More than 50 science organisations in Europe have written an open letter expressing concern about the impact of recent US policies on science, research and innovation. The 10 February letter, which was organised by EuroScience (founder of the EuroScience Open Forum, ESOF), asks that the principles and values that underpin scientific progress are upheld. It is addressed to the presidents of the European Council and European Commission, and prime ministers and science ministers in individual European countries.
The European Physical Society (EPS) is among the many signatories of the letter, as are the Marie Curie Alumni Association, the Royal Society and the Royal Swedish Academy of Sciences. Explaining the decision to sign, outgoing EPS president Christophe Rossel says: “Science was and will never be restrained by physical, cultural and political barriers. In our globalised world, where international scientific collaboration has become the rule, there is no place for discrimination and censorship. Any measure that restricts the freedom of movement and communication of our US colleagues will have a profound impact on science and innovation in Europe and other continents.”
Three chief concerns are outlined in the letter: the recent Executive Order discriminating against persons on the basis of their nationality; indications that US government scientists might be affected by new policies that limit their communication with the press; and the unwarranted credibility given to views that are not based on facts and sound evidence in areas such as climate science. It states that all of these are at odds with the principles of transparency, open communication and the mobility of scholars and scientists, “which are vital to scientific progress and to the benefit of our societies, economies and cultures deriving from it”.
2016 was a remarkably successful year for CERN’s Large Hadron Collider (LHC), marked by excellent peak performance, good availability and operational flexibility (CERN Courier December 2016 p5). Targeting further improvement, a thorough review of LHC operation and system performance was the focus of discussions in the first phase of the annual LHC performance workshop, which took place from 23 to 26 January in Chamonix, France.
Experts from the accelerator sector, CERN management and members of the CERN Machine Advisory Committee explored the operational scenarios for the remainder of Run 2 and made preliminary decisions regarding optics and machine parameters. Beam is due back in the LHC this year at the beginning of May, and the rest of the year will essentially be dedicated to proton–proton physics, with the usual mix of machine development and special physics runs. By quantifying the limitations to peak luminosity from electron-cloud effects, the cryogenics system and other factors, luminosity estimates for the coming years were also drawn up: in 2017, the peak luminosity should be at least 1.7 × 1034 cm–2 s–1 and the integrated luminosity target for ATLAS and CMS is 45 fb–1.
One open question about future LHC operations concerns the increase of the beam energy from 6.5 to 7 TeV per beam, which would see the machine reach its design specification. To gain input on high-field magnet behaviour, a dipole training campaign was conducted at the start of the year-end technical stop (CERN Courier March 2017 p9). Experience from this and previous training campaigns was reviewed and the duration, timing and associated risks of pushing up to 7 TeV – including implications for other accelerator systems, such as the LHC beam dump – were explored. There will be no change of beam energy in 2017 and 2018. The goal is to prepare the LHC to run at 14 TeV during Run 3 with the experiments expressing a clear preference to make the change in energy in a single step.
Regarding the longer-term future of the LHC, the High-Luminosity LHC (HL-LHC) demands challenging proton and ion beam parameters from the injector complex. The LHC injector upgrade (LIU) project is charged with planning and executing wide-ranging upgrades to the complex to meet these requirements. Both the LIU and HL-LHC projects have come through a recent cost-and-schedule review, and at present are fully funded and on schedule. The injector upgrades will be deployed during Long Shutdown 2 (LS2) in 2019/2020, while the HL-LHC will see the major part of its upgrades implemented in LS3, which is due to start in 2024.
With only two more years of operation before the next long shutdown, planning for LS2 is already well advanced. For the LHC itself, LS2 will not require the same level of intervention as seen in LS1. Nonetheless, here is still a major amount of work planned across the complex including major upgrades to the injectors in the framework of LIU, and significant upgrades to the LHC experiments.
The exploitation of the LHC and the injector complex has been impressive recently, but work across the Organization continues unabated in the push to get the best out of the LHC in both the medium and long term.
At the beginning of March, the CMS collaboration successfully replaced the heart of its detector: the pixel tracker. This innermost layer of the CMS detector, a cylindrical device containing 124 million sensitive silicon sensors that record the trajectories of charged particles, is the first to be encountered by debris from the LHC’s collisions.
The original three-layer 64 Mpix tracker, which has been in place since the LHC started operations in 2008, was designed for a lower collision rate than the LHC will deliver in the coming years. Its replacement contains an additional layer and has its first layer placed closer to the interaction point. This will enable CMS to cope with the harsher collision environment of future LHC runs, for which the detector has to simultaneously handle the products from a large number of simultaneous collisions. The new pixel detector will also be better at pinpointing where individual collisions occurred and will therefore enhance the precision with which predictions of the Standard Model can be tested. The new silicon pixel tracker being installed in the central region of the CMS detector. Image credit: M Brice/CERN.
After a week of intense activity, and a few frayed nerves, the new subdetector was safely in place by 8 March. After testing is complete, CMS will be closed ready for the LHC to return to action in May.
The excellent theoretical understanding of the production of electroweak W and Z gauge bosons in proton–proton collisions at the LHC makes these “standard-candle” processes ideal for studying the detailed performance of the ATLAS detector, and thus improves the precision on measurements. Specifically, differences in the couplings of the W+, W–, Z and γ* bosons to quarks and antiquarks appear as differences in rapidity distributions that reveal additional information about the structure of the proton.
Protons are often considered to be composed of two up quarks and one down quark, but when probed at small distances they reveal additional content. This includes a “sea” of up and down quarks, strange quarks from the heavier second generation of particles, and the gluons that bind the quarks together into the proton.
The ATLAS collaboration has now shed light on the least-known component of the proton – its content of strange quarks – based on sub-per-cent measurements of the kinematic dependencies of the W and Z boson cross-sections using LHC data recorded in 2011 at an energy of 7 TeV. Previous determinations of the strange-quark content of the proton were based on neutrino scattering, in which charged-current interaction muons from the fragmentation of charm quarks were detected. Contrary to theoretical expectations, these data revealed a suppression of strange quarks relative to the up and down quarks.
Gaining further insight into the proton structure using inclusive W and Z boson production required significant experimental improvements, with painstaking calibration efforts revealing detection efficiencies in real and simulated data at the per-mille level using both the electron and muon channels. Indeed, thanks to these studies, the ATLAS data provided a new test of electron–muon universality in the weak-interaction sector that is in excellent agreement with the Standard Model at the sub-per-cent level.
The combined electron and muon data, including the correlations of systematic uncertainties, were compared to predictions performed at next-to-next-to leading order (NNLO) in QCD and next-to-leading order in electroweak theory. Using various parton distribution functions, the comparisons revealed significant tensions between measurement and theory. Interpreting HERA-inclusive deep-inelastic-scattering data including the ATLAS data in an NNLO QCD fit pointed to a new sensitivity to the strangeness suppression factor Rs = (s + s)/(d + u), as shown in the figure. The data confirm with significantly improved precision the previous ATLAS determination of an unsuppressed strange-quark content (shown as ATLAS-epWZ12) based on 2010 data.
The result may have important implications for further precision measurements of Standard Model parameters, in particular the mass of the W boson and the weak-mixing angle, since these are affected by the second generation of quarks. The ATLAS measurement challenges the current paradigm of a suppression of the strange- compared to other light-quark distributions, but the quest continues.
Heavy-ion collisions at LHC energies create a hot and dense medium of deconfined quarks and gluons, known as the quark–gluon plasma (QGP). The QGP fireball first expands, cools and then freezes out into a collection of final-state hadrons. Correlations between the free particles carry information about the space–time extent of the emitting source, and are imprinted on the final-state spectra due to a quantum-mechanical interference effect. To measure these correlations and to determine the space–time parameters of the source, physicists utilise Hanbury Brown and Twiss (HBT) interferometry, a technique first used in astronomy for determining the angular sizes of stars. Using azimuthally differential HBT interferometry, the ALICE collaboration has recently measured the shape of the fireball at freeze-out.
In a non-central collision, the nuclear overlap region is almond shaped with the longer axis oriented perpendicular to the reaction plane (defined by the impact parameter and the beam direction). The spatial anisotropies in the initial state are converted, via pressure gradients, to momentum anisotropies, leading to anisotropic particle flow. The magnitudes of the momentum anisotropies are quantified by the so-called vn coefficients, where the second harmonic coefficient (v2) is generated from the system’s approximately elliptic shape. This is usually called elliptic flow, and the direction of the strongest component of elliptic flow is defined as the elliptic-flow plane.
The HBT radius, measured as a function of the pair-emission azimuth relative to the elliptic-flow plane, exhibits oscillations and thus provides information on the eccentricity of the source at freeze-out, when the particles cease to interact. The source eccentricity at freeze-out can be estimated from oscillations of the HBT radius at low pion-pair transverse momentum. ALICE has measured the pion HBT-radius oscillations for different transverse-momentum ranges as a function of centrality in lead–lead collisions at an energy of 2.76 TeV per nucleon pair and plotted the results as a function of the initial eccentricity (see figure on previous page).
The final eccentricities are significantly below the initial eccentricities due to a larger expansion in the in-plane direction. The freeze-out eccentricities measured by ALICE are smaller than those measured at RHIC energies, likely reflecting the longer lifetime of the system at the LHC. Hydrodynamic calculations performed for similar centralities and pair transverse-momentum ranges as in the ALICE experiment show a similar trend, but predict smaller final-source eccentricity corresponding to a more spherical source.
The final-state source eccentricity remains positive for all the pair transverse-momentum ranges, indicating that even after a stronger expansion in the in-plane direction, the pion source at freeze-out is still elongated in the out-of-plane direction. In the future, the ALICE collaboration intends to measure the azimuthal dependence of the HBT radii relative to the higher-harmonic (n ≥ 3) flow planes, which is directly sensitive to anisotropies in the system’s collective velocity fields.
The decay rate of the B0s meson to two muons is a flagship measurement in flavour physics. It is extremely rare and well predicted in the Standard Model (SM), with a branching fraction of (3.65±0.23) × 10–9. It proceeds via a loop diagram that involves the heaviest known particles: the Z and W bosons and the top quark. Any unknown heavier particles that exist are likely to also contribute to this decay, which makes it a very sensitive probe of physics beyond the SM. After three decades of unsuccessful searches, the observation of the decay was first announced in a joint paper in Nature in 2015 by the CMS and LHCb collaborations using LHC data from Run 1.
Recently the LHCb collaboration reported an improved analysis of this decay with data from 2015 and 2016 added to the Run-1 sample. Work during the long shutdown allowed significant improvements to be made in background rejection, which increased the experiment᾿s sensitivity. The B0s → μ+μ– peak is clearly visible in the resulting mass plot, with a small bump possibly due to the B0 meson to its left (see figure, top). The significance of the former is 7.8σ, corresponding to the first observation of this decay by a single experiment. At just 1.6σ, the B0 peak is not significant.
Using the well-known decays B0→ K+π– and B+→ J/ψK+ to calibrate and normalise the efficiencies, the B0s → μ+μ– branching fraction is measured to be (3.0±0.6) × 10–9, which is the most precise measurement to date. Although consistent with the SM, the experimental precision still has to improve before it matches the present theoretical accuracy.
For the first time, LHCb also measured the effective lifetime of the B0s → μ+μ– decay. The Bs meson system has much in common with that of the K0 meson, in that it exhibits a heavier long-lived state and a lighter shorter-lived state. Only the former is allowed to decay into μ+μ– in the SM, but that may not be the case in other scenarios. The contributions of the two states can be disentangled by fitting a single exponential to the lifetime distribution (figure, below). The fitted effective lifetime is consistent within 1σ with the hypothesis of only the heavier state contributing, and within 1.4σ of the opposite. While this result does not yet tell us anything about new physics, it allows the sensitivity to be extrapolated to larger data samples. With the 300 fb–1 integrated-luminosity target of the LHCb phase-II upgrade, the two states could be disentangled at the 5σ level and thus provide a new and important test of the SM.
Dark photons, are hypothetical low-mass spin-1 particles that couple to dark matter but have vanishing couplings with normal matter. Such a boson, which may be associated with a U(1) gauge symmetry in the dark sector and mix kinetically with the Standard Model photon, offers an explanation for puzzling astrophysical observations such as the positron abundance in cosmic rays reported by the PAMELA satellite. Dark photons have also been invoked as possible explanations to the muon g-2 anomaly.
Based on single-photon events in 53 fb−1 of e+e– collision data collected at the PEP-II B factory in SLAC, California, the BaBar collaboration has now completed a thorough search for these particles (Aʹ) via the process e+e–→γ Aʹ. The search was based on the assumption that the dark photon decays almost entirely to dark-matter particles and therefore that no energy would be deposited in the BaBar detector from its decay products. Finding no evidence for such processes, the analysis places 90% confidence-level upper limits on the coupling strength of Aʹ to e+e– for dark photons lighter than 8 GeV. In particular, the BaBar limits exclude values of the Aʹ coupling suggested by the dark-photon interpretation of the muon g-2 anomaly, as well as a broad range of parameters for dark-sector models (see figure).
“This paper is the final word from BaBar on a search where the dark photon decays invisibly,” says BaBar spokesperson Michael Roney. “But we are continuing to search for dark photons and other dark-sector particles that have visible decay modes.”
The BaBar result follows another direct search for sub-GeV dark photons carried out recently by CERN’s NA64 experiment, in which electrons incident on an active target probe the process e− Z → e− Z Aʹ. Again, no evidence for such decays was found, and NA64 was able to exclude dark photons with a mass less than around 0.1 GeV.
“The thing is, there are dark photons and dark photons,” says theoristSean Carroll of Caltech, who has worked on dark-photon models. “In contrast to massless dark photons, which are analogous to ordinary photons, this experiment constrains a slightly different idea of dark force-carrying particles that are associated with a broken symmetry, which therefore get a mass and then can decay. They are more like ‘dark Z bosons’ than dark photons.”
Using galaxies as vast gravitational lenses, an international group of astronomers has made an independent measurement of how fast the universe is expanding. The newly measured expansion rate is consistent with earlier findings in the local universe based on more traditional methods, but intriguingly remains higher than the value derived by the Planck satellite – a tension that could hint at new physics.
The rate at which the universe is expanding, defined by the Hubble constant, is one of the fundamental quantities in cosmology and is usually determined by techniques that use Cepheid variables and supernovae as points of reference. A group of astronomers from the H0LiCOW collaboration led by Sherry Suyu of the Max Planck Institute for Astrophysics in Germany, ASIAA in Taiwan and the Technical University of Munich, used gravitational lensing to provide an independent measurement of this constant. The gravitational lens is made of a galaxy that deforms space–time and hence bends the light travelling from a background quasar, which is an extremely luminous and variable galaxy core. This bending results in multiple images, as seen from Earth, of the same quasar that are almost perfectly aligned with the lensing galaxy (see image).
While being simple in theory, in practice the new technique is rather complex. A straightforward equation relates the Hubble constant to the length of the deflected light rays between the quasar and Earth. Since the brightness of a quasar changes over time, astronomers can see the different images of the quasar flicker at different times, and the delays between them depend on the lengths of the paths the light has taken. Deriving the Hubble constant therefore depends on very precise modelling of the distribution of the mass in the lensing galaxy, as well as on several hundred accurate measurements of the multiple images of the quasar to derive its variability pattern over many years.
A possible explanation of this discrepancy… could involve an additional source of dark radiation in the early universe.
This complexity explains why the measurement of the Hubble constant – reported in a separate publication by H0LiCOW collaborator Vivien Bonvin from the EPFL in Switzerland and co-workers – relies on a total of four papers by the H0LiCOW collaboration. The obtained value of H0 = 71.9±2.7 km s–1 Mpc–1 is in excellent agreement with other recent determinations in the local universe using classical cosmic-distance ladder methods. One of these, by Adam Riess and collaborators, finds an even higher value of the Hubble constant (H0 = 73.2±1.7 km s–1 Mpc–1) and has therefore triggered a lot of interest in recent months.
The reason is that such values are in tension with the precise determination of the Hubble constant by the Planck satellite. Assuming standard “Lambda Cold Dark Matter” cosmology, the Planck collaboration derived from the cosmic-microwave-background radiation a value of H0 = 67.9±1.5 km s–1 Mpc–1 (CERN Courier May 2013 p12). The discrepancy between Planck’s probe of the early universe and local values of the Hubble constant could be an indication that we are missing a vital ingredient in our current understanding of the universe.
A possible explanation of this discrepancy, according to Riess and colleagues, could involve an additional source of dark radiation in the early universe, corresponding to a significant increase in the effective number of neutrino species. It will be interesting to follow this debate in the coming years, when new observing facilities and also new parallax measurements of Cepheid stars by the Gaia satellite will reduce the uncertainty of the Hubble constant determination to a per cent or less.
Studying matter at the highest energies possible has transformed our understanding of the microscopic world. CERN’s Large Hadron Collider (LHC), which generates proton collisions at the highest energy ever produced in a laboratory (13 TeV), provides a controlled environment in which to search for new phenomena and to address fundamental questions about the nature of the interactions between elementary particles. Specifically, the LHC’s main detectors – ATLAS, CMS, LHCb and ALICE – allow us to measure the cross-sections of elementary processes with remarkable precision. A great challenge for theorists is to match the experimental precision with accurate theoretical predictions. This is necessary to establish the Higgs sector of the Standard Model of particle physics and to look for deviations that could signal the existence of new particles or forces. Pushing our current capabilities further is key to the success of the LHC physics programme.
Underpinning the prediction of LHC observables at the highest levels of precision are perturbative computations of cross-sections. Perturbative calculations have been carried out since the early days of quantum electrodynamics (QED) in the 1940s. Here, the smallness of the QED coupling constant is exploited to allow the expressions for physical quantities to be expanded in terms of the coupling constant – giving rise to a series of terms with decreasing magnitude. The first example of such a calculation was the one-loop QED correction to the magnetic moment of the electron, which was carried out by Schwinger in 1948. It demonstrated for the first time that QED was in agreement with the experimental discovery of the anomalous magnetic moment of the electron, ge-2 (the latter quantity was dubbed “anomalous” precisely because, prior to Schwinger’s calculation, it did not agree with predictions from Dirac’s theory). In 1957, Sommerfeld and Petermann computed the two-loop correction, and it took another 40 years until, in 1996, Laporta and Remiddi computed analytically the three-loop corrections to ge-2 and, 10 years later, even the four- and five-loop corrections were computed numerically by Kinoshita et al. The calculation of QED corrections is supplemented with predictions for electroweak and hadronic effects, and makes ge-2 one of the best known quantities today. Since ge-2 is also measured with remarkable precision, it provides the best determination of the fine-structure constant with an error of about 0.25 ppb. This determination agrees with other determinations, which reach an accuracy of 0.66 ppb, showcasing the remarkable success of quantum field theory in describing material reality.
In the case of proton–proton collisions at the LHC, the dominant processes involve quantum chromodynamics (QCD). Although in general the calculations are more complex than in QED due to the non-abelian nature of this interaction, i.e. the self-coupling of gluons, the fact that the QCD coupling constant is small at the high energies relevant to the LHC means that perturbative methods are possible. In practice, all of the Feynman diagrams that correspond to the lowest-order process are drawn by considering all possible ways in which a given final state can be produced. For instance, in the case of Drell–Yan production at the LHC, the only lowest-order diagram involves an incoming quark and an incoming antiquark from the proton beams, which annihilate to produce a Z, γ* or a W boson, which then decays into leptons. Using the Feynman rules, such pictorial descriptions can be turned into quantum-mechanical amplitudes. The cross-section can then be computed as the square of the amplitude, integrated over the phase space and appropriately summing and averaging over quantum numbers.
This lowest-order description is very crude, however, since it does not account for the fact that quarks tend to radiate gluons. To incorporate such higher-order quantum corrections, next-to-leading order (NLO) calculations that describe the radiation of one additional gluon are required. This gluon can either be real, giving rise to a particle that is recorded by a detector, or virtual, corresponding to a quantum-mechanical fluctuation that is emitted and reabsorbed. Both contributions are divergent because they become infinite in the limit when the energy of the gluon is infinitesimally small, or when the gluon is exactly collinear to one of the emitting quarks. When real and virtual corrections are combined, however, these divergences cancel out. This is a consequence of the so-called Kinoshita–Lee–Nauenberg theorem, which states that low-energy (infrared) divergences must cancel in physical (measurable) quantities.
Even if divergences cancel in the final result, a procedure to handle divergences in intermediate steps of the calculations is still needed. How to do this at the level of NLO corrections has been well understood for a number of years. The first successes of NLO QCD calculations came in the 1990s with the comparison of Drell–Yan particle-production data recorded by CERN’s SPS and Fermilab’s Tevatron experiments to leading-order and NLO QCD predictions, which had first been computed in 1979 by Altarelli, Ellis and Martinelli. The comparison revealed unequivocally that NLO corrections are required to describe Drell–Yan data, and marked the first great success of perturbative QCD (figure 1).
Things have changed a lot since then. Today, NLO corrections have been calculated for a large class of processes relevant to the LHC programme, and several tools have been developed to even compute them in a fully automated way. As a result, the problem of NLO QCD calculations is considered solved and comparing these to data has become standard in current LHC data analysis. Thanks to the impressive precision now being attained by the LHC experiments, however, we are now being taken into the complex realm of higher-order calculations.
The NNLO explosion
The new frontier in perturbative QCD is the calculation of next-to-next-to-leading order (NNLO) corrections. At the level of diagrams, the picture is once again pretty simple: at NNLO level, it is not just one extra particle emission but two extra emissions that are accounted for. These emissions can be two real partons (quarks or gluons), a real parton and a virtual one, or two virtual partons.
The first NNLO computation for a collider process concerned “inclusive” Drell–Yan production, by Hamberg, Van Neerven and Matsuura in 1991. Motivated by the SPS and Tevatron data, and also by the planned LHC and SSC experiments, this was a pioneering calculation that was performed analytically. The second NNLO calculation, in 2002, was for inclusive Higgs production in gluon–gluon fusion by Harlander and Kilgore. Inclusive calculations refer only to the total cross-section for producing a Higgs boson or a Drell–Yan pair without any restriction on where these particles end up, which is not measurable because detectors do not cover the entire phase space such as the region close to the beam.
The first “exclusive” NNLO calculations, which allow kinematic cuts to be applied to the final state, started to appear in 2004 for Drell–Yan and Higgs production. These calculations were motivated by the need to predict quantities that can be directly measured, rather then relying on extrapolations to describe the effects of experimental cuts. The years 2004–2011 saw more activity, but limited progress: all calculations were essentially limited to “2 → 1” scattering processes, in essence Higgs and Drell–Yan production, as well as Higgs production in association with a Drell–Yan pair. From a QCD point of view, the latter process is simply off-shell Drell–Yan production in which the vector boson radiates a Higgs. A few 2 → 2 calculations started to appear in 2012, most notably top-pair production and the production of a pair of vector bosons. It is only in the past two years, however, that we have witnessed an explosion of NNLO calculations (figure 2). Today, all 2 → 2 Standard Model LHC scattering processes are known to NNLO, thanks to remarkable progress in the calculation of two-loop integrals and in the development of procedures to handle intermediate divergences.
Compared to NLO calculations, NNLO calculations are substantially more complex. Two main difficulties must be faced: loop integrals and divergences. Two-loop integrals have been calculated in the past by explicitly performing the multi-dimensional integration, in which each loop gives rise to a “D-dimensional” integration. For simple cases, analytical expressions can be found, but in many cases only numerical results can be obtained for these integrals. The complexity increases with the number of dimensions (i.e. the number of loops) and with the number of Lorentz-invariant scales involved in the process (i.e. the number of particles involved, and in particular the number of massive particles).
Recently, new approaches to these loop integrals have been suggested. In particular, it has been known since the late 1990s that integrals can be treated as variables entering a set of differential equations, but solutions to those equations remained complicated and could be found only on a case-by-case basis. A revolution came about just three years ago when it was realised that the differential equations can be organised in a simple form that makes finding solutions, i.e. finding expressions for the wanted two-loop integrals, a manageable problem. Practically, the set of multi-loop integrals to be computed can be regarded as a set of vectors. Decomposing these vectors in a convenient set of basis vectors can lead to significant simplifications of the differential equations, and concrete criteria were proposed for finding an optimal basis. The very important NNLO calculations of diboson production have benefitted from this technology.
Currently, when only virtual massless particles are involved and up to a total of four external particles are considered, the two-loop integral problem is considered solved, or at least solvable. However, when massive particles circulate in the loop, as is the case for a number of LHC processes, the integrals give rise to a new class of functions, elliptic functions, and it is not yet understood how to solve the associated differential equations. Hence, for processes with internal masses we still face a conceptual bottleneck. Overcoming this will be very important for Higgs studies at large transverse momentum, where the top loop to which the Higgs couples is resolved. The calculation of these integrals is today an area with tight connections to more formal and mathematical areas, leading to close collaborations between the high-energy physics and the mathematical/formal-oriented communities.
The second main difficulty in NNLO calculations is that, as at NLO, individual contributionsare divergent in the infrared region, i.e. when particles have a very small momentum or become collinear with respect to one another, and the structure of these singularities is now considerably more complex because of the extra particle radiated at NNLO. All singularities cancel when all contributions are combined, but to have exclusive predictions it is necessary to cancel the singularities before performing integrations over the phase space. Compared to NLO, where systematic ways to treat these intermediate divergences have been known for many years, the problem is more difficult at NNLO because there are more divergent configurations and different divergences overlap. The past few years have seen remarkable developments in the understanding and treatment of infrared singularities in NNLO computations of cross-sections, and a range of methods based on different physical ideas have been successfully applied.
Beyond NNLO
Is the field of precision calculations close to coming to an end? The answer is, of course, no. First, while the problem of cancelling singularities is in principle solved in a generic way, in practice all methods have been applied to 2 → 2 processes only, and no 2 → 3 cross-section calculation is foreseen in the near future. For instance, the very important processes of three-jet production or Higgs production in association with a top-quark pair are known to NLO accuracy only. Similarly, two-loop pentagon integrals required for the calculation of 2 → 3 scatterings are at the frontier of what can be done today. Furthermore, most of the existing NNLO computer codes require extremely long runs on large computer farms, with typical run times of several CPU years. It could be argued that this is not an issue in an age of large computer farms and parallel processing and when CPU time is expected to become cheaper over the years, however, the number of phenomenological studies that can be done with a theory prediction is much larger when calculations can be performed quickly on a single machine. Hence, in the coming years NNLO calculations will be scrutinised and compared in terms of their performances. Ultimately, only one or a few of the many existing methods to perform integrals and to treat intermediate divergences is likely to take over.
Given how hard and time-consuming NNLO calculations are, we should also ask if it is worth the effort. A comparison with data for the diboson (WZ) production process at different LHC beam energies to NLO and NNLO calculations (figure 3) provides an indication of the answer. It is clear that LHC data already indicate a clear preference for NNLO QCD predictions and that, once more data are accumulated, NLO will likely be insufficient. While it is early days for NNLO phenomenology, the same conclusion applies to other measurements examined so far.
In the past, accurate precision measurements have provided a strong motivation to push the precision of theoretical predictions. On the other side, very precise theory predictions have stimulated even more precise measurements. Today, the accuracy reached by LHC measurements is by far better than what anybody could have predicted when the LHC was designed. For instance, the Z transverse momentum spectrum reaches an accuracy of better than a per cent over a large range of transverse momentum values, which will be important to further constrain parton-distribution functions, and the mass of the W boson, which enters precision tests of the Standard Model, is measured with better than 20 MeV accuracy. In the future, one should expect that high-precision theoretical predictions will push the experimental precision beyond today’s foreseeable boundaries. This will usher in the next phase in perturbative QCD calculations: next-to-next-to-next-to-leading order, or N3LO.
Today we have two pioneering calculations beyond NNLO: the N3LO calculation of inclusive Higgs production (in the large top-mass approximation), and the N3LO calculation of inclusive vector-boson-fusion Higgs production. Both calculations are inclusive over radiation, exactly in the same way that the first NNLO calculations were. These calculations are now suggestive of a good convergence of the perturbative expansion, meaning that the N3LO correction is very small and that the N3LO result lies well within the theoretical uncertainty band of the NNLO result. Turning these calculations into fully exclusive predictions is the next theoretical challenge.
As its name suggests, the Large Hadron Collider (LHC) at CERN smashes hadrons into one another – protons, to be precise. The energy from these collisions gets converted into matter, producing new particles that allow us to explore matter at the smallest scales. The LHC does not fire protons into one another individually; instead, they are circulated in approximately 2000 bunches each containing around 100 billion protons. When two bunches are focused magnetically to cross each other in the centre of detectors such as CMS and ATLAS, only 30 or so protons actually collide. The rest continue to fly through the LHC unimpeded until the next time that two bunches cross.
Occasionally, something very different happens. If two protons travelling in opposite directions pass very close to one another, photons radiated from each proton can collide and produce new particles. The two parent protons remain completely intact, continuing their path in the LHC, but the photon–photon interaction removes a fraction of their initial energy and causes them to be slightly deflected from their original trajectories. By identifying the deflected protons, one can determine whether such photon interactions took place and effectively turn the LHC into a photon collider. It is also possible for the two protons to exchange pairs of gluons, which is another interesting process.
The idea of tagging deflected protons has been pursued at previous colliders, and also at the LHC back in 2012 and 2015 using only low-intensity beams. The proposal to pursue this type of physics with the LHC’s CMS and/or ATLAS experiments was first presented many years ago, but the project (under the name FP420) did not materialise.
A new project called the CMS-TOTEM Precision Proton Spectrometer (CT-PPS) has now taken up the challenge of making photon–photon physics possible at the LHC when operating at nominal luminosity. While CMS is a general-purpose detector for LHC physics, CT-PPS uses two sets of detectors placed 200 m either side of the CMS interaction point to measure protons in the forward direction. A parallel project called ATLAS Forward Physics (AFP) is also being developed by ATLAS, and both experiments aim to be in operation throughout this year’s LHC proton–proton run.
Despite photons being electrically neutral, the Standard Model (SM) allows two photons to interact via the exchange of virtual charged particles. Several final states are possible (figure 1), including a pair of photons. The latter process (γγ → γγ, or “light-by-light scattering”) has been known since the development of quantum electrodynamics (QED) and tested indirectly in several experiments, but the first direct evidence came last year from ATLAS in low-luminosity measurements of lead–lead collisions (CERN Courier December 2016 p9). Since the probability of emitting photons scales with the square of the electrical charge, the cross-section for lead–lead collisions is significantly higher than for proton–proton collisions. By searching for two photons and nothing else in the central detector and using kinematics cut to suppress backgrounds, the invariant mass of the two photons was in the region of 10 GeV. The measured cross-section was compatible with the QED prediction and, since no deviations are expected in this low-mass range, the ATLAS result was interesting but somewhat expected.
In forward experiments such as CT-PPS and AFP, however, the high-luminosity proton collisions allow a much higher mass region to be probed – between 300 GeV and 2 TeV in the case of CT-PPS. Proton tagging is possible because centrally produced high-mass systems cause the protons to lose enough energy to be deflected into the CT-PPS detectors. The study of photon interactions in this region could therefore provide new insights about the electroweak interaction, in particular the quartic gauge couplings predicted by the SM. These are interactions where two photons annihilate upon collision to produce two W bosons, implying four particles at the same vertex in a Feynman diagram (figure 1). Deviations from the SM prediction would point to new physics in the same way as the observations of deviations from the quartic coupling in Fermi’s beta-decay theory in the 1930s were the forerunner to the discovery of the W boson 50 years later.
If there are new particles with masses above 300 GeV, CT-PPS could also improve CMS’s general discovery potential. For example, diphoton resonances at high mass have a very clean signature almost free of any background. Thus, in addition to precision electroweak tests, forward experiments such as CT-PPS provide an important cross-check of “bumps” in invariant mass distributions by offering complementary information about the production mechanism, coupling and quantum numbers of a possible new resonance. An example of this complementarity concerns the now-infamous 750 GeV bump in the diphoton invariant-mass distributions from the LHC’s 2015 data set. Although the bump turned out to be a statistical effect, it provided strong motivation to advance the CT-PPS physics programme at the time. Were similar bumps to be observed by CMS and ATLAS in future, CT-PPS and AFP will play an important role in determining whether a real resonance is responsible for the excesses seen in the data.
Forward thinking
Given their potential for revealing new physics, photon–photon collisions have been a topic of some interest for many decades. For example, photon–photon collisions were studied at CERN’s Large Electron Positron (LEP), while studies at DESY’s HERA and Fermilab’s Tevatron colliders concentrated on interactions of protons through the exchange of gluons to probe quantum chromodynamics in the non-perturbative regime. The LHC achieves a much higher energy and luminosity than LEP, but at the price of colliding particles that are not elementary. Therefore, the elementary interactions between gluons and quarks do not have well-defined energies and the interaction products include the remnants of the two protons, making physics analyses more difficult in general.
Proton-tagged photon collisions at the LHC, on the other hand, are very clean. Since photons are elementary particles and there are no proton remnants, the photon–photon collision energy at the LHC is precisely defined by the kinematics of the two tagged protons. In conjunction with CT-PPS, CMS can therefore probe anomalous quartic couplings with much better sensitivity than before.
The physics we are interested in corresponds to the process pp → ppX, where the “pp” part is measured by the CT-PPS detectors and the system “X” is measured in the other CMS sub-detectors. In the case of the quartic coupling γγWW, for instance, the process is pp → ppWW. The two photons that merge into two W are not measured directly, but energy-momentum conservation allows all of the kinematic properties of the WW pair to be deduced much more precisely from the CT-PPS proton measurements than could be achieved from the measurements of W decay products with the CMS detector alone.
The CT-PPS detectors are located on either side of CMS, 200 m from the interaction point. They rely on objects called Roman Pots (RP), which are cylinders that allow small detectors to be moved into the LHC beam pipe so that they sit a mere few mm from the beam. The RPs of TOTEM are designed to operate under special LHC runs with a small number of collisions per second. However, the physics goals of CT-PPS require the RPs to operate during normal CMS data-taking, when the LHC provides a much higher number of collisions per second. The first and most important goal of the CT-PPS project was therefore to demonstrate that the detectors could operate successfully only a few millimetres from the LHC’s high-intensity beams. The final demonstration happened between April and May 2016, and the green light for CT-PPS operation in regular high-luminosity LHC running was given the following month.
Success so far
The CT-PPS project redesigned the RPs to suit these harsh operating conditions. In collaboration with LHC teams, they also conducted a thorough programme of RP insertions at increasingly closer distances to the beam, measuring its impact on beam monitors. Great care must be taken not to disrupt the beam, since if the protons start to scrape the RPs there would be an increase in secondary particles that would trigger a beam dump. In 2016, CT-PPS used non-final detectors to collect 15.2 fb–1 of data integrated in the CMS data set. CT-PPS has proven for the first time the feasibility of operating a near-beam proton spectrometer at high luminosity on a regular basis and has paved the way for other such spectrometers.
CT-PPS is also facing big challenges in the development of the final detectors. The tracking detectors have a surface area of just 2 cm2 and reside in two RPs located 10 m apart on either side of the collision point (for a total of four stations). Six planes of silicon pixels on each station will detect the track of the flying protons to provide direction information, and the magnetic field of the LHC’s magnets will serve as the proton-deflecting field. The devices themselves have to sustain exceedingly high radiation fluxes given their proximity to the beam: a proton fluence in excess of 5 × 1015 particles/cm2 is expected after an integrated luminosity of 100 fb–1. CMS’s own tracker will not face these radiation conditions until the HL-LHC enters operation in the mid 2020s.
From 2017 onwards, CT-PPS will be using new 3D pixel technology that has been developed in view of upgrades to the CMS tracker and therefore provide valuable experience with the new sensors. The project also relies on high-precision timing detectors. CT-PPS matches the primary vertex of the collision measured in the central detector with the vertex position obtained from the difference of the time-of-arrival to the two protons, so that it can reject the background from spurious collisions piling up in the same bunch crossing. A time precision of 20 ps makes it possible to estimate the z-vertex with the 3 mm accuracy needed to reduce the background sufficiently. The timing detectors had used diamond sensors in 2016 and will add silicon low-gain avalanche diodes this year. Again, the experience acquired in a high-rate and high-radiation environment will be most valuable for CMS upgrades for HL-LHC.
Meanwhile, the ATLAS collaboration installed one arm of the AFP experiment in early 2016 and has taken data in special low-luminosity runs to study diffraction. The second AFP arm, with horizontal RP stations similar to those of CT-PPS, has also since been installed and its four-layer 3D silicon pixel detectors and new Cherenkov-based time-of-flight detectors are being assembled. They will be installed and commissioned before the LHC restarts in May this year. Like CT-PPS, AFP aims to participate in high-luminosity running throughout the year, with both operating in tandem to enhance the LHC’s search for new physics.
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