Beam dynamics corrections to the Run-1 measurement of the muon anomalous magnetic moment at Fermilab

Abstract

This paper presents the beam dynamics systematic corrections and their uncertainties for the Run-1 dataset of the Fermilab Muon g−2 Experiment. Two corrections to the measured muon precession frequency ω m a are associated with well-known effects owing to the use of electrostatic quadrupole (ESQ) vertical focusing in the storage ring. An average vertically oriented motional magnetic field is felt by relativistic muons passing transversely through the radial electric field components created by the ESQ system. The correction depends on the stored momentum distribution and the tunes of the ring, which has relatively weak vertical focusing. Vertical betatron motions imply that the muons do not orbit the ring in a plane exactly orthogonal to the vertical magnetic field direction. A correction is necessary to account for an average pitch angle associated with their trajectories. A third small correction is necessary, because muons that escape the ring during the storage time are slightly biased in initial spin phase compared to the parent distribution. Finally, because two highvoltage resistors in the ESQ network had longer than designed RC time constants, the vertical and horizontal centroids and envelopes of the stored muon beam drifted slightly, but coherently, during each storage ring fill. This led to the discovery of an important phase-acceptance relationship that requires a correction. The sum of the corrections to ω m a is 0.50 ± 0.09 ppm; the uncertainty is small compared to the 0.43 ppm statistical precision of ω m a .

A dispersive analysis of $$\varvec{\eta '\rightarrow \pi ^+\pi ^-\gamma }$$ and $$\varvec{\eta '\rightarrow \ell ^+\ell ^-\gamma }$$

“…Currently, the main uncertainty in the Standard-Model prediction a SM μ = 116 591 810(43) × 10 −11 (1.4) originates from hadronic vacuum polarization, see, e.g., Refs. [20,[49][50][51][52][53][54] for further discussion, but to match the final projected precision of the Fermilab experiment, which will improve upon the current world average [55][56][57][58][59] a exp μ = 116 592 061(41) × 10 −11 (1.5) by more than another factor of two, also the uncertainties in 123 the subleading HLbL contribution, in Ref. [20] estimated as [33][34][35][36][37][38][39][40][41][42][43][44][45][46][60][61][62][63][64][65] a HLbL μ = 90(17) × 10 −11 , (1.6) need to be reduced accordingly.…”

Short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude: an update

“…, with coefficients determined via decay constants in analogy to (4), see [70]. This implies that, asymptotically,…”

“…The recent measurement of (g − 2) µ by the Fermilab Muon g − 2 collaboration [1][2][3][4] has made the discrepancy with the Standard-Model prediction more serious, by bringing it from the 3.7σ to the 4.2σ level when combined with the previous Brookhaven measurement [30]. The concrete perspective of additional reductions of the experimental uncertainty in the near future-mainly from subsequent Runs at Fermilab [31], but also the future J-PARC experiment [32] using a different technique-makes the need of further theoretical improvements more urgent.…”

Chiral perturbation theory: reflections on effective theories of the standard model

“…These results can be found in a set of publications in refs. [138][139][140][141]. The main source of the discrepancy comes from the hadronic vacuum polarization contributions and another somewhat less numerically important but relatively larger uncertainty known as the hadronic light by light scattering contributions.…”