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Register a new userBeam dynamics corrections to the Run-1 measurement of the muon anomalous magnetic moment at Fermilab
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T. Albahri
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This paper presents the beam dynamics systematic corrections and their uncertainties for the Run-1 data set of the Fermilab Muon g-2 Experiment. Two corrections to the measured muon precession frequency $omega_a^m$ 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 high-voltage 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 $omega_a^m$ is 0.50 $pm$ 0.09 ppm; the uncertainty is small compared to the 0.43 ppm statistical precision of $omega_a^m$.
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The Neutrinos at the Main Injector (NuMI) facility at Fermilab began operations in late 2004. NuMI will deliver an intense muon neutrino beam of variable energy (2-20 GeV) directed into the Earth at 58 mrad for short (~1km) and long (~700-900 km) baseline experiments. Several aspects of the design and results from early commissioning runs are reviewed.
After a brief self-contained introduction to the muon anomalous magnetic moment, (g-2), we review the status of lattice calculations of the hadronic vacuum polarization contribution and present first results from lattice QCD for the hadronic light-by-light scattering contribution. The signal for the latter is consistent with model calculations. While encouraging, the statistical error is large and systematic errors are mostly uncontrolled. The method is applied first to pure QED as a check.
We present the first results of the Fermilab Muon g-2 Experiment for the positive muon magnetic anomaly $a_mu equiv (g_mu-2)/2$. The anomaly is determined from the precision measurements of two angular frequencies. Intensity variation of high-energy positrons from muon decays directly encodes the difference frequency $omega_a$ between the spin-precession and cyclotron frequencies for polarized muons in a magnetic storage ring. The storage ring magnetic field is measured using nuclear magnetic resonance probes calibrated in terms of the equivalent proton spin precession frequency ${tilde{omega}^{}_p}$ in a spherical water sample at 34.7$^{circ}$C. The ratio $omega_a / {tilde{omega}^{}_p}$, together with known fundamental constants, determines $a_mu({rm FNAL}) = 116,592,040(54)times 10^{-11}$ (0.46,ppm). The result is 3.3 standard deviations greater than the standard model prediction and is in excellent agreement with the previous Brookhaven National Laboratory (BNL) E821 measurement. After combination with previous measurements of both $mu^+$ and $mu^-$, the new experimental average of $a_mu({rm Exp}) = 116,592,061(41)times 10^{-11}$ (0.35,ppm) increases the tension between experiment and theory to 4.2 standard deviations
The MUonE experiment aims at a precision measurement of the hadronic vacuum polarization contribution to the muon $g-2$, via elastic muon-electron scattering. Since the current muon $g-2$ anomaly hints at the potential existence of new physics (NP) related to the muon, the question then arises as to whether the measurement of hadronic vacuum polarization in MUonE could be affected by the same NP as well. In this work, we address this question by investigating a variety of NP explanations of the muon $g-2$ anomaly via either vector or scalar mediators with either flavor-universal, non-universal or even flavor-violating couplings to electrons and muons. We derive the corresponding MUonE sensitivity in each case and find that the measurement of hadronic vacuum polarization at the MUonE is not vulnerable to any of these NP scenarios.
We review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant $alpha$ and is broken down into pure QED, electroweak, and hadronic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including $mathcal{O}(alpha^5)$ with negligible numerical uncertainty. The electroweak contribution is suppressed by $(m_mu/M_W)^2$ and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at $mathcal{O}(alpha^2)$ and is due to hadronic vacuum polarization, whereas at $mathcal{O}(alpha^3)$ the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads $a_mu^text{SM}=116,591,810(43)times 10^{-11}$ and is smaller than the Brookhaven measurement by 3.7$sigma$. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce the theoretical uncertainty in the near future-which are also discussed here-make this quantity one of the most promising places to look for evidence of new physics.
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