We present a new measurement of the positive muon magnetic anomaly, a µ ≡ (gµ − 2)/2, from the Fermilab Muon g −2 Experiment based on data collected in 2019 and 2020. We have analyzed more than four times the number of positrons from muon decay than in our previous result from 2018 data. The systematic error is reduced by more than a factor of two due to better running conditions, a more stable beam, and improved knowledge of the magnetic field weighted by the muon distribution, ω′ p , and of the anomalous precession frequency corrected for beam dynamics effects, ωa. From the ratio ωa/ω ′ p , together with precisely determined external parameters, we determine a µ = 116 592 057(25) × 10 −11 (0.21 ppm). Combining this result with our previous result from the 2018 data, we obtain a µ (FNAL) = 116 592 055(24) × 10 −11 (0.20 ppm). The new experimental world average is aµ(Exp) = 116 592 059(22) × 10 −11 (0.19 ppm), which represents a factor of two improvement in precision.

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The physics programme and the design are described of a new collider for particle and nuclear physics, the Large Hadron Electron Collider (LHeC), in which a newly built electron beam of 60 GeV, to possibly 140 GeV, energy collides with the intense hadron beams of the LHC. Compared to the first ep collider, HERA, the kinematic range covered is extended by a factor of twenty in the negative four-momentum squared, Q 2 , and in the inverse Bjorken x, while with the design luminosity of 10 33 cm −2 s −1 the LHeC is projected to exceed the integrated HERA luminosity by two orders of magnitude. The physics programme is devoted to an exploration of the energy frontier, complementing the LHC and its discovery potential for physics beyond the Standard Model with high precision deep inelastic scattering measurements. These are designed to investigate a variety of fundamental questions in strong and electroweak interactions. The LHeC thus continues the path of deep inelastic scattering (DIS) into unknown areas of physics and kinematics. The physics programme also includes electron-deuteron and electron-ion scattering in a (Q 2 1/x) range extended by four orders of magnitude as compared to previous lepton-nucleus DIS experiments for novel investigations of neutron's and nuclear structure, the initial conditions of Quark-Gluon Plasma formation and further quantum chromodynamic phenomena. The LHeC may be realised either as a ring-ring or as a linac-ring collider. Optics and beam dynamics studies are presented for both versions, along with technical design considerations on the interaction region, magnets including new dipole prototypes, cryogenics, RF, and further components. A design study is also presented of a detector suitable to perform high precision DIS measurements in a wide range of acceptance using state-ofthe art detector technology, which is modular and of limited size enabling its fast installation. The detector includes tagging devices for electron, photon, proton and neutron detection near to the beam pipe. Civil engineering and installation studies are presented for the accelerator and the detector. The LHeC can be built within a decade and thus be operated while the LHC runs in its high-luminosity phase. It so represents a major opportunity for progress in particle physics exploiting the investment made in the LHC.

The Large Hadron–Electron Collider (LHeC) is designed to move the field of deep inelastic scattering (DIS) to the energy and intensity frontier of particle physics. Exploiting energy-recovery technology, it collides a novel, intense electron beam with a proton or ion beam from the High-Luminosity Large Hadron Collider (HL-LHC). The accelerator and interaction region are designed for concurrent electron–proton and proton–proton operations. This report represents an update to the LHeC’s conceptual design report (CDR), published in 2012. It comprises new results on the parton structure of the proton and heavier nuclei, QCD dynamics, and electroweak and top-quark physics. It is shown how the LHeC will open a new chapter of nuclear particle physics by extending the accessible kinematic range of lepton–nucleus scattering by several orders of magnitude. Due to its enhanced luminosity and large energy and the cleanliness of the final hadronic states, the LHeC has a strong Higgs physics programme and its own discovery potential for new physics. Building on the 2012 CDR, this report contains a detailed updated design for the energy-recovery electron linac (ERL), including a new lattice, magnet and superconducting radio-frequency technology, and further components. Challenges of energy recovery are described, and the lower-energy, high-current, three-turn ERL facility, PERLE at Orsay, is presented, which uses the LHeC characteristics serving as a development facility for the design and operation of the LHeC. An updated detector design is presented corresponding to the acceptance, resolution, and calibration goals that arise from the Higgs and parton-density-function physics programmes. This paper also presents novel results for the Future Circular Collider in electron–hadron (FCC-eh) mode, which utilises the same ERL technology to further extend the reach of DIS to even higher centre-of-mass energies.

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