Confronting spectral functions from ee annihilation and $\tau$ decays: consequences for the muon magnetic moment

Vacuum polarization integrals involve the vector spectral functions which can be experimentally determined from two sources: (i) e ⁺ e ^- annihilation cross sections and (ii) hadronic decays. Recently results with comparable precision have become available from CMD-2 on one side, and ALEPH, CLEO and OPAL on the other. The comparison of the respective spectral functions involves a correction from isospin-breaking effects, which is evaluated. After the correction it is found that the dominant spectral functions do not agree within experimental and theoretical uncertainties. Some disagreement is also found for the spectral functions. The consequences of these discrepancies for vacuum polarization calculations are presented, with the emphasis on the muon anomalous magnetic moment. The work includes a complete re-evaluation of all exclusive cross sections, taking into account the most recent data that became available in particular from the Novosibirsk experiments and applying corrections for the missing radiative corrections. The values found for the lowest-order hadronic vacuum polarization contributions are where the errors have been separated according to their sources: experimental, missing radiative corrections in e ⁺ e ^- data, and isospin breaking. The Standard Model predictions for the muon magnetic anomaly read where the errors account for the hadronic, light-by-light scattering and electroweak contributions. We observe deviations with the recent BNL measurement at the 3.0 (e ⁺ e ^- ) and 0.9 () level, when adding experimental and theoretical errors in quadrature. Received: 27 August 2002 / Revised version: 10 January 2003 / Published online: 26 February 2003 RID="a" ID="a" e-mail: davier@lal.in2p3.fr RID="b" ID="b" e-mail: simon.eidelman@cern.ch RID="c" ID="c" e-mail: hoecker@lal.in2p3.fr RID="d" ID="d" e-mail: zhangzq@lal.in2p3.fr     

Higher-order hadronic contributions to the anomalous magnetic moment of leptons

Higher-order hadronic contributions to the anomalous magnetic moment of the electron, muon, and π lepton are considered in detail. As a main result we find a reduction by −11 × 10⁻¹¹ for the g-2 of the muon as compared to previous calculations. Analytical expressions for the kernel functions of higher-order hadronic effects are presented. We employ the method of asymptotic expansions to calculate kernel functions analytically in terms of a series expansion in the lepton mass.     

Muon anomalous magnetic moment: A consistency check for the next-to-leading-order hadronic contributions

A duality-inspired model for verifying a consistency of the evaluation of the next-to-leadingorder hadronic contributions to the muon anomalous magnetic moment with that of the leading-order ones is proposed. A part of the next-to-leading-order hadronic contributions related to the photon vacuum polarization function is rather accurately reproduced in the model. I find a new numerical value for the light-by-light hadronic contribution that leads to the agreement of the Standard Model theoretical prediction for the muon anomalous magnetic moment with the recent experimental result.     

Pseudo scalar contributions to light-by-light correction of muon in AdS/QCD

We have performed a holographic calculation of the hadronic contributions to the anomalous magnetic moment of the muon, using the gauge/gravity duality. As a gravity dual model of QCD with three light flavors, we study a U(3)_L×U(3)_R flavor gauge theory in the five-dimensional AdS background with a hard-wall cutoff. The anomalous (electromagnetic) form factors for the pseudo scalars, π⁰, η and η^′, are obtained from the 5D Chern–Simons term of the gravity dual, which correctly reproduce the asymptotic behavior of the form factor, dictated by QCD. We find the total light-by-light contributions of pseudo scalars to the muon anomalous magnetic moment, , which is consistent with previous estimates, based on other approaches.     

The τ lepton as a laboratory for quantum chromodynamics

Decays of the τ lepton provide a clean environment to study hadron dynamics in an energy regime dominated by resonances. Inclusive spectral functions are the basis for quantum chromodynamics (QCD) analyses, providing a most accurate determination of the strong coupling constant and quantitative information on nonperturbative contributions. The τ vector spectral function is used together with e⁺e⁻ data in order to compute vacuum polarization integrals arising in the calculations of the anomalous magnetic moment of the muon and the running of the electromagnetic coupling constant. To cite this article: M. Davier, A. Höcker, C. R. Physique 3 (2002) 1223–1233.     

New definition for the hadronic contribution to the muon anomalous magnetic moment

A new definition is proposed for the hadronic contribution to the muon anomalous magnetic moment that is based on the inclusion of the effects of vacuum polarization by leptons into the cross section for one-photon annihilation of a lepton pair into hadrons. The formula for the hadronic contribution includes the convolution of the measured cross section for annihilation into hadrons with a certain standard function. This remark concerns radiative correction to this function. A particular form has been proposed for this correction. It has been shown that the use of the new function makes it possible to reduce the uncertainty in such contributions due to radiative correctioins to δa _h/a _h ～ 10^?4.     

Effect of the neutrino magnetic moment on the properties of the muon

The effect of the neutrino dipole magnetic moment on the properties of the muon is investigated within the standard model of electroweak interactions and a model based on the SU(2) _L × SU(2) _R × U(1) _B-L gauge group (left-right model). In the case of the Dirac neutrino, muon decay through the channel µ^? → e ^?γ is studied with allowance for the neutrino dipole magnetic moment. It is shown that, both in the standard model supplemented with an SU(2) _L right-handed neutrino singlet and in the standard model featuring two doublets of Higgs fields, radiative muon decay is unobservable. In the left-right model, the contributions of diagrams associated with the neutrino dipole magnetic moment become significant only in the case of a mutual compensation of the contributions of diagrams involving the electromagnetic vertices of charged gauge bosons and singly charged Higgs bosons. At specific values of the parameters of the left-right model, one can then obtain an experimental upper limit on the branching fraction of this reaction. The contributions of the neutrino dipole magnetic moment to the muon anomalous magnetic moment are found for the Dirac and the Majorana neutrino. It is established that, both in the standard model and in the left-right model, values of the neutrino anomalous magnetic moment that are required for explaining the (g ? 2)_µ anomaly are in excess of the theoretical predictions for this moment.     

Light by light in the muon g-2

Theoretical calculations of hadronic contributions to the muon anomalous magnetic moment are briefly reviewed. We present a model for the hadronic light-by-light scattering amplitude consistent with the short-distance constraints from the operator product expansion. The text was submitted by the authors in English.     

Stokes parameters of γ-quanta in the e+ + e− → Z + γ reaction

A general analysis is made of the polarization properties of γ-quanta in the e⁺ + e^? → Z + γ reaction. Besides the standard mechanism of this reaction; which is determined by the eeZ interaction (neutral weak currents), the possible anomalous magnetic moment χ of the Z boson is also taken into account. A linear contribution in χ. to the differential cross section of the e⁺ + e^? → Z + γ process (with unpolarized particles in the initial and final states) leads to CP-odd asymmetry of the angular distribution of γ-quanta relative to the substitution cos Θ→?cos Θ, where Θ is the angle of emission of the γ-quantum relative to the electron. Measurement of this asymmetry with an accuracy of the order of 1% makes it possible to get a “sense” of the contribution of the magnetic moment of a Z boson of the order of 10^?3 GeV^?1.     

Contributions to the muon’s anomalous magnetic moment from a hidden sector

The measurement of the anomalous magnetic moment of the muon provides a stringent test of the standard model and of any physics that lies beyond it. There is currently a deviation of 3.1σ between the standard model prediction for the muon’s anomalous magnetic moment and its experimental value. We calculate the contribution to the anomalous magnetic moment in theories where the muon couples to a particle in a hidden sector (that is, uncharged under the standard model) and a connector (which has nontrivial standard model gauge and hidden sector quantum numbers).     

Electric dipole moments of charged leptons in the split fermion scenario in the two Higgs doublet model

We predict the charged lepton electric dipole moments in the split fermion scenario in the framework of the two Higgs doublet model. We observe that the numerical value of the muon (tau) electric dipole moment is of the order of the magnitude of 10^-22 e cm (10^-20 e cm) and there is an enhancement in the case of two extra dimensions, especially for the tau lepton electric dipole moment. Received: 15 July 2005, Published online: 6 October 2005     

Hadronic light-by-light scattering contribution to the muon magnetic anomaly: Constituent quark loops and QCD effects

The hadronic light-by-light scattering contribution to the muon anomalous magnetic moment can be estimated by computing constituent quark loops. Such an estimate is very sensitive to the numerical values of the constituent quark masses. These can be fixed by computing the hadronic vacuum polarization contribution to the muon magnetic anomaly within the same model. In this Letter, we demonstrate the stability of this framework against first-order perturbative QCD corrections.     

Letter: Antisymmetric Tensor Contribution to the Muon g − 2

We investigate the Kalb-Ramond antisymmetric tensor field as a solution to the muon g – 2 problem. In particular we calculate the lowest-order Kalb-Ramond contribution to the muon anomalous magnetic moment and find that we can fit the new experimental value for the anomaly by adjusting the coupling without affecting the electron anomalous magnetic moment results.     

Recent progress on isospin breaking corrections and their impact on the muon g-2 value

We describe some recent results on isospin breaking corrections which are of relevance for predictions of the leading order hadronic contribution to the muon anomalous magnetic moment ahμa d,LOwhen using τ lepton data.When these corrections are applied to the new combined data on the π±π0 spectral function,the prediction for aμha d,LObased on τ lepton data gets closer to the one obtained using e+e-data.     

Vector correlators in lattice QCD: Methods and applications

We discuss the calculation of the leading hadronic vacuum polarization in lattice QCD. Exploiting the excellent quality of the compiled experimental data for the e ⁺ e ⁻ → hadrons cross-section, we predict the outcome of large-volume lattice calculations at the physical pion mass, and design computational strategies for the lattice to have an impact on important phenomenological quantities such as the leading hadronic contribution to (g − 2) _μ and the running of the electromagnetic coupling constant. First, the R(s) ratio can be calculated directly on the lattice in the threshold region, and we provide the formulae to do so with twisted boundary conditions. Second, the current correlator projected onto zero spatial momentum, in a Euclidean time interval where it can be calculated accurately, provides a potentially critical test of the experimental R(s) ratio in the region that is most relevant for (g − 2) _μ . This observation can also be turned around: the vector correlator at intermediate distances can be used to determine the lattice spacing in fm, and we make a concrete proposal in this direction. Finally, we quantify the finite-size effects on the current correlator coming from low-energy two-pion states and provide a general parametrization of the vacuum polarization on the torus.     

Physics with high energy electron-positron colliding beams with the MARK J detector

This report reviews the experimental investigation of high energy e⁺e^? interactions by the MARK J collaboration at PETRA, the electron-positron colliding beam accelerator at DESY in Hamburg, Germany. The physics objectives include studies of several purely electromagnetic processes and hadronic final states, which further our knowledge of the nature of the fundamental constituents and of their strong, electromagnetic and weak interactions. Before discussing the physics results, the main features and the principal components of the MARK J detector are discussed in terms of design, function, and performance. Several aspects of the on-line data collection and the off-line analysis are also outlined. Results are presented on tests of quantum electrodynamics using e⁺e^? → e⁺e^?, μ⁺μ^? and τ⁺τ^?, on the measurement of R, the ratio of the hadronic to the point-like muon pair cross section, on the search for new quark flavors, on the discovery of three jet events arising from the radiation of hard noncollinear gluons as predicted by quantum chromodynamics, and on the determination of the strong coupling constant α_s.     

Finite volume corrections to the electromagnetic current of the nucleon

We compute corrections to both the isovector anomalous magnetic moment and the isovector electromagnetic current of the nucleon to O(p³)\ensuremath O(p^3) in the framework of covariant two-flavor Baryon Chiral Perturbation Theory. We then apply these corrections to lattice data for the anomalous magnetic moment from the LHPC, RBC & UKQCD and QCDSF Collaborations.     

Long-range potentials and the electromagnetic polarizabilities

The long-range spin and velocity independent forces of electromagnetic origin which act between any two systems are studied for those cases in which no forces of this type exist to order e². It is shown that they are uniquely determined by the charge, magnetic moment, and polarizabilities of both systems, not only to the dominant order r^?n, but also to the next one r^?(n+1). These potentials provide the link between Compton scattering polarizabilities (response to real photons) and classically defined polarizabilities (response to static electromagnetic field). The two definitions are shown to be equivalent for neutral spinless systems; the problems arising for a neutral particle with magnetic moment are studied in detail. The r^?(n+1) terms have no classical counterpart, since they are due to the relativistic quantum propagation of the system which carries charge or magnetic moment. The results are of general validity with analyticity, crossing, unitarity, and gauge invariance as only inputs. The most general conclusion is that the polarizabilities represent electromagnetic properties of a system at order e², as the charge and magnetic moment do at order e. Thus they give the strength of the response to electric and magnetic fields, independently of the specific characteristics of the electromagnetic agent.     

Hadronic loop corrections to the muon anomalous magnetic moment

The dominant theoretical uncertainties in both the anomalous magnetic moment of the muon and the value of the electromagnetic coupling at the Z scale, M(Z), arise from their hadronic contributions. Since these will ultimately dominate the experimental errors, we study the correlation between them, as well as with other fundamental parameters. To this end we present analytical formulas for the QCD contribution from higher energies and from heavy quarks. Including these correlations affects the Higgs boson mass extracted from precision data.     

$VA\widetilde{V}$ correlator within the instanton vacuum model

The correlator of vector and non-singlet axial-vector currents in the external electromagnetic field is calculated within the instanton liquid model of the QCD vacuum. In general the correlator has two Lorentz structures: longitudinal, w_L, and transversal, w_T, with respect to the axial-vector index. Within the instanton model the saturation of the anomalous w_L structure is demonstrated. It is known that in the chiral limit the transversal structure w_T is free from perturbative corrections. In this limit within the instanton model we calculate the transversal invariant function w_T at arbitrary space-like momentum transfer q and show the absence of power corrections to this structure at large q². Instead there arise exponential corrections to w_T at large q² reflecting non-local properties of the QCD vacuum. The slope of w_T at zero virtuality, the QCD vacuum magnetic susceptibility of the quark condensate and its momentum dependence are estimated.Received: 7 May 2005, Published online: 6 July 2005