Physics Archives – Page 78 of 144

A watershed: the emergence of QCD

David Gross and Frank Wilczek, when they received the Nobel prize in 2004.
Image credit: D Gross.

In a recent article, Harald Fritzsch shared his perspective on the history of the understanding of the strong interaction (CERN Courier October 2012 p21). Here, we’d like to supplement that view. Our focus is narrower but also sharper. We will discuss a brief but dramatic period during 1973–1974, when the modern theory of the strong interaction – quantum chromodynamics, or QCD – emerged, essentially in its current form. While we were active participants in that drama, we have not relied solely on memory but have carefully reviewed the contemporary literature.

At the end of 1972 there was no fundamental theory of the strong interaction – and no consensus on how to construct one. Proposals based on S-matrix philosophy, dual-resonance models, phenomenological quark models, current algebras, ideas about “partons” and chiral dynamics – the logical descendant of Hideki Yukawa’s original pion-exchange idea – created a voluminous and rapidly growing literature. None of those competing ideas, however, offered a framework in which uniquely defined calculations leading to sharp, testable predictions could be carried out. It seemed possible that strong-interaction physics would evolve along the lines of nuclear physics: one would gradually accumulate insight experimentally, and acquire command of an ever-larger range of phenomena through models and rules of thumb. An overarching theory worthy to stand beside Maxwell’s electrodynamics or Einstein’s general relativity was no more than a dream – and not a widely shared one.

Within less than two years the situation had transformed radically. We had arrived at a very specific candidate theory of the strong interaction, one based on precise, beautiful equations. And we had specific, quantitative proposals for testing it. The theoretical works ^[1–5] that were central to this transformation can be identified, we think, with considerable precision.

First clues

Let us briefly recall the key lines of evidence and thought that those works reconciled, synthesized and brought to fruition. They can be summarized under three headings: quarks and colour; scaling and partons; quantum field theory and the renormalization group.

Quarks and colour: A large body of strong-interaction phenomenology, including the particle spectrum and magnetic moments, had been organized using the idea that mesons and baryons are composite particles made from combinations of a small number of more fundamental constituents: quarks. This approach, which had its roots in the ideas of Murray Gell-Mann ^[6] and George Zweig ^[7], is reviewed in a nice book by J J J Kokkedee ^[8]. For the model to work, the quarks were required to have bizarre properties – qualitatively different from the properties of any known particles. Their electric charges had to be fractional. They had to have an extra internal “colour” degree of freedom ^[9,10]. Above all, they had to be confined. Extensive experimental searches for individual quarks gave negative results. Within the model quark–antiquark pairs made mesons, while quark–quark–quark triplets made baryons; single quarks had to be much heavier than mesons and baryons – if, indeed, they existed at all.

Scaling and partons: The famous electroproduction experiments at SLAC revealed, beginning in the late 1960s, that inclusive cross-sections did not exhibit the “soft” or “form factor” behaviour familiar in exclusive and purely hadronic processes (as explored up to that time). Richard Feynman ^[11]interpreted these experiments as indicating the existence of more fundamental point-like constituent particles within protons, which he called partons. His approach was intuitive, employing a form of impulse approximation. James Bjorken ^[12]arrived at related results earlier, using more formal operator methods (local current algebra). Current-algebra sum rules were derived using “quark–gluon” models with Abelian, flavourless gluons. The agreement of these sum rules with experimental results on electron and neutrino deep-inelastic scattering gave strong evidence that charged partons are spin 1/2 particles ^[13] and that they have baryon number 1/3 ^[14], i.e. that charged partons are quarks.

Quantum field theory and the renormalization group: Martinus Veltman and Gerardus ’t Hooft ^[15] brought powerful new tools to the study of perturbative renormalization theory, leading to a more rigorous, quantitative formulation of gauge theories of electroweak interactions. Kenneth Wilson introduced a wealth of new ideas, conveniently though rather obscurely referred to as the renormalization group, into the study of quantum field theory beyond the limits of perturbation theory. He used these ideas with great success to study critical phenomena. Neither of those developments related directly to the strong interaction problem but they formed an important intellectual background and inspiration. They showed that the possibilities for quantum field theory to describe physical behaviour were considerably richer than previously appreciated. Wilson ^[16] also sketched how his renormalization-group ideas might be used to study short-distance behaviour, with specific reference to problems in the strong interaction.

These various clues appeared to be mutually exclusive, or at least in considerable tension. The parton model is based on neglect of interference terms whose existence, however, is required by basic principles of quantum mechanics. Attempts to identify partons with dynamical quarks ^[17] were partially successful but ascribed a much more intricate structure to protons than was postulated in the simplistic quark models and unambiguously required additional, non-quark constituents. The confinement of quarks contradicted all previous experience in phenomenology. Furthermore, such behaviour could not be obtained within perturbative quantum field theory. There were numerous technical challenges in combining re-scaling transformations, as used in the renormalization group, with gauge symmetry.

But the most concrete, quantitative tension, and the one whose resolution ultimately broke the whole subject open, was the tension between the scaling behaviour observed experimentally at SLAC and the basic principles of quantum field theory. Several workers ^[18] expanded Wilson’s somewhat sketchy indications into a precise mapping between calculable properties of quantum field theories and observable aspects of inclusive cross-sections. Specifically, this work made it clear that the scaling behaviour observed at SLAC could be obtained only in quantum field theories with very small anomalous dimensions. (Strict scaling, which is equivalent to vanishing anomalous dimensions, cannot occur in a non-trivial – interacting – quantum field theory ^[19].) A few realized that approximate scaling could be achieved in an interacting quantum theory, if the effective interaction approached zero at short distances. Anthony Zee called such field theories “stagnant”(they are essentially what we now call asymptotically free theories) and he ^[20], Kurt Symanzik ^[21] and Giorgio Parisi ^[22] searched for such theories. However, none found any physically acceptable examples. Indeed, a powerful no-go result ^[23] demonstrated that no four-dimensional quantum field theory lacking non-Abelian gauge symmetry can be asymptotically free.

The tension between scaling and quantum field theory might be resolved but only within a special, limited class of theories

Our paper, submitted in April 1973 ^[1], alludes directly to these motivating issues in its opening: “Non-Abelian theories have received much attention recently as a means of constructing unified and renormalizable theories of the weak and electromagnetic interactions. In this note we report an investigation of the ultraviolet (UV) asymptotic behaviour of such theories. We have found that they possess the remarkable feature, perhaps unique among renormalizable theories, of asymptotically approaching free-field theory. Such asymptotically free theories will exhibit, for matrix elements between on-mass-shell states, Bjorken scaling. We therefore suggest that one should look to a non-Abelian gauge theory of the strong interactions to provide the explanation for Bjorken scaling, which has so far eluded field-theoretic understanding.”

Thus the tension between scaling and quantum field theory might be resolved but only within a special, limited class of theories. The paper surveys those possibilities and concludes: “One particularly appealing model is based on three triplets of fermions, with Gell-Mann’s SU(3)xSU(3) as a global symmetry and an SU(3) “colour” gauge group to provide the strong interactions. That is, the generators of the strong-interaction gauge group commute with ordinary SU(3)xSU(3) currents and mix quarks with the same isospin and hypercharge but different “colour”. In such a model the vector mesons are neutral and the structure of the operator product expansion of electromagnetic or weak currents is (assuming the strong coupling constant is in the domain of attraction of the origin!) essentially that of the free quark model (up to calculable logarithmic corrections).*” This was the first clear formulation of the theory that we know today as QCD. The footnote indicated by * refers to additional work, which became the core of our two subsequent papers ^{[3, 4]}.

David Politzer’s paper ^[2] contains calculations of the renormalization group coefficients for non-Abelian gauge theories with fermions, broadly along the same lines as in our first paper quoted above ^[1]. It does not refer to the problem of understanding scaling in the hadronic strong interaction. (The reference to “strong interactions” in the title is generic.) Politzer emphasized the importance of the converse of asymptotic freedom – that is, that the effective coupling grows at long distances. He remarks that this could lead to surprises regarding the particle content of asymptotically free theories and support dynamical symmetry breaking. Although we arrived at our results independently, we and Politzer learnt of each other’s work before publication, compared results, requested simultaneous publication and referred to one another. The paper by Howard Georgi and Politzer ^[5] adopts QCD without comment and independently derives predictions for deviations from scaling parallel to the corresponding parts of our papers ^{[3, 4]}.

Further reflections

The preceding account omits several sidelights and near misses, and lots of prehistory. But, although it is incomplete, we do not think it is distorted.

It may be appropriate to mention explicitly contributions by two extremely eminent physicists (with collaborators) that are often cited together with papers 1–5 in ways that can be misleading.

’t Hooft, together with Veltman, had developed effective methods for calculating quantum corrections in non-Abelian gauge theories. They had worked out many examples, specifically including one-loop wave function and vertex divergences ^[24]. It would not have been very difficult, as a technical matter, to re-assemble pieces of those calculations to construct calculations of renormalization group coefficients. ’t Hooft attests – and Symanzik corroborated – that he announced a negative value of the β function for non-Abelian gauge theories with fermions at a conference in Marseilles in the summer of 1972. Unfortunately, there is no record of this in the workshop proceedings, nor in the contemporary literature, so there is no documentation regarding the exact content of the announcement or its context. It had no influence on papers 1–5. In his contemporary work on the strong interaction, ’t Hooft adopted a completely different perspective from that of Gross-Wilczek and Georgi-Politzer, a perspective from which it would be very difficult to arrive at QCD and its property of asymptotic freedom as we understand them today. Specifically, ’t Hooft’s work considered a spontaneously broken gauge theory with hadrons as the fundamental objects, e.g. ρ mesons as gauge particles. His relevant publications immediately following papers 1–5 supply alternative methods for calculating renormalization group coefficients but do not propose specific physical applications.

Fig. 1. Asymptotic freedom, a principal dynamical property of QCD, predicts the logarithmic decrease of the strong interaction coupling as energy increases or distance decreases. This figure shows the current agreement of QCD predictions with many experiments.
Image credit: From figure 3 in Siegfried Bethke “World Summary of α_s (2012)” MPP-2012-132 arXiv:1210.0325 [hep-ex].

Two contributions involving Gell-Mann and collaborators are sometimes cited as sources of QCD. The first is the “Rochester Conference” at Fermilab in the summer of 1972 ^[25]. It contains two relevant presentations, Gell-Mann’s summary talk and a contributed paper with Fritzsch, entitled “Current Algebra: Quarks and What Else?” In the summary talk, SLAC scaling is mentioned and interpreted in terms of “quarks, treated formally”. The discussion is not rooted in quantum field theory; indeed, most of the discussion of the strong interaction, by far, is given over to S-matrix and dual-resonance ideas. The presentation with Fritzsch briefly mentions the possibility of using colour octet gluons, as one among several possibilities for extending light-cone current algebra (again, not within a quantum field theory).

The second contribution ^[26] appeared after 1–5 and refers to them. From a historical perspective, what is particularly revealing about it is the comment: “For us, the result that the colour octet field theory model comes closer to asymptotic scaling than the colour singlet model is interesting, but not necessarily conclusive, since we conjecture that there may be a modification at high frequencies that produces true asymptotic scaling.”

As events unfolded, the most profound and most fruitful aspects of QCD and asymptotic freedom proved to be their embodiment in a rigorously defined, quantitatively precise quantum field theory, which could be tested through its prediction of deviations from scaling. Yet just those aspects are what the authors hesitated to accept, even after they had been analysed.

The emergence of a specific, precise quantum field theory for the strong interaction – featuring beautiful equations – marked a watershed. Remarkable progress ensued on several fronts.

The realization that basic strong interaction processes at high energy could be calculated in a practical, controlled and systematically improvable way opened up many applications (figure 1). The subject now called perturbative QCD, which refines and improves parton model ideas, is a direct outgrowth of papers 1–5 but extends their scope almost beyond recognition. Perturbative QCD is the subject of several large textbooks, dozens of conference proceedings, etc. It has become the essential foundation for analysing experimental results from high-energy accelerators including, notably, the LHC. It justifies, in particular, the identification of “jets” with quarks and gluons (figure 2), and allows calculation of their production rates.

Fig. 2. Hadrons emerging from high-energy collisions at large transverse momentum occur in nearly collinear “jets”. According to QCD the jets are initiated by quarks, antiquarks, and gluons, and inherit their energy and momentum. Pictured here is an event from the CMS collaboration at the LHC, which features six jets. CCqcd2_01_13

The paradoxical heuristics of the quark model, with its juxtaposition of free-particle properties with confinement, became physically plausible and matured into a well posed mathematical problem ^[4]. For the growth of the effective coupling with increasing distance, together with the existence of formally massless (colour) charged particles, brought the theory into uncharted territory. Because uncancelled field energy threatens to build up catastrophically, it was plausible that only singlet states might emerge with finite energy. Essentially new mathematical techniques were invented to address this challenge. The most successful of these, based on direct numerical solution of the equations (so-called “lattice gauge theory”) has gone far beyond demonstrating confinement to yield sharp quantitative results for the mass spectrum and for many detailed properties of hadrons.

The equations of QCD are rooted in the same mathematics of gauge symmetry

More generally, the dramatic success of a fully realized quantum field theory in yielding a wealth of striking physical phenomena that are not evident in a linear approximation – including emergence of a dynamical scale (“mass without mass”), dynamical symmetry breaking, a rich physical spectrum and, of course, confinement – helped catalyse a renewed interest in the deep possibilities of quantum field theory. It continues to surprise us today.

Prior to papers 1–5, the behaviour of matter at ultrahigh temperatures and densities seemed utterly inaccessible to theoretical understanding. After these papers, it was understood instead to be remarkably simple. That circumstance opened up the earliest moments of the Big Bang to scientific analysis. It is the foundation of what has become a large and fruitful field: astroparticle physics.

The equations of QCD are rooted in the same mathematics of gauge symmetry ^[27] that underlies the modern theory of electroweak interactions. They are worthy to stand beside Maxwell’s equations; one might even say they are an enriched version of those equations. It becomes possible to contemplate still more extensive symmetries, unifying the different forces. The methods used to establish asymptotic freedom – specifically, running couplings – provide quantitative tools for exploring that idea. Intriguing, encouraging results have been obtained along these lines. They suggest, in particular, the possibility of low-energy supersymmetry, such as might be observed at the LHC.

ICFP 2012 opens up interdisciplinarity

CCicf1_01_13 — Participants at ICFP 2012. Image credit: Helmut Oeschler.

The International Conference on New Frontiers in Physics (ICFP) aims to promote scientific exchange between different areas of fundamental physics, with particular emphasis on future plans and related open questions. The first in the new series, ICFP 2012, which took place in Kolymbari, Crete, attracted 140 participants from fields ranging from particle physics and cosmology to quantum physics and the foundations of quantum mechanics – a discipline awarded the 2012 Nobel Prize in Physics. The following highlights reflect the main themes of the plenary talks, which were further elaborated in many parallel sessions.

One of the last conferences to hear enticing hints of an imminent Higgs-boson discovery

ICFP 2012 was one of the last conferences to hear enticing hints of an imminent Higgs-boson discovery, as the ATLAS and CMS collaborations at the LHC presented candidate signals for the Higgs boson with a local significance of 2.5–2.8σ at a mass of 125–126 GeV. At the same time, the CDF and DØ collaborations from the Tevatron at Fermilab also reported an excess near the same mass region with a local significance of 2.7σ. In other presentations, state-of-the-art theoretical calculations of the cross-section for a Standard Model Higgs boson were described, as well as a prediction for the Higgs boson mass of 121–126 GeV and the supersymmetric spectrum from finite unified theories. Implications beyond the Standard Model of both the mass and the large diphoton rate observed were also discussed. Reports on experimental searches for new physics, such as excited leptons, heavy neutrinos, new bosons, supersymmetry and gravity signatures, went further beyond the Standard Model, as did discussions of string theory and extra dimensions. Results from the LHC on di-jets accompanying vector bosons excluded at 95% confidence level the structure that the CDF experiment saw two years ago.

Talks on hadrons and QCD covered the latest lattice QCD results and presented theoretical predictions and the status of new states with heavy quarks and exotic hadrons, such as the Z_b states discovered in 2011 by the Belle experiment at KEK. The latter are consistent with a minimal content of two quarks and two antiquarks. Within a new extended quark model that has both quarks and diquarks as building blocks, new QCD effects and interpretations emerge; for example, there are no radial excitations in low-energy QCD and hadrons can shrink. Reflecting the interdisciplinary theme of the conference, one approach to the description of the QCD phase diagram that was discussed involves a holographic model; Lorentz violation and holography were also discussed.

Highlights from heavy-ion experiments confirm that the hot and dense medium created in heavy-ion collisions behaves like a strongly interacting, almost perfect liquid – the strongly interacting quark–gluon plasma. The estimates of shear viscosity are consistent with the lower bound of the anti-de Sitter/conformal field-theory correspondence. The generated flow seems to affect even heavy particles, while jets and hadrons with high-transverse momentum are strongly quenched traversing this medium. An analogy was made between the higher-order flow coefficients that originate from the initial fluctuations of the “Little Bang” in central heavy-ion collisions and the measurements of the cosmic microwave background radiation that explore the initial fluctuations of the early universe after the Big Bang. Outstanding results have come from measurements of quarkonia, such as the indication of sequential suppression of quarkonia and of possible J/ψ regeneration at the LHC. The direct Υ(1S) state is not suppressed either at Brookhaven’s Relativistic Heavy-Ion Collider (RHIC) or at the LHC, while charmonium and bottomonium states with smaller dissociation temperatures than the Υ(1S), show a suppression at both RHIC and the LHC – as expected for a deconfined plasma of quarks and gluons within a colour-screening scenario.

An overview described the status of rare decays and CP violation, while results on the latter from LHCb and other LHC experiments set strong constraints on models and led to intriguing results that await an explanation either inside or outside the Standard Model. In particular, the isospin asymmetry in B → K μ⁺μ^– differs from the expectation by 4σ, while CP violation in the charm sector shows a 3.5σ deviation from the CP-conserving hypothesis. Results from the BaBar experiment at SLAC highlight a significant excess of events in B → D*τ ν decays at 3.4σ above the Standard-Model expectation, thus ruling out the type II two-Higgs-doublet model. BaBar has also made a direct observation of time-reversal violation at the 14σ level. The CP violation seen by LHCb in D-meson decays could arise from a fourth generation of quarks and leptons.

In the neutrino sector, an overview described the status of experiments on neutrinoless double-beta decay and their expected reach. According to the “forecast” given, the claimed evidence of the signal reported in 2001 by a subset of the Heidelberg-Moscow collaboration will be checked by the GERDA experiment in the Gran Sasso National Laboratory in the near future. Currently, the EXO-200 experiment sets the most competitive limit in the field and almost completely rules out the claim. The OPERA collaboration reported on new oscillation results from the search for ν_τ appearance, preliminary limits on oscillation parameters from the search for ν_μ → ν_e and an update on the measurement of neutrino velocity. New results from the T2K experiment in Japan confirm the first evidence for ν_e appearance presented in 2011 and provide a measurement of sin²2θ₁₃. In reactor experiments, the Double Chooz collaboration presented results on sin²2θ₁₃ that exclude the non-oscillation scenario at 3.1σ, while the high-precision measurements of sin²2θ₁₃ presented by the Daya Bay collaboration exclude a zero value for θ₁₃ at more than 7σ.

The quest to dark matter

The quest to determine the nature of dark matter is a challenge at the boundary of particle physics and astrophysics. Possible hints, for example from the Fermi Gamma-ray Space Telescope and the PAMELA experiment in space, were discussed in an overview of experimental searches and theoretical implications and expectations. Other results included limits on compact halo objects as dark matter obtained from gravitational microlensing, as well as the status of the Alpha Magnetic Spectrometer (AMS-02), which has been in orbit since May 2011. The status and recent upgrades of the DAMA/LIBRA experiment and its observation at 8.9σ for a candidate signal for dark-matter particles in the galactic halo, through an annual modulation signature, were reviewed at the conference, together with detailed studies of background. Other talks covered primordial scalar perturbations via conformal mechanisms and the experimental status of the Dark Energy Survey.

At a more mathematical level, participants learnt how gravity can be viewed as emerging out of the differential calculus in non-commutative geometry, with effects that include a separation of the inertial and gravitational masses of a test particle as its mass approaches the Planck mass. Aspects of string cosmology included a review of bouncing string-cosmologies in which the Big Bang is no longer regarded as the beginning of time, as well as a presentation on how dilaton-field dominance in early epochs enlarges the cosmologically allowed parameter space for supersymmetry at the LHC.

Talks on quantum physics covered, for example, Aharonov’s two-state vector formalism, in which hidden variables may exist if the requirement of causality is relaxed to allow – under appropriate circumstances – the effects of future events on past measurements. Transaction and non-locality in quantum field theory and cosmological consequences of a de Sitter non-local vacuum, involving David Bohm’s “holomovement” ideas, were also discussed, providing a link between cosmology and quantum physics, as were classical and quantum information acquisition, measurement and the positive-operator valued measure. An overview of quantum physics with massive objects included among other topics, the possibility of testing the predictions of quantum gravity, as well as the experimental perspectives of atom–photon interactions.

The future of physics

At a broader level, an overview talk presented the European Physical Society and its activities. Moreover, looking forward to the future generations of physicists, a presentation on educational projects was given to high-school teachers in nearby Chania, the second-largest city on Crete.

Sessions during the last two days of the conference addressed the future plans of particle and nuclear physics. These included the status of the eRHIC electron–ion collider project at Brookhaven and the Nuclotron-based Ion Collider facility at JINR, as well as an overview and outlook on heavy-ion collisions at the LHC. There were also presentations on the status and plans of major particle-physics projects, namely the Muon Collider, the International Linear Collider, the Compact Linear Collider and Super B. In addition, CERN’s future plans were highlighted, as were the ideas and actions of the European Strategy for Particle Physics group and its update plan, which is currently under preparation. The conference closed with an overview of the activities of the European Committee for Future Accelerators.

To prepare not only the students but all of the audience for an interdisciplinary week, a day of lectures preceded the conference. Discussions during the sessions and more informally, then offered the possibility to explore interdisciplinary knowledge. Results from these interactions appear in the papers contributed to the conference proceedings, which will be peer reviewed and published in the EPJ Web of Conferences in 2013.

First results from proton–lead colliding beams

On 12 September, during a short, highly successful pilot run, the LHC operated with protons in one beam and lead ions in the other, so providing the LHC experiments with their first proton–nucleus collision data and opening new horizons for the heavy-ion community at CERN. During these few hours of pilot running, the ALICE experiment collected about 2 million events, sufficient not only to check the readiness of the detector for the long proton-ion run scheduled for the beginning of 2013, but also to perform a first analysis of the data and produce important physics results.

After the start of the heavy-ion physics programme in 2010, the LHC experiments obtained many striking results related to the formation of the hot and dense hadronic state of matter emerging from the collisions of lead nuclei. This state – the quark–gluon plasma (QGP) – is expected to manifest itself through various signatures, such as the suppression of high-energetic jets in the medium, collective particle motion, enhancement of strange-particle production and suppressed quarkonia production. In addition, surprising scaling effects were observed in the particle multiplicity compared with measurements at lower energies. However, given the complexity of the lead–lead (PbPb) colliding system, an important step in the quest for QGP lies in decoupling the effects of cold nuclear matter that arise at the initial stage of the collisions.

The proton–nucleus system represents the perfect benchmark for studying these effects because the colliding components are elementary and give rise to processes where the effects of the medium produced in the collision are either small or even totally absent. The collisions are also interesting because they allow the exploration of nuclear parton distributions in the region of small parton fractional momenta, which are so far unmeasured. Proton–nucleus collisions can therefore provide the data needed to understand better the properties of PbPb collisions at the energy of the LHC. The study of the dense initial state also provides access to a completely new QCD regime where the parton densities are expected to be saturated.

CCnew5_10_12 — Fig. 1. Pseudorapidity density of charged particles measured in NSD pPb collisions at √s_NN = 5.02 TeV compared with theoretical predictions.

Using the newly acquired data, the ALICE collaboration has been able to measure the charged-particle multiplicity density in proton–lead (pPb) collisions at a centre-of-mass energy of √s_NN = 5.02 TeV (ALICE collaboration 2012a). Figure 1 compares this measurement with two main groups of theoretical models. The first group consists of models that incorporate nuclear modification – for example, shadowing – of the initial parton distributions; the second includes various saturation models. While the current experimental and theoretical precision is not sufficient for a detailed comparison, the figure shows that the data are described best by the model where the gluon shadowing parameter (s_g) is tuned to previous experimental data at lower energies. Saturation models predict much steeper dependence on the pseudorapidity, which is not confirmed by the measurement.

CCnew4_10_12 — Fig. 2. The nuclear-modification factor of charged particles as a function of transverse momentum in NSD pPb collisions at √s_NN = 5.02 TeV. The data for |η_cms | < 0.3 are compared with measurements in central (0–5% centrality) and peripheral (70–80%) PbPb collisions at √s_NN = 2.76 TeV.

Another important result from the analysis of the proton–nucleus data concerns the charged-particle transverse-momentum spectrum and the corresponding nuclear-modification factor (ALICE collaboration 2012b). The latter is calculated using the proton–proton data at collision energies of 2.76 TeV and 7 TeV as reference (figure 2). The result clearly indicates little or no modification of the production of charged particles with transverse momentum greater than 2 GeV/c, thus confirming that the suppression of high-energy jets in PbPb collisions is not a result of cold nuclear-matter effects. The comparison with the available theoretical predictions suggests that the models require further development because they have difficulties in describing the multiplicity and the transverse-momentum spectrum simultaneously.

Measurement of photons stimulates quest for QGP temperature

One of the classic signals expected for a quark–gluon plasma (QGP) is the radiation of “thermal photons”, with a spectrum reflecting the temperature of the system. With a mean-free path much larger than nuclear scales, these photons leave the reaction zone created in a nucleus–nucleus collision unscathed. So, unlike hadrons, they provide a direct means to examine the early hot phase of the collision.

However, thermal photons are produced throughout the entire evolution of the reaction and also after the transition of the QGP to a hot gas of hadrons. In the PbPb collisions at the LHC, thermal photons are expected to be a significant source of photons at low energies (transverse momenta, p_T, less than around 5 GeV/c). The experimental challenge in detecting them comes from the huge background of photons from hadron decays, predominantly from the two-photon decays of neutral pions and η mesons.

CCnew7_10_12 — The transverse-momentum (p_T) spectrum of direct photons in central (0–40%) PbPb collisions at the LHC. At high p_T, the spectrum agrees with a next-to-leading-order perturbative QCD calculation. The spectrum is exponential at low p_T, with an inverse slope parameter of T = 304 ± 51 (stat.+syst.).

The ALICE experiment has measured photons produced in central PbPb collisions at a centre-of-mass energy per colliding nucleon pair, √s_NN = 2.76 TeV, by reconstructing with the time-projection chamber the tracks of e⁺e^– pairs produced by the conversion of photons in the inner detectors. The same sample of photons was also used to measure the p_T spectrum of neutral pions. The analysis found an excess of direct photons of around 15% for 1 < p_T < 5 GeV/c compared with the calculated decay-photon yields from neutral pions, η mesons and other mesons, with a somewhat larger excess at higher p_T.

Direct photons are defined as photons not coming from decays of hadrons, so photons from initial hard parton-scatterings (prompt photons and photons produced in the fragmentation of jets) – i.e. processes already present in proton–proton collisions – contribute to the signal. Indeed, for p_T greater than around 4 GeV/c, the measured spectrum agrees with that for photons from initial hard scattering obtained in a next-to-leading-order perturbative QCD calculation. For lower p_T, however, the spectrum has an exponential shape and lies significantly above the expectation for hard scattering, as the figure shows.

The inverse slope parameter measured by ALICE, T_LHC = 304 ± 51 (stat.+syst.) MeV, is larger than the value observed in gold–gold collisions at √s_NN = 0.2 TeV at Brookhaven’s Relativistic Heavy-Ion Collider (RHIC), T_RHIC = 221 ± 19 (stat.) ± 19 (syst.) MeV. In typical hydrodynamic models, this parameter corresponds to an effective temperature averaged over the time evolution of the reaction. The measured values suggest initial temperatures well above the critical temperature of 150–160 MeV (approx. 1.8 × 10¹² K) at which the transition between ordinary hadronic matter and the QGP occurs. The ALICE measurement also indicates that the LHC has produced the hottest piece of matter ever formed in a laboratory.

Leptons on the trail of the unexpected

Searches in LHC data that do not depend on specific theoretical models provide a valuable complement to optimized, model-dependent searches because they have the capacity to uncover hints of the completely unexpected. In this spirit, the ATLAS collaboration has recently looked for events with like-sign leptons and three or more leptons, using the full 2011 LHC data set of nearly 5 fb^–1, in the pursuit of signs of new physics. Unfortunately, no excess events compared against the Standard Model have been observed. However, the analyses have provided the information needed to set limits on a range of models and to set limits on the production of doubly charged Higgs bosons.

Prompt like-sign lepton pairs are rarely produced in Standard Model processes but they may be produced by fourth-generation quarks, supersymmetry, universal extra dimensions or processes in non-Standard Model Higgs models or new models. A recent study by ATLAS selected isolated electrons and muons and divided the events into dielectron, dimuon, and electron-muon categories. This analysis yielded upper limits on the cross-section of anomalous production of like-sign lepton pairs ranging between 1.7 fb and 64 fb (ATLAS 2012a). An extension to the analysis set limits on the production of doubly charged Higgs bosons decaying to pairs of electrons or muons (ATLAS 2012b).

CCnew9_10_12 — The observed 95% upper limits on the visible cross-section as a function of increasing lower bounds on missing transverse momentum, compared with the limits expected with backgrounds from the Standard Model only. The four panels show the four signal channels studied.

Events with three or more prompt leptons in the final state are also rare in the Standard Model. A recent search for multilepton events by ATLAS identified isolated electrons, isolated muons and hadronically decaying taus and found only 1827 events with three or more leptons. These events were divided into four categories; depending on whether or not a Z boson was reconstructed from two opposite-charge electrons or muons in the event, and whether or not a tau candidate was present.

The figure shows results for these four categories: the limits on the number of events from non-Standard Model sources have been calculated and converted into limits on the “visible cross-section”, i.e. the cross-section that is observable after event selection. The limits on the visible cross-section are given as a function of increasing lower bounds on the missing transverse momentum, a quantity that may be large in models with new physics. The smallest lower bound, “X”, is 0 GeV for the off-Z channels (no reconstructed Z) and 20 GeV for the on-Z channels (with reconstructed Z). Limits are shown for events with more than 100 GeV of transverse momenta for the jets in the event (H_T^jets); an upcoming publication includes the corresponding limits for lower values of H_T^jets and other variables of interest. These visible cross-section limits can be converted into upper limits on the cross-section for many specific models, including the doubly charged Higgs and new theories yet to come.

CMS homes in on the heaviest quark

The top quark is the heaviest point-like particle known. It weighs about as much as an atom of tungsten yet is an elementary building block of the Standard Model of particle physics. Its mass is one of the model’s important parameters and is directly related via radiative corrections to the masses of the W and Higgs bosons. Precise knowledge of the top quark’s mass is therefore extremely valuable to constrain theoretical models.

The CMS collaboration has measured the top-quark mass by exploiting all possible final states originating from different decays of W bosons produced in the decays of top quarks. Final states where the W boson decays into leptons are particularly “clean” (see figure). Such events are selected by requiring energetic jets in the central region of the CMS detector, of which at least one must be compatible with originating from a bottom quark (“b-tagged jet”), together with one or two isolated and high-energy leptons. The selected samples are extremely pure in top-quark-pair events, with estimated purities greater than 95% for events containing at least one electron or a muon.

CCnew11_10_12 — Example of a top-quark-pair decay chain leading to a final state with a charged lepton (e/μ) and four jets, two of which originate from the b quarks.

For hadronically decaying W bosons, the reconstruction techniques make use of kinematic fits to improve the energy resolution and the likelihood methods that can handle the combinatorial ambiguities in finding the triplet of jets corresponding to the top-quark decay. The use of b-tagging helps considerably in constraining these ambiguities further. For dilepton events, the presence of two neutrinos accompanying the charged leptons from the W-boson decays requires alternative techniques.

All of the methods and channels used give consistent measurements of the top-quark mass. The results are now fully dominated by uncertainties other than statistical, with major contributions coming from the uncertainty associated with the jet-energy scale and how well the Monte Carlo simulations model the details of the top decay. The best single measurement of the mass of the top quark, from the e/μ+jets channel, results in a statistical uncertainty of 0.4 GeV and a systematic uncertainty of around 1 GeV.

The combined CMS measurement, accounting for correlations between uncertainties obtained in the individual channels, yields a total uncertainty of about 1 GeV. This result is already competitive (and in agreement) with the combined measurement from the CDF and DØ experiments at Fermilab’s Tevatron, as the figure shows. For a further reduction of the uncertainty, it will become important to employ novel measurement techniques.

CCnew12_10_12 — The CMS measurement of the top-quark mass, using combined data from 2010 and 2011 at the centre-of-mass energy of 7 TeV, as presented at the TOP2012 conference.

The CMS collaboration has also measured the difference in mass between the top quark and its antiquark – an important test of the symmetry between matter and antimatter. This is done by splitting the sample of events with e/μ+jets into two subsamples with opposite lepton charges. The difference in quark–antiquark masses is compatible with zero with an uncertainty of about 0.5 GeV. This is the best precision on this mass difference to date.

After more than 15 years of precision top physics at the Tevatron, the baton in the race to understand nature’s heaviest quark has now passed to the LHC. With an uncertainty on the top-quark mass of 1 GeV, CMS is now at the forefront of precision physics in the top sector.

LHCb reports first 5σ observation of charm mixing

The large cross-section for charm production at the LHC, and the geometry and instrumentation of the LHCb detector, provide samples of charmed hadrons far larger than those accumulated by previous experiments. These allow the Standard Model to be tested by studying various interesting phenomena such as CP violation and mixing in D⁰ mesons.

The electroweak force can cause D⁰ mesons (consisting of a charm quark and an anti-down quark) to transform into their antiparticle, D⁰ (anti-charm and down), and back. Such “ﬂavour oscillations” or “mixing” have been observed and studied in detail in K⁰, B⁰ and B_s⁰ mesons. In the charm system, however, the period of the oscillations is so long – over one hundred times the average lifetime of a D⁰ meson – that although the BaBar, Belle and CDF collaborations have reported strong evidence of the effect, none of them has been able to claim an unambiguous observation.

CCnew14_10_12 — Decay-time evolution of the ratio WS/RS (points) with the projection of the mixing allowed (solid line) and no-mixing (dashed line) ﬁts overlaid.

One of the best channels to search for charm mixing is the decay D⁰ → Kπ. The initial ﬂavour can be identified by the charge of the accompanying pion in the decay D^*+→D⁰π⁺ or D^*–→D⁰π^–. The mixing effect appears as a decay-time dependence of the ratio R between the number of reconstructed “wrong-sign” (WS) and “right-sign” (RS) processes: D⁰→K⁺π^– and D⁰→K^–π⁺, respectively, and their charge conjugates. The WS process can proceed either by a Cabibbo-suppressed decay or through ﬂavour oscillation followed by a favoured decay. In the absence of mixing, R will be constant as a function of the D⁰ decay time, t, while, in the case of mixing, it is predicted to be an approximately parabolic function of t. Determining R in bins of t therefore allows a measurement of the mixing parameters, while also cancelling many potential sources of systematic uncertainty.

The figure shows the ratio WS/RS, measured by the LHCb experiment, as a function of decay time, from a total of 36,000 WS and 8.4 million RS decays selected from the 1.0 fb^–1 of data recorded in 2011. The horizontal dashed line shows the no-mixing hypothesis; the solid line is the best ﬁt to data when mixing is allowed. The clear time-dependence observed excludes the no-mixing hypothesis by 9.1σ. The oscillation parameters are determined with uncertainties about a factor two smaller than in previous measurements.

Since the Standard Model predictions for the mixing parameters have large uncertainties, the next step will be to focus on cleaner observables to search for possible contributions from new physics. In particular, LHCb is now well placed to investigate whether there is a CP-violating contribution to the oscillations, in contrast to the Standard Model expectation. This will be achieved by studying charm mixing in this and other decay channels and exploiting the large increase in data following the successful 2012 LHC run.

XMM-Newton discovers new source of cosmic rays

Researchers using the European X-ray astronomy satellite XMM-Newton have discovered a new source of low-energy cosmic rays in the vicinity of the Arches cluster, near the centre of the Milky Way. Their origin differs from that of higher-energy cosmic rays that originate in the explosions of supernovae.

Low-energy cosmic rays with kinetic energy less than half a billion electronvolts are not detected at Earth, since the solar wind prevents them from entering the heliosphere. Therefore little is known about their chemical composition and flux outside the solar system.

V Tatischeff, A Decourchelle and G Maurin, from the institutes of CNRS and CEA in France began by studying the X-ray emission that should theoretically be generated by low-energy cosmic rays in the interstellar medium. They then looked for signs of this in X-ray data collected by XMM-Newton since its launch in 1999. By analysing the properties of the X-ray emission of interstellar iron recorded by the satellite, they found the signature of a large population of fast-moving ions in the vicinity of the Arches cluster, about 100 light-years from the centre of the Milky Way. The stars in this cluster are travelling together at approximately 700,000 km/h. The cosmic rays are in all likelihood produced in the high-speed collision of the star cluster with a gas cloud in its path.

This is the first time that a major source of low-energy cosmic rays has been discovered outside the solar system. It shows that the shock waves of supernovae are not the only objects that can cause mass acceleration of atomic nuclei in the galaxy. These findings should make it possible to identify new sources of ions in the interstellar medium, and may lead to a better understanding of the effects of these energetic particles on star formation.

RIKEN gets clear view of element 113

Researchers at the RIKEN Nishina Center for Accelerator-based Science have obtained the most unambiguous data to date on element 113. A chain of six consecutive α decays, produced in experiments at the RIKEN Radioisotope Beam Factory, conclusively identifies the element through connections to well known daughter nuclides.

In the experiment at the RIKEN Linear Accelerator Facility in Wako, near Tokyo, Kosuke Morita and his team fired zinc ions travelling at 10% the speed of light at a thin target of bismuth and used a custom-built gas-filled recoil ion separator coupled to a position-sensitive semiconductor detector to identify the reaction products. On 12 August they detected the production of a very heavy ion followed by a chain of six consecutive α decays, which they identified as the products of an isotope of element 113. The chain began with the decay to roentgenium-274 (element 111) and ended in mendelevium-254 (element 101).

The team previously detected element 113 in experiments conducted in 2004 and 2005, but were then able to identify only four α decays followed by spontaneous fission of dubnium-262 (element 105), which is not a well known process. The decay chain detected in the latest experiments takes an alternative route via α-decay, the data indicating that the dubnium decayed into lawrencium-258 (element 103) and finally into mendelevium-254. The decay of dubnium-262 to lawrencium-258 is well known and provides unambiguous proof that element 113 is the origin of the chain.

One CP-violating phase, three beautiful results

Three independent measurements — Fig. 1. An illustration of the three independent measurements of γ, as presented at CKM2012. The colouring gives an impression of the total uncertainty based on a combination of the three results. The large black dot indicates the expectation based on measurements of other Standard Model parameters.

The last day of September saw an exciting coincidence of three competing experiments simultaneously releasing three new and directly similar results. The occasion was the CKM2012 workshop in Cincinnati and the subject of interest: excellent new measurements of the CKM phase, γ.

Two of the contenders were well known to each other, having battled for supremacy in B physics for more than a decade. The “B factory” experiments, Belle and BaBar, were designed on the same principle: e⁺e^– collisions at the Υ(4S) resonance produce large numbers of BB pairs, which can be cleanly reconstructed in isolation. Except for a few selective technology choices, their most obvious dissimilarity is their location: Belle is at KEK in Japan while BaBar resides at SLAC in the US.

The meeting in Cincinnati saw these old foes joined by a new competitor, LHCb, which unlike the B factories collects its huge samples of bottom hadrons from high-energy proton–proton collisions at the LHC. Although there is little doubt that the CERN-based experiment will ultimately triumph with precision measurements of γ, on the morning of 30 September no one yet knew if that time had come.

Among the fundamental forces of nature, the weak force is special. Not only does it have a unique structure that gives rise to fascinating and often counter-intuitive physical effects, it is also highly predictive, making it excellent territory for searches for new physics. Perhaps the most celebrated phenomenon is CP violation – a common short-hand for saying that weak interactions of matter differ subtly from those of antimatter. Discovered in 1964 as a small effect (10^–3) in K_L⁰ decays, CP violation has more recently been observed as a large effect (10^–2–10^–1) in several B-meson decay modes.

The CKM matrix

The size and variety of CP violation in b-quark transitions is widely acknowledged as a triumphant validation of the Cabibbo-Kobayashi-Maskawa (CKM) description of quarks coupling to W^±bosons. This mechanism explains three-generation quark-mixing – up-type quarks (u, c, t) transmuting to and from down-type quarks (d, s, b) via the charged weak current – in terms of a 3 × 3 matrix rotation of the quarks’ mass eigenstates into their weak-interaction eigenstates. CP violation arises naturally through the mathematically mandatory presence of one complex phase in this generically complex matrix. Furthermore, if nature indeed has only three quark generations and probability is conserved, then the CKM transformation must be unitary.

Unitary matrices have a property that the scalar product of any two rows or columns must equate to zero. In the case of the 3 × 3 CKM matrix, six equations can be written down that must hold true if there are three – and only three – generations of quarks. Of these six relations, which are all triangles on the Argand plane, the most celebrated is

V^*_ubV_ud +V^*_cbV_cd +V^*_tbV_td = 0

where each V_XY is one of nine CKM matrix elements that encode the strength with which quark X couples to quark Y. This triangle, whose internal angles are usually labelled α, β and γ, is widely publicized because it summarizes concisely the largest CP-violating processes in B mesons. Studying the geometry of this unitarity triangle (UT) tests the internal consistency of the three-generation CKM picture of quark mixing. The lengths of the sides of the UT are measured in CP-conserving processes, whereas the size of the angles (or phases) can be measured only via CP-violating decays.

In Cincinnati, the BaBar collaboration announced that it had achieved a measurement of γ = 69⁺¹⁷_–16° from a combination of many analyses of B^± → D^(*)K^± decays. The precision of around 25% can be compared with the precision with which the other two UT angles are known. The smallest of the three angles, β, is known to less than 4%, β = 21.4 ± 0.8°, principally from measuring the time-dependent CP asymmetry in the mixing and decay of B⁰→ J/ψK⁰ decays. The angle subtended by the apex of the triangle, α, is known to around 5%, α = 88.7^+4.6_–4.2°, from similar, time-dependent analyses of B⁰ → ππ and B⁰ → ρρ decays. Remembering that the three angles of a triangle always add up to 180°, it is clear that BaBar’s central value is remarkably close to the CKM expectation.

The Belle collaboration’s presentation quickly followed and explained a similar measurement of γ = 68⁺¹⁵_–14°, the modest improvement perhaps being a result of the almost twice-as-large data set. As with BaBar, this number results from the careful combination of various measurements of CP-violating properties of B^±→ DK^± and B^± → D^*K^± decays.

Interfering amplitudes

The B factories’ common choice of B^± → DK^± decays is not a coincidence. Among the current UT angle analyses, only γ measurements use direct CP violation in charged B decays. This promises a simple asymmetry of matter versus antimatter but requires two interfering amplitudes resulting in the same, indistinguishable final state. They must have different CP-conserving phases (generally true for any two quantum processes) and be of similar magnitude, or the influence of the less-likely process is too hard to detect.

Accessing γ in B± → DK± decays — ± → DK^± decays” width=”700″ height=”624″> Fig. 2. The basic principle of accessing γ in B^± → DK^± decays. Two processes of similar magnitude are needed, one based on a b → c transition and the other b → u. These two paths must arrive at an indistinguishable final state such that phase information may be accessed via quantum interference.

In the UT definition, γ is identified as the weak phase difference between b → c and b → u quark transitions. Figure 2 shows Feynman diagrams for two paths of B^± → DK^±. The one involving a b → c quark transition is labelled “favoured” because a b quark is most likely to decay to a c quark. The second diagram involves a b → u quark transition and is labelled “suppressed” because the chance of its occurrence is around 1% of that of the favoured process (i.e. the ratio of amplitudes, r_B is around 0.1).

This all looks good except for the detail in figure 2 that the favoured diagram results in a D⁰ while the suppressed diagram yields a D⁰. For the two B decays to interfere, the two neutral particles must be reconstructed in a final state that is common to both, i.e. the D⁰and D⁰should be indistinguishable. This might occur in the following ways, all of which are studied by Belle, BaBar and to some extent, LHCb.

• CP-eigenstate decays of neutral D mesons are by definition equally accessible to D⁰ and D⁰. In this case, the interference – and hence the size of the direct CP violation – is around 10% (from r_B in figure 2). Examples of this type are B^± → [K⁺K^–]_DK^± and B^± → [K_S⁰π⁰]_DK^± decays, where the D indicates that the particles in parentheses originated from a D meson.

• The unequal rate of the favoured and suppressed B decays can be redressed by selecting D final states that have an opposite suppression. Such combinations are referred to as ADS decays, after their original proponents. The most obvious example is B^± → [π^±K^+–]_DK^± decays where, importantly, the kaon from the D decay is of an opposite charge to that emanating from the B decay. In this particular case, the favoured B decay from figure 2 is followed by the doubly Cabibbo-suppressed D⁰ → π^–K⁺ decay, whereas the suppressed B decay precedes a favoured D⁰→ K⁺π^– decay. With this opposite suppression, the total ratio of amplitudes (r_B/r_D) is much closer to unity than the first case, so larger CP violation, and hence greater sensitivity to γ, is achieved.

• A third possibility considers multi-body D decays such as B^± → [K_S⁰π⁺π^–]_DK^±. In this case, the kinematics of the three-body D decay is studied across a 2D histogram, the Dalitz plot. When the D → K_S⁰π⁺π^– Dalitz plot for B^– → DK^– decays is compared with that of B⁺ → DK⁺ decays, they look identical except for a few places where γ has induced CP violation. Some places on the Dalitz plot have large sensitivity to γ, others less, but a big advantage comes from understanding the CP-conserving phases that vary smoothly across the Dalitz plot. Such an analysis is complicated, but worth it as the patterns of CP asymmetry across the Dalitz plane can be solved by only one value of γ (modulo 180°). This compares well to the first two cases whose interpretations suffer from trigonometric ambiguities because of their non-trivial sinusoidal dependence on γ.

Both the Belle and BaBar results combine all of these methods using B^± → DK^± and B^± → D^*K^± decays. This diversity is vital since the branching fraction of γ-sensitive decays is so small (proportional to |V_ub|²) and only a few hundred events have been collected in these experiments, even after a decade of operation.

Fig. 3. Invariant mass distributions of ADS candidates from LHCb. The left plots are B^– events, B⁺ events are on the right. The data, which were collected during 2011, are shown as black markers. The total fitted function is shown in blue and the signal, which exhibits a large asymmetry, is highlighted in red.

LHCb has different advantages and challenges. On one hand the huge cross-section for B production at the LHC means that LHCb has a considerable advantage in the number of charged-track-only decays that it can gather. On the other hand, because of the hadronic environment LHCb fairs less well with modes containing neutral particles. The D → K_S⁰π⁺π^– mode is still useful, but cannot be relied on as heavily as at the B factories. Modes with a π⁰ or a photon, notably the otherwise important B^± → D^*K^±, D^* → D⁰π⁰/D⁰γ suite of modes, have not yet been attempted at LHCb.

Nevertheless for the charged-track final states, such as the easiest ADS modes, LHCb has triumphed with first observations of the B^±→ [π^±K^+–]_DK^± mode (see figure 3), as well as the similarly interesting B^± → [π^±K^+–π^–π⁺]_DK^± mode. By measuring the large CP asymmetries in these modes, and with the help of an ambiguity-busting B^± → [K_S⁰π⁺π^–]_DK^± analysis, the LHCb collaboration concluded the CKM2012 session by announcing a measurement of γ = (71.1^+16.6_–15.7)° from B^± → DK^± decays.

Such exotic processes are the reason for well established phenomena such as B-mixing and flavour-changing neutral-current decays

The simple combination of these three independent results (neglecting their common systematics) leads to the conclusion that γ is known to better than 14% accuracy: γ = 69.3^+9.4_–8.8°. This is illustrated in figure 1, which also shows the remarkable similarity of the three measurements and their mutual agreement with the expectation based on the world-average values of β and α.

The concluding theme in Cincinnati was that despite LHCb’s coming of age since CKM2010, the CKM description of the quarks’ weak interactions continues to prove impressively complete. It was noted however, that many flagship B-physics measurements, including the UT angles α and β, involve processes that contain quantum loops and/or boxes. Such exotic processes are the reason for well established phenomena such as B-mixing and flavour-changing neutral-current decays. Standard Model loop-processes contain the virtual existence of high-mass particles such as W^±, top quarks and by extension, possibly non-Standard Model particles too. If they exist, and if they couple to quarks, such new-physics particles could be altering the physical behaviour of B mesons from the CKM-based expectation.

Detection of non-CKM effects is possible only if loop-sensitive observations can be compared with a gold-standard CKM process. B^± → DK^± decays provide exactly this. They are “tree-level” measurements (meaning, no loops) that are almost unique in heavy-flavour physics for their theoretical cleanliness. The measurement of γ in these modes is a measurement of γ_CKM, something the other two angles of the UT cannot boast with such certainty.

Though γ is currently the least well known UT property, by the end of this decade LHCb will have reduced its uncertainty to less than 5° (less than about 8%). By the end of the epoch of the Belle and LHCb upgrades, sub-degree precision looks likely. Such stunning precision will mean that this phase will become the CKM standard candle against which loop processes will be compared increasingly carefully.

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First clues

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The CKM matrix

Interfering amplitudes