scattered off matter. Second, the particle-number density for axion dark-matter, due to its low mass, is about 15 orders of magnitude larger than it is for WIMP dark matter. In fact, cold dark-matter axions and ALPs behave like a highly degenerate Bose–Einstein condensate with a de Broglie wavelength of the order of metres or kilometres for μeV and neV masses, respectively. Dark-matter axions and ALPs are thus much better pictured as a classical-field oscillation. In a magnetic field, they induce tiny electric-field oscillations with a frequency determined by the axion mass. If the de Broglie wavelength of the dark-matter axion is larger than the experimental setup, the tiny oscillations are spatially coherent in the experiment and can, in principle, be “easily” detected using a resonant microwave cavity tuned to the correct but unknown frequency. The sensitivity of such an experiment increases with the magnetic field strength squared, the volume of the cavity and its quality factor. Unfortunately, since the range of axion mass predicted by theories is huge, methods are required to tune the cavity to the frequency range corresponding to the respective axion masses.

This cavity approach has been the basis of most searches for axion dark-matter in the past decades, in particular the Axion Dark Matter Experiment (ADMX) at the University of Washington, US. Using a tuning rod inside the cavity to change the resonance frequency and, recently, by reducing noise in its detector system, the ADMX team has shown that it can reach axion dark-matter sensitivity. ADMX, which has been pioneering the field for two decades, is currently taking data and could find dark-matter axions at any time, provided the axion mass lies in the range 2–10 μeV. Meanwhile, the HAYSTAC collaboration at Yale University has very recently demonstrated that the same experimental approach can be expanded up to an axion mass of around 30 μeV. Since smaller-volume cavities (usually with lower quality factors) are needed to probe higher frequencies, however, the single-cavity approach is limited to axion masses below about 40 μeV. One novel method to probe higher masses is to use multiple matched cavities, as for example followed by the ADMX and the South Korean Center for Axion and Precision Physics.

Transitions

A different way to exploit the tiny electric-field oscillations from dark-matter axions in a strong magnetic field is to use transitions between materials with different dielectric constants: at surfaces, the axion-induced electromagnetic oscillations have a discontinuity, which is to be balanced by radiation from the surface. For a mirror with a surface area of 1 m² in a 10 T field, this would lead to an undetectable emission of around 10^–27 W if axions make up all of the dark matter. Furthermore, the emission power does not depend on the axion mass. In principle, if a parabolic mirror with a surface area of 10,000 m² could be magnetised with a 10 T field, the predicted radiation power (10^–23 W) could be focused and detected using state-of-the-art amplification techniques, but such an experiment seems impractical at present.

Fig. 4. Schematic principle of a helioscope (top) and light-shining-through-walls experiment (bottom). Credits: (top) IAXO collaboration; (bottom) A Spector

Alternatively, many magnetised dielectric discs in parallel can be placed in front of a mirror (figure 3): since the emission from all surfaces is coherent, constructive interference can boost the signal sensitivity for a given frequency range determined by the spacing between the discs. First studies performed in the past years at the Max Planck Institute for Physics in Munich have revealed that, for axion masses around 100 μeV, the sensitivity could be good enough to cover the predicted dark-matter axion mass range. The MADMAX (Magnetized Disc and Mirror Axion Experiment) collaboration, formed in October 2017, aims to use this approach to close the sensitivity gap in the well-motivated range for dark-matter axions with masses around 100 μeV. First design studies indicate that it is feasible to build a dipole magnet with the required properties using established niobium-titanium superconductor technology. As a first step, a prototype experiment is planned consisting of a booster with a reduced number of discs installed inside a prototype magnet. The experiment will be located at DESY in Hamburg, and first measurements sensitive to new ALPs parameter ranges are planned within the next few years.

Model independent searches

These direct searches for axion dark matter are very promising, but they are hampered at present by the unknown axion mass and rely on cosmological assumptions. Other, less-model dependent, experiments are required to further probe the existence of ALPs.

Fig. 5. The CAST experiment at CERN, which reuses a prototype dipole magnet from the LHC, photographed in December 2016. Credit: CERN-201612-318-35

ALPs with energies of the order of a few keV could be produced in the solar centre, and could be detected on Earth by pointing a strong dipole magnet at the Sun: axions entering the magnet could be converted into photons in the same way they are in cavity experiments. The difference is that the Sun would emit relativistic axions with an energy spectrum very similar to the thermal spectrum in its core, so experiments need to detect X-ray photons and are sensitive to axion masses up to a maximum depending on the length of the apparatus (figure 4, top). This helioscope technique was brought to the fore by the CERN Axion Solar Telescope (CAST), shown in figure 5, which began operations in 2002 and has excluded axion masses above 0.02 eV. As a successor, the International Axion Observatory (IAXO) was formally founded in July 2017 and received an advanced grant from the European Research Council earlier this year. The near-term goal of the collaboration is to build a scaled-down prototype version of the experiment, called babyIAXO, which is under discussion for possible location at DESY.

Fig. 6. Schematic of the ALPS II experiment’s final stage, which will re-use 20 HERA straightened dipoles in a section of the tunnel at DESY. Credit: DESY

The third, laboratory-based, approach to search for WISPs also aims to generate and detect ALPs without any model assumption. In the first section of such an experiment, laser light is sent through a strong magnetic field so that ALPs might be generated via interactions of optical photons with the magnetic field. The second section is separated from the first one by a light-tight wall that can only be penetrated by ALPs. These would stream through a strong magnetic field behind the wall, allowing them to be re-converted into photons and giving the impression of light shining through a wall (figure 4, bottom).

Such experiments have been performed since the early 1990s, but no hint for any ALP has shown up. Today, the most advanced project in this laboratory-based category is ALPS II, currently being set up at DESY (figure 6). This experiment will use two optical resonators implemented into the apparatus to “recycle” the light before and increase the re-conversion probability of ALPs into photons behind the wall, allowing ALPS II to reach sensitivities beyond ALP–photon coupling limits from helioscopes. It also plans to use 20 dipoles from the former HERA collider, each of which has to be mechanically straightened, to generate the magnetic field.

Gaining momentum

Fig. 7. Axion mass versus axion–photon coupling parameter space showing sensitivities and regions that could explain dark matter, stellar anomalies and TeV-transparency hints. Credit: B Majorovits

Searches for very lightweight axions and ALPs, potentially explaining all of the dark matter around us, are strongly gaining momentum. CERN has been supporting such activities in the past (with solar-axion and dark-matter searches at CAST, and the OSQAR and CROWS experiments using the shining-light-through-walls approach) and is also involved in the R&D phase for next-generation experiments such as IAXO (CERN Courier September 2014 p17). With the new initiatives of MADMAX and IAXO, both of which could be located at DESY, and the ALPS II experiment under construction there, experimental axion physics in Europe is set to probe a large fraction of a well-motivated parameter space (figure 7). In addition to complementary experiments worldwide, the next 10 years or so should shine a bright light on WISPs as the solution to the dark-matter riddle, with thrilling data runs expected to start in the early 2020s.

Cosmic Anger: Abdus Salam – The First Muslim Nobel Scientist

by Gordon Fraser. Oxford University Press. Hardback ISBN 9780199208463 £25 ($49.95).

The late Abdus Salam – the only Nobel scientist from Pakistan – came from a small place in the Punjab called Jhang. The town is also famous for “Heer-Ranjha”, a legendary love story of the Romeo-and-Juliet style that has a special romantic appeal in the countryside around the town. Salam turned out to be another “Ranjha” from Jhang, whose first love happened to be theoretical physics. Cosmic Anger, Salam’s biography by Gordon Fraser, is a new, refreshing look at the life of this scientific genius from Pakistan.

I have read several articles and books about Salam and also met him several times, but I still found Fraser’s account instructive. What I find intriguing and interesting about Cosmic Anger is first the title, and second that each chapter of the book gives sufficient background and historical settings of the events that took place in the life of Salam. In this regard the first three chapters are especially interesting, in particular the third, where the author talks about Messiahs, Mahdis and Ahmadis. This shows in a definitive way the in-depth knowledge that Fraser has about Islam and the region where Salam was born.

In chapter 10, Fraser discusses the special relationship between Salam and the former President of Pakistan, Ayub Khan. I feel that more emphasis was required about the fact that for 16 years, from 1958 to 1974, Salam had the greatest influence on the scientific policies of Pakistan. On 4 August 1959, while inaugurating the Atomic Energy Commission, President Ayub said: “In the end, I must say how happy I am to see Prof. Abdus Salam in our midst. His attainments in the field of science at such a young age are a source of pride and inspiration for us and I am sure that his association with the commission will help to impart weight and prestige to the recommendations.” Salam was involved in setting up the Atomic Energy Commission and other institutes such as the Pakistan Institute of Nuclear Science and Technology and the Space and Upper Atmosphere Research Commission in Pakistan.

Finally, I find the book to be a well written account of the achievements of a genius who was a citizen of the world, destined to play a memorable role in the global development of science and technology. At the same time, in many ways Salam was very much a Pakistani. In the face of numerous provocations and frustrations, he insisted on keeping his nationality. He loved the Pakistani culture, its language, its customs, its cuisine and its soil where he was born and is buried.

Gravitational Waves Vol 1: Theory and Experiments

By Michele Maggiore, Oxford University Press. Hardback ISBN 9780198570745 £45 ($90).

This is a complete book for a field of physics that has just reached maturity. Gravitational wave (GW) physics recently arrived at a special stage of development. On the theory side, most of the generation mechanisms have been understood and some technical controversies have been settled. On the experimental side, several large interferometers are now operating around the world, with sensitivities that could allow the first detection of GWs, even if with a relatively low probability. The GW community is also starting vigorous upgrade programmes to bring the detection probability to certitude in less than a decade from now.

The need for a textbook that treats the production and detection of GWs systematically is clear. Michele Maggiore has succeeded in doing this in a way that is fruitful not only for the young physicist starting to work in the field, but also for the experienced scientist needing a reference book for everyday work.

In the first part, on theory, he uses two complementary approaches: geometrical and field-theoretical. The text fully develops and compares both, which is of great help for a deep understanding of the nature of GWs. The author also derives all equations completely, leaving just the really straightforward algebra for the reader. A basic knowledge of general relativity and field theory is the only prerequisite.

Maggiore explains thoroughly the generation of gravitational radiation by the most important astrophysical sources, including the emitted power and its frequency distribution. One full chapter is dedicated to the Hulse-Taylor binary pulsar, which constituted the first evidence for GW emission. The “tricky” subject of post-Newtonian sources is also clearly introduced and developed. Exercises that are completely worked out conclude most of these theory chapters, enhancing the pedagogical character of the book.

The second part is dedicated to experiments and starts by setting up a background of data-analysis techniques, including noise spectral density, matched filtering, probability and statistics, all of which are applied to pulse and periodic sources and to stochastic backgrounds. Maggiore treats resonant mass detectors first, because they were the first detectors chronologically to have the capability of detecting signals, even if only strong ones originating in the neighbourhood of our galaxy. The study of resonant bar detectors is instructive and deals with issues that are also very relevant to understanding interferometers. The text clearly explains fundamental physics issues, such as approaching the quantum limits and quantum non-demolition measurements.

The last chapter is devoted to a complete and detailed study of the large interferometers – the detectors of the current generation – which should soon make the first detection of GWs. It discusses many details of these complex devices, including their coupling to gravitational waves, and it makes a careful analysis of all of the noise sources.

Lastly, it is important to remark on a little word that appears on the cover: “Volume 1”. As the author explains in the preface, he is already working on the second volume. This will appear in a few years and will be dedicated to astrophysical and cosmological sources of GWs. The level of this first book allows us to expect an interesting description of all “we can learn about nature in astrophysics and cosmology, using these tools”.

The Cosmological Singularity

By Vladimir Belinski and Marc Henneaux
Cambridge University Press

This monograph discusses at length the structure of the general solution of the Einstein equations with a cosmological singularity in Einstein-matter systems in four and higher space–time dimensions, starting from the fundamental work of Belinski (the book’s lead author), Khalatnikov and Lifshitz (BKL) – published in 1969.

The text is organised in two parts. The first, comprising chapters one to four, is dedicated to an exhaustive presentation of the BKL analysis. The authors begin deriving the oscillatory, chaotic behaviour of the general solution for pure Einstein gravity in four space–time dimensions by following the original approach of BKL. In chapters two and three, homogeneous cosmological models and the nature of the chaotic behaviour near the cosmological singularity are discussed. In these three chapters, the properties of the general solution of the Einstein equation are studied in the case of empty space in four space–time dimensions. The fourth chapter instead deals with different systems: perfect fluids in four space–time dimensions; gauge fields of the Yang–Mills and electromagnetic types and scalar fields, also in four space–time dimensions; and pure gravity in higher dimensions.

The second part of the book (chapters five to seven) is devoted to a model in which the chaotic oscillations discovered by BKL can be described in terms of a “cosmological billiard” system. In chapter five, the billiard description is provided for pure Einstein gravity in four dimensions, without any simplifying symmetry assumption, while the following chapter extends this analysis to arbitrary higher space–time dimensions and to general systems containing gravity coupled to matter fields. Finally, chapter seven covers the intriguing connection between the BKL asymptotic regime and Coxeter groups of reflections in hyperbolic space. Four appendices complete the treatment.

Quite technical and advanced, this book is meant for theoretical and mathematical physicists working on general relativity, supergravity and cosmology.

Gravitational Lensing

By Scott Dodelson
Cambridge University Press

Based on university lectures given by the author, this book provides an overview of gravitational lensing, which has emerged as a powerful tool in astronomy with numerous applications, ranging from the quest for extrasolar planets to the study of the cosmic mass distribution.

Gravitational lensing is a consequence of general relativity (GR): the gravitational field of a massive object causes light rays passing close to it to bend and refocus somewhere else. As a consequence, any treatment of this topic has to make reference to GR theory; nevertheless, as the author highlights, not much formalism is required to learn how to apply lensing to specific problems. Thus, using very little GR and not too complex mathematics, this text presents the basics of gravitational lensing, focusing on the equations needed to understand the phenomenon. It then dives into a number of applications, including multiple images, time delays, exoplanets, microlensing, cluster masses, galaxy shape measurements, cosmic shear and lensing of the cosmic microwave background.

Written with a pedagogical approach, this book is meant as a textbook for one-semester undergraduate or graduate courses. But it can also be used for independent study by researchers interested in entering this fascinating and fast-evolving field.

Quantum Fields: From the Hubble to the Planck Scale

By Michael Kachelriess
Oxford University Press

This book treats two fields of physics that are usually taught separately – quantum field theory (QFT) on one side and cosmology and gravitation on the other – in a more unified manner. Kachelriess uses this unusual approach because he is convinced that, besides studying a subject in depth, what is often difficult is to put the pieces into a general picture. Thus, he makes an effort
to introduce QFT together with its most important applications to cosmology and astroparticle physics in a coherent framework.

The path-integral approach is employed from the start and the use of tools such as Green’s functions in quantum mechanics and in scalar field-theory is illustrated. Massless spin-1 and spin-2 fields are introduced on an equal footing, and gravity is presented as a gauge theory in analogy with the Yang–Mills case. The book also deals with various concepts relevant to modern research, such as helicity methods and effective theories, as well as applications to advanced research topics.

This volume can serve as a textbook for courses in QFT, astroparticle physics and cosmology, and students interested in working at the interface between these fields can certainly appreciate the uncommon approach used. It was also the intention of the author to make the book suitable for self study, so all explanations and derivations are given in detail. Nevertheless, a solid knowledge of calculus, classical and quantum mechanics, electrodynamics and special relativity is required.

What goes up… Gravity and Scientific Method

By Peter Kosso
Cambridge University Press

Peter Kosso states that his book is “about the science of gravity and the scientific method”; I would say that it is about how scientific knowledge develops over time, using the historical evolution of our understanding of gravity as a guiding thread. The author has been a professor of philosophy and physics, with expert knowledge on how the scientific method works, and this book was born out of his classes. The topic is presented in a clear way, with certain subjects explored more than once as if to ensure that the student gets the point. The text was probably repeatedly revised to remove any wrinkles in its surface and provide smooth reading, setting out a few basic concepts along the way. The downside of this “textbook style” is that it is unexpectedly dry for a book aimed at a broad audience.

As the author explains, a scientific observation must refer to formal terms with universally-agreed meaning, ideally quantifiable in a precise and systematic way, to facilitate the testing of hypotheses. Thinking in the context of a certain theory will specify the important questions and guide the collection of data, while irrelevant factors are to be ignored (Newton’s famous apple could just as well have been an orange, for example). But theoretical guidance comes with the risk that the answers might too easily conform to the expectation and, indeed, the nontrivial give-and-take between theory and observation is a critical part of scientific practice. In particular, the author insists that it is naïve to think that a theory is abandoned or significantly revised as soon as an experimental observation disagrees with the corresponding prediction.

Considering that the scientific method is the central topic of this book, it is surprising to notice that no reference is made to Karl Popper and many other relevant thinkers; this absence is even more remarkable since, on the contrary, Thomas Kuhn is mentioned a few times. One might expect such a book to reflect a basic enlightenment principle more faithfully: the price of acquiring knowledge is that it will be distorted by the conditions of its acquisition, so that keeping a critical mind is a mandatory part of the learning process. For instance, when the reader is told that the advancement of science benefits from the authority of established science (the structural adhesive of Kuhn’s paradigm), it would have been appropriate to also mention the “genetic fallacy” committed when we infer the validity and credibility of an idea from our knowledge of its source. The author could then have pointed the interested reader to suitable literature, one option (among many) being Kuhn vs. Popper; the struggle for the soul of science by Steve Fuller.

What goes up… is certainly an excellent guide to the science of gravity and its historical evolution, from the standpoint of a 21st-century expert. It is interesting, for instance, to compare the “theories of principle” of Aristotle and Einstein with the “constructive theory” of Newton. While Newton started from a wealth of observations and looked for a universal description, unifying the falling apple with the orbiting Moon, Einstein gave more importance to the beauty of the concepts at the heart of relativity than to its empirical success. I enjoyed reading about the discovery of Neptune from the comparison between the precise observations of the orbit of Uranus and the Newtonian prediction, and about the corresponding (unsuccessful) search for the planet Vulcan, supposedly responsible for Mercury’s anomalous orbit until general relativity provided the correct explanation. And it is fascinating to read about the “direct observation” of dark matter in the context of the searches for Neptune and Vulcan. It is important (but surely not easy) to ensure “that a theory is accurate in the conditions for which it is being used to interpret the evidence”, and that it is “both well-tested and independent of any hypothesis for which the observations are used as evidence”.

The text is well written and accessible. My teenage children learned about non-Euclidean geometry from figures in the book and were intrigued by the thought that gravity is not a force field but rather a metric field, which determines the straightest possible lines (geodesics) between two points in space–time. I think, however, that progress in humankind’s understanding of gravity and related topics could be narrated in a more captivating way. People who prefer more vivid and passionate accounts of the lives and achievements of Copernicus, Brahe, Kepler, Galileo, Newton and many others would more likely enjoy The Sleepwalkers by Arthur Koestler or From the Closed World to the Infinite Universe by Alexandre Koyré. I also vehemently recommend chapter one of Only the Longest Threads by Tasneem Zehra Husain, a delightful account of Newton’s breakthrough from the perspective of someone living in the early 18th century.

Welcome to the Universe

by Neil deGrasse Tyson, Michael A Strauss and J Richard Gott
Princeton University Press

It is commonly believed that popular-science books should abstain as much as possible from using equations, apart from the most iconic ones, such as E = mc². The three authors of Welcome to the Universe boldly defy this stereotype in a book that is intended to guide readers with no previous scientific education from the very basics (the first chapters explain the scientific notation, how to round-up numbers and some trigonometry) to cutting-edge research in astrophysics and cosmology.

This book reflects the content of a course that the authors gave for a decade to non-science majors at Princeton University. They are a small dream team of teachers and authors: Tyson is a star of astrophysics outreach, Strauss a renowned observational astronomer and Gott a theoretical cosmologist with other successful popular-science books to his name. The authors split the content of the book into three equal parts (stars and planets, galaxies, relativity and cosmology), making no attempt at stylistic uniformity. Apparently this was the intention, as they keep their distinct voices and refer frequently to their own research experiences to engage the reader. Despite this, the logical flow remains coherent, with a smooth progression in complexity.

Welcome to the Universe promises and delivers a lot. Non-scientist readers will get a rare opportunity to be taken from a basic understanding of the subject to highly advanced content, not only giving them the “wow factor” (although the authors do appeal to this a lot) but also approaching the same level of depth as a masters course in physics. A representative example is the lengthy derivation of E = mc², the popular formula that everyone is familiar with but few know how to explain. And while that particular example is probably demanding to the layperson, most chapters are very pleasant to read, with a good balance of narration and analysis. The authors also make a point of explaining why recognised geniuses such as Einstein and Hawking got their fame in the first place. Scientifically-educated readers will find many insights in this volume too.

While I generally praise this book, it does have a few weak points. Some of the explanations are non-rigorous and confusing at the same time (an example of this is the sentence: “the formula has a constant h that quantises energy”). In addition, an entire chapter boasts of the role of one of the authors in the debate on whether Pluto has the status of a planet or not, which I found a bit out of place. But these issues are more irritating than harmful, and overall this book achieves an excellent balance between clarity and accuracy. The authors introduce several original analogies and provide an excellent non-technical explanation of the counterintuitive behaviour of the outer parts of a dying star, which expand while the inner parts contract.

I also appreciated the general emphasis on how measurements are done in practice, including an interesting digression on how Cavendish measured Newton’s constant more than two centuries ago. However, there are places where one feels the absence of such an explanation, for example, the practical limitations of measuring the temperatures of distant bodies are glossed over with a somewhat patronising “all kinds of technical reasons”.

This text comes with a problem book that is a real treasure trove. The exercises proposed are very diverse, reflecting the variety of audiences that the authors clearly target with their book. Some are meant to practice basic competences about units, orders of magnitude and rounding. Others demand readers to think outside of the box (e.g. by playing with geodesics in flatland, we see how to construct an object that is larger inside than outside, and have to estimate its mass using only trigonometry). For some of the quantitative exercises, the solution is provided twice: once in a lengthy way and then in a clever way. People more versed in literature than mathematics will find an exercise that demands you write a scientifically accurate, short science-fiction story (guidelines for grading are offered to the teachers) and one that simply asks, “If you could travel in time, which epoch would you visit and why?”

The book ends with a long and inspiring digression on the role of humans in the universe, and Gott’s suggestion of using the Copernican principle to predict the longevity of civilisations – and of pretty much everything – is definitely food for thought.

Loops and legs in quantum field theory

The international conference Loops and Legs in Quantum Field Theory 2018 took place from 29 April to 4 May near Rheinfels Castle in St Goar, Rhine, Germany. The conference brought together more than 100 researchers from 18 countries to discuss the latest results in precision calculations for particle physics at colliders and associated mathematical, computer-algebraic and numerical calculation technologies. It was the 14th conference in the series, with 87 talks delivered.

Organised biennially by the theory group of DESY at Zeuthen, the locations for Loops and Legs are usually remote parts of the German countryside to provide a quiet atmosphere and room for intense scientific discussions. The first conference took place in 1992, just as the HERA collider started up, and the next event, close to the start of LEP2 in 1994, concentrated on precision physics at e⁺e^– colliders. Since 1996, general precision calculations for physics at high-energy colliders form its focus.

This year, the topics covered new results on: the physics of jets; hadronic Higgs-boson and top-quark production; multi-gluon amplitudes; multi-leg two-loop QCD corrections; electroweak corrections at hadron colliders; the Z resonance in e⁺e^– scattering; soft resummation, e⁺e^– → tt̅; precision determinations of parton distribution functions; the heavy quark masses and the fundamental coupling constants; g-2; and NNLO and N³LO QCD corrections for various hard processes.

On the technologies side, analytic multi-summation methods, Mellin–Barnes techniques, the solution of large systems of ordinary differential equations and large-scale computer algebra methods were discussed, as well as unitarity methods, cut-methods in integrating Feynman integrals, and new developments in the field of elliptic integral solutions. These techniques finally allow analytic and numeric calculations of the scattering cross-sections for the key processes measured at the LHC.

All of these results are indispensable to make the LHC, in its high-luminosity phase, a real success and to help hunt down signs of physics beyond the Standard Model (CERN Courier April 2017 p18). The calculations need to match the experimental precision in measuring the couplings and masses, in particular for the top-quark and the Higgs sector, and an even more precise understanding of the strong interactions.

Since the first event, when the most advanced results were single-scale two-loop corrections in QCD, the field has taken a breath-taking leap to inclusive five-loop results – like the β functions of the Standard Model, which control the running of the coupling constant to high precision – to mention only one example. In general, the various subfields of this discipline witness a significant advance every two years or so. Many promising young physicists and mathematicians participate and present results. The field became interdisciplinary very rapidly because of the technologies needed, and now attracts many scientists from computing and mathematics.

The theoretical problems, on the other hand, also trigger new research, for example in algebraic geometry, number theory and combinatorics. This will be the case even more with future projects, like an ILC, and planned machines such as the FCC, which needs even higher precision. The next conference will be held at the beginning of May 2020.

Heavy-flavour highlights from Beauty 2018

The international conference devoted to B physics at frontier machines, Beauty 2018, was held in La Biodola, Isola d’Elba, Italy, from 6–11 May, organised by INFN Pisa. The aims of the conference series are to review the latest results in heavy-flavour physics and discuss future directions. This year’s edition, the 17th in the series, attracted around 80 scientists from all over the world. The programme comprised 58 invited talks, of which 13 were theory-based.

In recent years, several puzzling anomalies have emerged from LHCb and b-factory data (CERN Courier April 2018 p23), and discussion of these set the scene for a very inspiring atmosphere at the conference.

Heavy-flavour decays, in particular those of hadrons that contain b quarks, offer powerful probes of physics beyond the Standard Model (SM). In recent years, several puzzling anomalies have emerged from LHCb and b-factory data (CERN Courier April 2018 p23), and discussion of these set the scene for a very inspiring atmosphere at the conference. In particular, the ratio of branching fractions R_D(_*₎ = BR(B → D⁽^*⁾τν)/BR(B → D⁽^*⁾lν), where l = μ, e, provide a test of lepton universality and, intriguingly, now give combined experimental values which are about 4σ away from the SM expectations. Furthermore, the ratios R_K = BR(B⁺ → K⁺μ⁺μ^–)/BR(B⁺ → K⁺e⁺e^–) and the corresponding measurement, R_K*, yield results that are each around 2.5σ away from unity. Other potential deviations from the SM are seen in the observable, P₅´, of the angular distribution of decay products in the rare decay B⁰ → K*μ⁺μ^–, and also measurements in related decay channels. Hence, the release of new LHCb results from LHC Run 2 is eagerly awaited later this year.

The rare decay B_s → μ⁺μ^–, already observed at the 6σ level two years ago by a combined analysis of CMS and LHCb data, has now been observed by LHCb alone at a level greater than 5σ, and is consistent with the SM. The effective lifetime of the decay offers additional tests of new physics, and a first measurement has now been made: 2.04 ± 0.44 (stat) ± 0.05 (syst) ps – also consistent with the SM but with large uncertainties.

Theoretical overview talks put recent results such as those above in context. Regarding the flavour anomalies, models involving leptoquarks and new Z´ bosons are currently receiving much attention. Impressive progress has also been made in lattice-QCD calculations and in our understanding of hadronic form factors, which are crucial as inputs for theoretical predictions. Continued interplay between theory and experiment will be essential to understand the emerging data from the LHC and also from the Belle-II experiment in Japan, which has recently started taking data (CERN Courier June 2018 p7).

Concerning CP violation in the b sector, LHCb reported a new world-best determination of the angle γ of the unitarity triangle from a combination of measurements: degrees, which differs from the prediction from other unitarity-triangle constraints by around 2σ. Regarding CP violation in B_s⁰ → J/ψ φ decays, which is predicted to be very small in the SM, the experimental knowledge from a combination of LHC experiments has now reached φ_s = 21 ± 31 mrad, which is compatible with the SM.

Presentations were also devoted to hadron spectroscopy and exotic states, where there has been huge interest since the recent discovery of pentaquark-like states by LHCb (CERN Courier April 207 p31). The udsb tetraquark candidate reported by the D0 experiment at Fermilab just over two years ago has not been confirmed in LHC data and, significantly, neither by its sister experiment CDF. A plethora of other new results were reported at Beauty 2018, including from LHCb: a doubly-charmed baryon, Ξ_cc⁺⁺, and a Ξ_b^**⁻ state, as well as a spectroscopy “gold mine” of X, Y and Z states from BES-III in China. Kaon physics was also discussed. With the completion of 2016 data analysis, the NA62 experiment at CERN has reached SM-sensitivity for the ultra-rare K⁺ → π⁺νν^– decay channel. A single candidate event was found with 0.15 background events expected, and a lower limit on the branching ratio of 14 × 10⁻¹⁰ at 95% confidence has been set.

The future experimental programme of flavour physics is full of promise. One of the highlights of the conference was a report on first data from Belle-II; further exciting options will emerge beyond 2021 when LHC Run 3 commences, with LHCb running at an increased luminosity of 2 × 10³³ cm⁻²s⁻¹ with an improved trigger, and high-luminosity upgrades to ATLAS and CMS to follow. The scientific programme of Beauty 2018 was complemented by a variety of social events, which, coupled with the stimulating presentations, made the conference a huge success at this exciting time for B physics.

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