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In this paper we describe the history of the LHCb experiment over the last three decades, and its remarkable successes and achievements. LHCb was conceived primarily as a b-physics experiment, dedicated to CP violation studies and measurements of very rare b decays, however the tremendous potential for c-physics was also clear. At first data taking, the versatility of the experiment as a general-purpose detector in the forward region also became evident, with measurements achievable such as electroweak physics, jets and new particle searches in open states. These were facilitated by the excellent capability of the detector to identify muons and to reconstruct decay vertices close to the primary pp interaction region. By the end of the LHC Run 2 in 2018, before the accelerator paused for its second long shut down, LHCb had measured the CKM quark mixing matrix elements and CP violation parameters to world-leading precision in the heavy-quark systems. The experiment had also measured many rare decays of b and c quark mesons and baryons to below their Standard Model expectations, some down to branching ratios of order 10-9. In addition, world knowledge of b and c spectroscopy had improved significantly through discoveries of many new resonances already anticipated in the quark model, and also adding new exotic four and five quark states.

A total of 628 bp-1 of data collected with the ALEPH detector at centre-of-mass energies from 189 to 209 GeV is analysed in the search for gauge mediated SUSY breaking (GMSB) topologies. These topologies include two acoplanar photons, non-pointing single photons, acoplanar leptons, large impact parameter leptons, detached slepton decay vertices, heavy stable charged sleptons and multi-leptons plus missing energy final states. No evidence is found for new phenomena, and lower limits on masses of supersymmetric particles are derived. A scan of a minimal GMSB parameter space is performed and lower limits are set for the next-to-lightest supersymmetric particle (NLSP) mass at 54 GeV/c2 and for the mass scale parameter \\(\\Lambda\\) at 10 TeV/c2, independently of the NLSP lifetime. Including the results from the neutral Higgs boson searches, a NLSP mass limit of 77 GeV/c2 is obtained and values of \\(\\Lambda\\) up to 16 TeV/c2 are excluded.

Cross sections, angular distributions and forward-backward asymmetries are presented, of two-fermion events produced in e+e- collisions at centre-of-mass energies from 189 to 209 GeV at LEP, measured with the ALEPH detector. Results for e+e-, mu+mu-, tau+tau-, qq, bb and cc production are in agreement with the Standard Model predictions. Constraints are set on scenarios of new physics such as four-fermion contact interactions, leptoquarks, Z' bosons, TeV-scale quantum gravity and R-parity violating squarks and sneutrinos.

A search for Higgs bosons produced in association with a fermion pair, and decaying to WW, is performed with the data collected by the ALEPH detector at centre-of-mass energies ranging from 191 to 209 GeV. The data correspond to an integrated luminosity of 453.2 pb⁻1. Thirteen exclusive selections are developed according to the different final state topologies. No statistically significant evidence for a Higgs boson decaying into a WW pair has been found. An upper limit is derived, as a function of the Higgs boson mass, on the product of the e+e- -> Hff cross section and the H -> WW branching ratio. The data on the search for H -> WW are combined with previously published ALEPH results on the search for H -> gamma gamma, to significantly extend the limits on the mass of a fermiophobic Higgs boson.

The mass of the W boson is determined from the direct reconstruction of its decays into purely hadronic and semi-leptonic events in e+e- collisions at LEP. The data sample corresponds to an integrated luminosity of 683 inverse picobarns collected with the ALEPH detector at centre-of-mass energies up to 209 GeV. To minimise any effect from colour reconnection a new procedure is adopted in which low energy particles are not considered in the mass determination from the purely hadronic channel. The combined result from all channels is Mw = 80.440+-0.043(stat.)+-0.024(syst.)+-0.009(FSI)+-0.009(LEP) GeV/c**2 where FSI represents the possible effects of final state interactions in the purely hadronic channel. From two-parameter fits to the W mass and width, the W width is found to be Gw = 2.14+-0.09(stat.)+-0.04(syst.)+-0.05(FSI)+-0.01(LEP) GeV

Using approximately 4 million hadronic Z decays recorded with the aleph detector from 1991 through 1995, the lifetime of the b baryon is measured with three independent methods. From the impact parameter distribution of candidate leptons in 1063 events with \\(\\Lambda\\ell^-\\) combinations, the average b baryon lifetime is measured to be \\(1.20\\pm{0.08}\\pm{0.06}\\) ps. From a sample of 193 fully reconstructed \\(\\Lambda^+_{\\rm c}\\) candidates correlated with a lepton and a sample of 46 \\(\\Lambda\\ell^+\\ell^-\\) combinations, the \\(\\Lambda_{\\rm b}\\) lifetime is measured to be \\(1.21\\pm{0.11}\\) ps. The product branching fractions to these final states are \\({\\rm Br(b\\to \\Lambda_{\\rm b}}\\cdot{\\rm BR (\\Lambda_{\\rm b} \\to \\Lambda\\ell^-\\overline\\nu X}) = 0.326\\pm{0.016}\\pm{0.039}\\)% for the first sample and \\({\\rm Br(b\\to \\Lambda_{\\rm b}}\\cdot{\\rm BR(\\Lambda_{ \\rm b} \\to \\Lambda^+_{\\rm c}\\ell^-\\overline\\nu X}) =0.86\\pm{0.07}\\pm{0.14}\\)% for the second and third samples combined.

In this chapter we explore a few examples of physics opportunities using the existing chain of accelerators at CERN, including potential upgrades. In this context the LHC ring is also considered as a part of the injector system. The objective is to find examples that constitute sensitive probes of New Physics that ideally cannot be done elsewhere or can be done significantly better at theCERN accelerator complex. Some of these physics opportunities may require a more flexible injector complex with additional functionality than that just needed to inject protons into the FCC-hh at the right energy, intensity and bunch structure. Therefore it is timely to discuss these options concurrently with the conceptual design of the FCC-hh injector system.

The hadronic final states observed with the ALEPH detector at LEP in e+e- annihilation are analysed using 730 pb-1 of data collected between 91 and 209 GeV in the framework of QCD. In particular event-shape variables and inclusive charged particle spectra are measured. The energy evolution of quantities derived from these measurements is compared to analytic QCD predictions. The mean charged particle multiplicity, the charged particle momentum spectrum and its peak position are compared to predictions of the modified-leading-logarithmic approximation. The strong coupling constant alpha_(s) is determined from a fit of the QCD prediction to distributions of six event-shape variables at eight centre-of-mass energies. A study of non-perturbative power law corrections is presented

The W+W- production cross section is measured from a data sample corresponding to a total integrated luminosity of 683 pb-1, collected by the Aleph experiment at LEP at centre-of-mass energies from 183 to 209 GeV. Individual cross sections for the different topologies arising from W decays into leptons or hadrons, as well as the total W-pair cross section are given at eight centre-of-mass energies. The results are found to be in agreement with recently developed Standard Model calculations at the one percent level. The branching fraction of the W boson into hadrons is measured to be B (W–> hadrons) = (67.15 +- 0.37(stat) +- 0.15(syst))%, from which the CKM matrix element |Vcs| is determined to be 0.959 +- 0.017(stat) +- 0.008(syst).