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.

The proposed International Linear Collider (ILC) is well-suited for discovering physics beyond the Standard Model and for precisely unraveling the structure of the underlying physics. The physics return can be maximized by the use of polarized beams. This report shows the paramount role of polarized beams and summarizes the benefits obtained from polarizing the positron beam, as well as the electron beam. The physics case for this option is illustrated explicitly by analyzing reference reactions in different physics scenarios. The results show that positron polarization, combined with the clean experimental environment provided by the linear collider, allows to improve strongly the potential of searches for new particles and the identification of their dynamics, which opens the road to resolve shortcomings of the Standard Model. The report also presents an overview of possible designs for polarizing both beams at the ILC, as well as for measuring their polarization.2

An experiment (E166) at the Stanford Linear Accelerator Center (SLAC) has demonstrated a scheme in which a multi-GeV electron beam passed through a helical undulator to generate multiMeV, circularly polarized photons which were then converted in a thin target to produce positrons (and electrons) with longitudinal polarization above 80% at 6 MeV. The results are in agreement with Geant4 simulations that include the dominant polarization-dependent interactions of electrons, positrons and photons in matter.PACS . Polarized positrons can be produced via the pair-production process initiated by circularly polarized photons [2]. In a scheme proposed by Balakin and Mikhailichenko [3] a multi-GeV electron beam is passed through a helical undulator [4] to generate the needed multi-MeV photons with circular polarization. Alternatively, the circularly polarized photons can be produced by laser backscattering off an electron beam [5,6]. An experiment (E166) has been performed to demonstrate that the undulatorbased scheme can produce polarized positron beams of sufficient quality for use at the proposed International Linear Collider (ILC) [7]. The main elements of the experiment were the SLAC linac

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A method of enhanced optical cooling (EOC) based on nonlinear selective interaction between particles and theirs amplified undulator radiation wavelets (URW) in storage rings is discussed. It leads to non-exponential fast damping. The selectivity is arranged by a moving screen located on the image plane of the optical system projecting URW there.