Andreas Nyffeler

The muon g−2

Abstract The muon anomalous magnetic moment is one of the most precisely measured quantities in particle physics. In a recent experiment at Brookhaven it has been measured with a remarkable 14-fold improvement of the previous CERN experiment reaching a precision of 0.54 ppm. Since the first results were published, a persistent “discrepancy” between theory and experiment of about 3 standard deviations is observed. It is the largest “established” deviation from the Standard Model seen in a “clean” electroweak observable and thus could be a hint for New Physics to be around the corner. This deviation triggered numerous speculations about the possible origin of the “missing piece” and the increased experimental precision animated a multitude of new theoretical efforts which lead to a substantial improvement of the prediction of the muon anomaly a μ = ( g μ − 2 ) / 2 . The dominating uncertainty of the prediction, caused by strong interaction effects, could be reduced substantially, due to new hadronic cross section measurements in electron-positron annihilation at low energies. Also the recent electron g − 2 measurement at Harvard contributes substantially to progress in this field, as it allows for a much more precise determination of the fine structure constant α as well as a cross check of the status of our theoretical understanding. In this report we review the theory of the anomalous magnetic moments of the electron and the muon. After an introduction and a brief description of the principle of the muon g − 2 experiment, we present a review of the status of the theoretical prediction and in particular discuss the role of the hadronic vacuum polarization effects and the hadronic light-by-light scattering correction, including a new evaluation of the dominant pion-exchange contribution. In the end, we find a 3.2 standard deviation discrepancy between experiment and Standard Model prediction. We also present a number of examples of how extensions of the electroweak Standard Model would change the theoretical prediction of the muon anomaly a μ . Perspectives for future developments in experiment and theory are briefly discussed and critically assessed. The muon g − 2 will remain one of the hot topics for further investigations.

Precision of a data-driven estimate of hadronic light-by-light scattering in the muon

The evaluation of the numerically dominant pseudoscalar-pole contribution to hadronic light-by-light scattering in the muon g-2 involves the pseudoscalar-photon transition form factor F_{P gamma^* gamma^*}(-Q_1^2, -Q_2^2) with P = pi^0, eta, eta^\prime and, in general, two off-shell photons with spacelike momenta Q_{1,2}^2. We show, in a largely model-independent way, that for pi^0 (eta, eta^\prime) the region of photon momenta below about 1 (1.5) GeV gives the main contribution to hadronic light-by-light scattering. We then discuss how the precision of current and future measurements of the single- and double-virtual transition form factor in different momentum regions impacts the precision of a data-driven estimate of this contribution to hadronic light-by-light scattering. Based on Monte Carlo simulations for a planned first measurement of the double-virtual form factor at BESIII, we find that for the pi^0, eta, eta^\prime-pole contributions a precision of 14\%, 23\%, 15\% seems feasible. Further improvements can be expected from other experimental data and also from the use of dispersion relations for the different form factors themselves.

g-2

A bstractWe present a calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment, aμhvp, in lattice QCD employing dynamical up and down quarks. We focus on controlling the infrared regime of the vacuum polarization function. To this end we employ several complementary approaches, including Padé fits, time moments and the time-momentum representation. We correct our results for finite-volume effects by combining the Gounaris-Sakurai parameterization of the timelike pion form factor with the Lüscher formalism. On a subset of our ensembles we have derived an upper bound on the magnitude of quark-disconnected diagrams and found that they decrease the estimate for aμhvp by at most 2%. Our final result is aμhvp=654±32−23+21

The hadronic vacuum polarization contribution to the muon g − 2 from lattice QCD

{a}_{\mu}^{\mathrm{hvp}} = \left(654 \pm {32}_{{}^{-23}}^{+21}\right)

The Electroweak chiral Lagrangian reanalyzed

·10−10, where the first error is statistical, and the second denotes the combined systematic uncertainty. Based on our findings we discuss the prospects for determining aμhvp with sub-percent precision.

STATUS OF HADRONIC LIGHT-BY-LIGHT SCATTERING IN THE MUON g – 2

Abstract We study the invisible decay of the Higgs boson into a pair of stable, heavy photons, H → A H A H , in the littlest Higgs model with T-parity. For a symmetry breaking scale of f = 450 GeV , the branching ratio H → A H A H can be as high as 93% for Higgs masses below 150 GeV . For f = 500 GeV , the invisible branching ratio is about 75% in the Higgs mass range 135 – 150 GeV and 10 ( 5.5 ) % for m H = 200 ( 600 ) GeV . It drops to a few percent for f larger than 600 GeV . We have found regions in parameter space, allowed by the electroweak precision data, with such low values of f for 115 GeV m H 650 GeV .

Distinguishing the Littlest Higgs model with T-parity from supersymmetry at the LHC using trileptons

In this paper we reanalyze the electroweak chiral Lagrangian with particular focus on two issues related to gauge invariance. Our analysis is based on a manifestly gauge-invariant approach that we introduced recently. It deals with gauge-invariant Greens functions and provides a method to evaluate the corresponding generating functional without fixing the gauge. First we show, for the case where no fermions are included in the effective Lagrangian, that the set of low-energy constants currently used in the literature is redundant. In particular, by employing the equations of motion for the gauge fields one can choose to remove two low-energy constants which contribute to the self-energies of the gauge bosons. If fermions are included in the effective field theory analysis the situation is more involved. Even in this case, however, these contributions to the self-energies of the gauge bosons can be removed. The relation of this result to the experimentally determined values for the oblique parameters S, T, and U is discussed. In the second part of the paper we consider the matching relation between a full and an effective theory. We show how the low-energy constants of the effective Lagrangian can be determined by matching gauge-invariant Greens functions in both theories. As an application we explicitly evaluate the low-energy constants for the standard model with a heavy Higgs boson. The matching at the one-loop level and at next-to-leading order in the low-energy expansion is performed employing functional methods.

Deconstructing non-abelian gauge theories at one loop

We give an update on the status of the hadronic light-by-light scattering contribution to the muon g – 2. We review recent work, list some open problems and give an outlook on how to better control the uncertainty of this contribution. We think the estimate still gives a fair description of the current situation.