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Register a new userThe Muon Anomalous Magnetic Moment and the Standard Model
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David W. Hertzog
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The muon anomalous magnetic moment measurement, when compared with theory, can be used to test many extensions to the standard model. The most recent measurement made by the Brookhaven E821 Collaboration reduces the uncertainty on the world average of a_mu to 0.7 ppm, comparable in precision to theory. This paper describes the experiment and the current theoretical efforts to establish a correct standard model reference value for the muon anomaly.
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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.
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
We report on a precision measurement of the cross section for the reaction $e^+e^-topi^+pi^-$ in the mass range $0.30<M_{pipi}<1.00$ GeV with the initial state radiation (ISR) method, using 817 pb$^{-1}$ of data at $e^+e^-$ center-of-mass energies near 3.77 GeV and 586 pb$^{-1}$ of data at $e^+e^-$ center-of-mass energies near 4.17 GeV, collected with the CLEO-c detector at the CESR $e^+e^-$ collider at Cornell University. The integrated cross sections in the range $0.30<M_{pipi}<1.00$ GeV for the process $e^+e^-topi^+pi^-$ are determined with a statistical uncertainty of $0.7%$ and a systematic uncertainty of $1.5%$. The leading-order hadronic contribution to the muon anomalous magnetic moment calculated using these measured $e^+e^-topi^+pi^-$ cross sections in the range $M_{pipi}=0.30$ to 1.00 GeV is calculated to be $(500.4pm3.6 (mathrm{stat})pm 7.5(mathrm{syst}))times10^{-10}$.
The anomalous magnetic moment of the muon, a_mu, has been measured with an overall precision of 540 ppb by the E821 experiment at BNL. Since the publication of this result in 2004 there has been a persistent tension of 3.5 standard deviations with the theoretical prediction of a_mu based on the Standard Model. The uncertainty of the latter is dominated by the effects of the strong interaction, notably the hadronic vacuum polarisation (HVP) and the hadronic light-by-light (HLbL) scattering contributions, which are commonly evaluated using a data-driven approach and hadronic models, respectively. Given that the discrepancy between theory and experiment is currently one of the most intriguing hints for a possible failure of the Standard Model, it is of paramount importance to determine both the HVP and HLbL contributions from first principles. In this review we present the status of lattice QCD calculations of the leading-order HVP and the HLbL scattering contributions, a_mu^hvp and a_mu^hlbl. After describing the formalism to express a_mu^hvp and a_mu^hlbl in terms of Euclidean correlation functions that can be computed on the lattice, we focus on the systematic effects that must be controlled to achieve a first-principles determination of the dominant strong interaction contributions to a_mu with the desired level of precision. We also present an overview of current lattice QCD results for a_mu^hvp and a_mu^hlbl, as well as related quantities such as the transition form factor for pi0 -> gamma*gamma*. While the total error of current lattice QCD estimates of a_mu^hvp has reached the few-percent level, it must be further reduced by a factor 5 to be competitive with the data-driven dispersive approach. At the same time, there has been good progress towards the determination of a_mu^hlbl with an uncertainty at the 10-15%-level.
We present the final report from a series of precision measurements of the muon anomalous magnetic moment, a_mu = (g-2)/2. The details of the experimental method, apparatus, data taking, and analysis are summarized. Data obtained at Brookhaven National Laboratory, using nearly equal samples of positive and negative muons, were used to deduce a_mu(Expt) = 11 659 208.0(5.4)(3.3) x 10^-10, where the statistical and systematic uncertainties are given, respectively. The combined uncertainty of 0.54 ppm represents a 14-fold improvement compared to previous measurements at CERN. The standard model value for a_mu includes contributions from virtual QED, weak, and hadronic processes. While the QED processes account for most of the anomaly, the largest theoretical uncertainty, ~0.55 ppm, is associated with first-order hadronic vacuum polarization. Present standard model evaluations, based on e+e- hadronic cross sections, lie 2.2 - 2.7 standard deviations below the experimental result.
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