LEP’s electroweak leap

In the early 1970s the term “Standard Model” did not yet exist – physicists used “Weinberg–Salam model” instead. But the discovery of the weak neutral current in Gargamelle at CERN in 1973, followed by the prediction and observation of particles composed of charm quarks at Brookhaven and SLAC, quickly shifted the focus of particle physicists from the strong to the electroweak interactions – a sector in which trailblazing theoretical work had quietly taken place in the previous years. Plans for an electron–positron collider at CERN were soon born, with the machine first named LEP (Large Electron Positron collider) in a 1976 CERN yellow report authored by a distinguished study group featuring, among others, John Ellis, Burt Richter, Carlo Rubbia and Jack Steinberger.

LEP’s size – four times larger than anything before it – was chosen from the need to observe W-pair production, and to check that its cross section did not diverge as a function of energy. The phenomenology of the Z-boson’s decay was to come under similar scrutiny. At the time, the number of fermion families was undefined, and it was even possible that there were so many neutrino families that the Z lineshape would be washed out. LEP’s other physics targets included the possibility of producing Higgs bosons. At the time, the mass of the Higgs boson was completely unknown and could have been anywhere from around zero to 1 TeV.

The CERN Council approved LEP in October 1981 for centre-of-mass energies up to 110 GeV. It was a remarkable vote of confidence in the Standard Model (SM), given that the W and Z bosons had not yet been directly observed. A frantic period followed, with the ALEPH, DELPHI, L3 and OPAL detectors approved in 1983. Based on similar geometric principles, they included drift chambers or TPCs for the main trackers, BGO crystals, lead–glass or lead–gas sandwich electromagnetic calorimeters, and, in most cases, an instrumented return yoke for hadron calorimetry and muon filtering. The underground caverns were finished in 1988 and the detectors were in various stages of installation by the end of spring 1989, by which time the storage ring had been installed in the 27 km-circumference tunnel (see The greatest lepton collider).

Expedition to the Z pole

The first destination was the Z pole at an energy of around 90 GeV. Its location was then known to ±300 MeV from measurements of proton–antiproton collisions at Fermilab’s Tevatron. The priority was to establish the number of light neutrino families, a number that not only closely relates to the number of elementary fermions but also impacts the chemical composition and large-scale structure of the universe. By 1989 the existence of the ν_e, ν_μ and ν_τ neutrinos was well established. Several model-dependent measurements from astrophysics and collider physics at the time had pointed to the number of light active neutrinos (N_ν) being less than five, but the SM could, in principle, accommodate any higher number.

The initial plan to measure N_ν using the total width of the Z resonance was quickly discarded in favour of the visible peak cross section, where the effect was far more prominent – and in first approximation, insensitive to new possible detectable channels. The LEP experiments were therefore thrown in at the deep end, needing to make an absolute cross-section measurement with completely new detectors in an unfamiliar environment that demanded triggers, tracking, calorimetry and the luminosity monitors to all work and acquire data in synchronisation.

On the evening of 13 August, during a first low-luminosity pilot run just one month after LEP achieved first turns, OPAL reported the first observation of a Z decay (see OPAL fruits). Each experiment quickly observed a handful more. The first Z-production run took place from 18 September to 9 October, with the four experiments accumulating about 3000 visible Z decays each. They took data at the Z peak and at 1 and 2 GeV either side, improving the precision on the Z mass and allowing a measurement of the peak cross section. The results, including those from the Mark II collaboration at SLAC’s linear electron–positron SLC collider, were published and presented in CERN’s overflowing main auditorium on 13 October.

After only three weeks of data taking and 10,000 Z decays, the number of neutrinos was found to be three. In the following years, some 17 million Z decays were accumulated, and cross-section measurement uncertainties fell to the per-mille level. And while the final LEP number – N_ν = 2.9840 ± 0.0082 – may appear to be a needlessly precise measurement of the number three (figure 1a), it today serves as by far the best high-energy constraint on the unitarity of the neutrino mixing matrix. LEP’s stash of a million clean tau pairs from Z → τ⁺ τ^–– decays also allowed the universality of the lepton–neutrino couplings to the weak charged current to be tested with unprecedented precision. The present averages are still dominated by the LEP numbers: g_τ/g_μ = 1.0010 ± 0.0015 and g_τ/g_e = 1.0029 ± 0.0015.

LEP continued to carry out Z-lineshape scans until 1991, and repeated them in 1993 and 1995. Two thirds of the total luminosity was recorded at the Z pole. As statistical uncertainties on the Z’s parameters went down, the experiments were challenged to control systematic uncertainties, especially in the experimental acceptance and luminosity. Monte Carlo modelling of fragmentation and hadronisation was gradually improved by tuning to measurements in data. On the luminosity front it soon became clear that dedicated monitors would be needed to measure small-angle Bhabha scattering (e⁺e^– → e⁺e^–), which proceeds at a much higher rate than Z production. The trick was to design a compact electromagnetic calorimeter with sufficient position resolution to define the geometric acceptance, and to compare this to calculations of the Bhabha cross section.

The final ingredient for LEP’s extraordinary precision was a detailed knowledge of the beam energy, which required the four experiments to work closely with accelerator experts. Curiously, the first energy calibration was performed in 1990 by circulating protons in the LEP ring – the first protons to orbit in what would eventually become the LHC tunnel, but at a meagre energy of 20 GeV. The speed of the protons was inferred by comparing the radio-frequency electric field needed to keep protons and electrons circulating at 20 GeV on the same orbit, allowing a measurement of the total magnetic bending field on which the beam energy depends. This gave a 20 MeV uncertainty on the Z mass. To reduce this to 1.7 MeV for the final Z-pole measurement, however, required the use of resonant depolarisation routinely during data taking. First achieved in 1991, this technique uses the natural transverse spin polarisation of the beams to yield an instantaneous measurement of the beam energy to a precision of ±0.1 MeV – so precise that it revealed minute effects caused, for example, by Earth’s tides and the passage of local trains (see Tidal forces, melting ice and the TGV to Paris). The final precision was more than 10 times better than had been anticipated in pre-LEP studies.

Electroweak working group

The LEP electroweak working group saw the ALEPH, DELPHI, L3 and OPAL collaborations work closely on combined cross-section and other key measurements – in particular the forward-backward asymmetry in lepton and b-quark production – at each energy point. By 1994, results from the SLD collaboration at SLAC were also included. Detailed negotiations were sometimes needed to agree on a common treatment of statistical correlations and systematic uncertainties, setting a precedent for future inter-experiment cooperation. Many tests of the SM were performed, including tests of lepton universality (figure 1b), adding to the tau lepton results already mentioned. Analyses also demonstrated that the couplings of leptons and quarks are consistent with the SM predictions.

The combined electroweak measurements were used to make stunning predictions of the top-quark and Higgs-boson masses, m_t and m_H. After the 1993 Z-pole scan, the LEP experiments were able to produce a combined measurement of the Z width with a precision of 3 MeV in time for the 1994 winter conferences, allowing the prediction m_t = 177 ± 13 ± 19 GeV where the first error is experimental and the second is due to m_H not being known. A month later the CDF collaboration at the Tevatron announced the possible existence of a top quark with a mass of 176 ± 16 GeV. Both CDF and its companion experiment D0 reached 5σ “discovery” significance a year later. It is a measure of the complexity of the Z-boson analyses (in particular the beam-energy measurement) that the final Z-pole results were published a full 11 years later, constraining the Higgs mass to be less than 285 GeV at 95% confidence level (figure 1c), with a best fit at 129 GeV.

From QCD to the W boson

LEP’s fame in the field tends to concern its electroweak breakthroughs. But, with several million recorded hadronic Z decays, the LEP experiments also made big advances in quantum chromodynamics (QCD). These results significantly increased knowledge of hadron production and quark and gluon dynamics, and drove theoretical and experimental methods that are still used extensively today. LEP’s advantage as a lepton collider was to have an initial state that was independent of nucleon structure functions, allowing the measurement of a single, energy-scale-dependent coupling constant. The strong coupling constant α_s was determined to be 0.1195 ± 0.0034 at the Z pole, and to vary with energy – the highlight of LEP’s QCD measurements. This so-called running of α_s was verified over a large energy range, from the tau mass up to 206 GeV, yielding additional experimental confirmation of QCD’s core property of asymptotic freedom (figure 2a).

Many other important QCD measurements were performed, such as the gluon self-coupling, studies of differences between quark and gluon jets, verification of the running b-quark mass, studies of hadronisation models, measurements of Bose–Einstein correlations and detailed studies of hadronic systems in two-photon scattering processes. The full set of measurements established QCD as a consistent theory that accurately describes the phenomenology of the strong interaction.

Following successful Z operations during the “LEP1” phase in 1989–1995, a second LEP era devoted to accurate studies of W-boson pair production at centre-of-mass energies above 160 GeV got under way. Away from the Z resonance, the electron-positron annihilation cross section decreases sharply; as soon as the centre-of-mass energy reaches twice the W and Z boson masses, the WW, then ZZ, production diagrams open up (figure 2b). Accessing the WW threshold required the development of superconducting radio-frequency cavities, the first of which were already installed in 1994, and they enabled a gradual increase in the centre-of-mass energy up to a maximum of 209 GeV in 2000.

The “LEP2” phase allowed the experiments to perform a signature analysis, which dated back to the first conception of the machine: the measurement of the WW-boson cross section. Would it diverge or would electroweak diagrams interfere to suppress it? The precise measurement of the WW cross section as a function of the centre-of-mass energy was a very important test of the SM since it showed that the sum and interference of three four-fermion processes were indeed acting in the WW production: the t-channel ν exchange, and the s-channel γ and Z exchange (figure 2c). LEP data proved that the γWW and ZWW triple gauge vertexes are indeed present and interfere destructively with the t-channel diagram, suppressing the cross section and stopping it from diverging.

The second key LEP2 electroweak measurement was of the mass and total decay width of the W boson, which were determined by directly reconstructing the decay products of the two W bosons in the fully hadronic (W⁺W^– → qqqq) and semi-leptonic (W⁺W^– → qqℓν_ℓ) decay channels. The combined LEP W-mass measurement from direct reconstruction data alone is 80.375 ± 0.025(stat) ± 0.022(syst) GeV, the largest contribution to the systematic uncertainties originating from fragmentation and hadronisation uncertainties. The relation between the Z-pole observables, m_t and m_W, provides a stringent test of the SM and constrains the Higgs mass.

To the Higgs and beyond

Before LEP started, the mass of the Higgs boson was basically unknown. In the simplest version of the SM, involving a single Higgs boson, the only robust constraints were its non-observation in nuclear decays (forbidding masses below 14 MeV) and the need to maintain a sensible, calculable theory (ruling out masses above 1 TeV). In 1990, soon after the first LEP data-taking period, the full Higgs-boson mass range below 24 GeV was excluded at 95% confidence level by the LEP experiments. Above this mass the main decay of the Higgs boson, occurring 80% of the time, was predicted to be its decays into b quark–antiquark pairs, followed by pairs of tau leptons, charm quarks or gluons, while the WW* decay mode starts to contribute at the maximum reachable masses of approximately 115 GeV. The main production process is Higgs-strahlung, whereby a Higgs is emitted by a virtual Z boson.

The combined electroweak measurements were used to make stunning predictions of the top quark and Higgs boson masses

During the full lifetime of LEP, the four experiments kept searching for neutral and charged Higgs bosons in several models and exclusion limits continued to improve. In its last year of data taking, when the centre-of-mass energy reached 209 GeV, ALEPH reported an excess of four-jet events. It was consistent with a 114 GeV Higgs boson and had a significance that varied as the data were accumulated, peaking at an instantaneous significance of around 3.9 standard deviations. The other three experiments carefully scrutinised their data to confirm or disprove ALEPH’s suggestion, but none observed any long-lasting excess in that mass region. Following many discussions, the LEP run was extended until 8 November 2000. However, it was decided not to keep running the following year so as not to impact the LHC schedule. The final LEP-wide combination excluded, at 95% confidence level, a SM Higgs boson with mass below 114.4 GeV.

The four LEP experiments carried out many other searches for novel physics that set limits on the existence of new particles. Notable cases are the searches for additional Higgs bosons in two-Higgs-doublet models and their minimal supersymmetric incarnation. Neutral scalar and pseudoscalar Higgs bosons lighter than the Z boson and charged Higgs bosons up to the kinematic limit of their pair production were also excluded. Supersymmetric particles suffered a similar fate, in the theoretically attractive assumption of R-parity conservation. The existence of sleptons and charginos was excluded in the largest part of the parameter space for masses below 70–100 GeV, near the kinematic limit for their pair production. Neutralinos with masses below approximately half the Z-boson mass were also excluded in a large part of the parameter space. The LEP exclusions for several of these electroweak-produced supersymmetric particles are still the most stringent and most model-independent limits ever obtained.

It is very hard to remember how little we knew before LEP and the giant step that LEP made. It was often said that LEP discovered electroweak radiative corrections at the level of 5σ, opening up a precision era in particle physics that continues to set the standard today and offer guidance on the elusive new physics beyond the SM.