Classical Electromagnetic Interaction of a Point Charge and a Magnetic Moment: Considerations Related to the Aharonov–Bohm Phase Shift

A fundamentally new understanding of the classical electromagnetic interaction of a point charge and a magnetic dipole moment through order v ² /c ² is suggested. This relativistic analysis connects together hidden momentum in magnets, Solem's strange polarization of the classical hydrogen atom, and the Aharonov–Bohm phase shift. First we review the predictions following from the traditional particle-on-a-frictionless-rigid-ring model for a magnetic moment. This model, which is not relativistic to order v ² /c ² , does reveal a connection between the electric field of the point charge and hidden momentum in the magnetic moment; however, the electric field back at the point charge due to the Faraday-induced changing magnetic moment is of order 1/c ⁴ and hence is negligible in a 1/c ² analysis. Next we use a relativistic magnetic moment model consisting of many superimposed classical hydrogen atoms (and anti-atoms) interacting through the Darwin Lagrangian with an external charge but not with each other. The analysis of Solem regarding the strange polarization of the classical hydrogen atom is seen to give a fundamentally different mechanism for the electric field of the passing charge to change the magnetic moment. The changing magnetic moment leads to an electric force back at the point charge which (i) is of order 1/c ² , (ii) depends upon the magnetic dipole moment, changing sign with the dipole moment, (iii) is odd in the charge q of the passing charge, and (iv) reverses sign for charges passing on opposite sides of the magnetic moment. Using the insight gained from this relativistic model and the analogy of a point charge outside a conductor, we suggest that a realistic multi-particle magnetic moment involves a changing magnetic moment which keeps the electromagnetic field momentum constant. This means also that the magnetic moment does not allow a significant shift in its internal center of energy. This criterion also implies that the Lorentz forces on the charged particle and on the point charge are equal and opposite and that the center of energy of each moves according to Newton's second law F=Ma where F is exactly the Lorentz force. Finally, we note that the results and suggestion given here are precisely what are needed to explain both the Aharonov–Bohm phase shift and the Aharonov–Casher phase shift as arising from classical electromagnetic forces. Such an explanation reinstates the traditional semiclassical connection between classical and quantum phenomena for magnetic moment systems.     

Optimal bounds for the pion form factor from analyticity and experimental data

Optimal bounds for the pion electromagnetic form factor F(t) below threshold and on the pion mean-square charge radius 〈r_π²〉 = 6F'(0) are derived. Use is made of analyticity arguments and of experimental data on F(t) from e⁺e^? → π⁺π^? as well as e^?p → e^?nπ⁺. The method accounts in an approximate way for the statistical errors of the experimental information. Numerical results for F(t) are calculated for the CEA as well as the DESY electroproduction data.     

An interpolation of the vacuum polarization function for the evaluation of hadronic contributions to the muon anomalous magnetic moment

We propose a simple parameterization of the two-point correlator of hadronic electromagnetic currents for the evaluation of the hadronic contributions to the muon anomalous magnetic moment. The parameterization is explicitly done in the Euclidean domain. The model function contains a phenomenological parameter which provides an infrared cutoff to guarantee the smooth behavior of the correlator at the origin in accordance with experimental data in e ⁺e^- annihilation. After fixing a numerical value for this parameter from the leading order hadronic contribution to the muon anomalous magnetic moment, the next-to-leading order results related to the vacuum polarization function are accurately reproduced. The properties of the four-point correlator of hadronic electromagnetic currents as for instance the so-called light-by-light scattering amplitude relevant for the calculation of the muon anomalous magnetic moment are briefly discussed. Received: 14 December 2001 / Published online: 7 June 2002     

Leptonic coupling-types in K+ → π++- decays and the question of strangeness-changing semileptonic neutral currents

A study of the leptonic coupling types in K⁺→π⁺?⁺?^? (? = e, μ) provides come model-independent distinction between the various underlying mechanism: lowest order weak cum electromagnetic vs higher order weak interactions vs genuine strangeness-changing semileptonic neutral currents. This distinction is necessary in order to know the existence of these neutral currents. Pion energy spectrum for ? = e and the ratio of the total rate for ? = e to that for ? = μ is useful for this purpose, and the pion energy spectrum for ? = μ is of further help. Available data (? = eonly) are inadequate to provide the above distinction. Estimates of various coupling strengths are made from the observed ? = e rate.     

Testing weak neutral currents in longitudinally polarized colliding beams

We study the effects of a weak neutral current as they show up in longitudinally polarized colliding beams. The reactions considered here are e⁺e^?→μ⁺μ^? and e⁺e^?→π⁺π^?. The electromagnetic background and means to suppress this are also discussed.     

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.     

Anomalous magnetic moment of the muon in the left-right model

The effect of Higgs bosons on the anomalous magnetic moment of the muon is considered within the model that is based on the SU(2)_L×SU(2)_R×U(1)_B–L gauge group and which involves a bidoublet and two triplets of Higgs fields (left-right model). For the Yukawa coupling constants and the masses of Higgs bosons, the regions are found where the model leads to agreement with experimental results obtained at the Brookhaven National Laboratory (BNL) for the anomalous magnetic moment of the muon. In order to explore corollaries from the constraints obtained for the parameters of the Higgs sector, the processes e⁺e^? → μ⁺μ^?, τ⁺τ^? and μ⁺μ^? → μ⁺μ^?, τ⁺τ^? are considered both within the left-right model and within the model involving two Higgs doublets (two-Higgs-doublet model). It is shown that, if the mass of the lightest neutral Higgs boson does indeed lie in the range 3.1–10 GeV, as is inferred from the condition requiring the consistency of the two-Higgs-doublet model with the data of the BNL experiment, this Higgs boson may be observed as a resonance peak at currently operating e⁺e^? colliders (VEPP-4M, CESR, KEKB, PEP-II, and SLC). In order to implement this program, however, it is necessary to reduce considerably the scatter of energy in the e⁺ and e^? beams used, since the decay width of the lightest neutral Higgs boson is extremely small at such mass values. It is demonstrated that, in the case of the left-right model, for which the mass of the lightest neutral Higgs boson is not less than 115 GeV, the resonance peak associated with it may be detected at a muon collider.     

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.     

Pionic contribution to the muon magnetic moment

A procedure is developed to derive an optimal lower bounds for the pionic contribution to the muon magnetic moment from analyticity of the pion form factor F(t), its normalization F(0)=1 and from experimental information from both the processes e^?p → e^?π⁺n and e⁺e^? → π⁺π^?. It represents essentially the solution of a certain kind of optimization problem in Hilbert space. Numerical results are presented and compared to the recent data for the muon magnetic moment; we find a_μ(π⁺π^?) ? 42 × 10^?9.     

Photon production in Au+Au collisions at \sqrt {s_{NN} } = 130 GeV

We report raw photon, neutral pion and eta measurements at RHIC. Photons in the energy range from 100MeV ? 4GeV were detected by reconstructing e ⁺ e ^? pair production, γ+Z→e ⁺+e ^?+Z, with the STAR Time Projection Chamber (TPC). Along with the photon detection technique we discuss the purity of the photon candidates and measurements of hadronic decays via their electromagnetic decay channels. The π⁰→γ and η→γγ decay channels are addressed.     

Classical Electromagnetism and the Aharonov–Bohm Phase Shift

Although there is good experimental evidence for the Aharonov–Bohm phase shift occurring when a solenoid is placed between the beams forming a double-slit electron interference pattern, there has been very little analysis of the relevant classical electromagnetic forces. These forces between a point charge and a solenoid involve subtle relativistic effects of order v ² /c ² analogous to those discussed by Coleman and Van Vleck in their treatment of the Shockley–James paradox. In this article we show that a treatment exactly analogous to that given by Coleman and Van Vleck predicts classical electromagnetic forces which provide the basis for the Aharonov–Bohm phase shift. The magnetic force on the solenoid due to the passing charge leads to a displacement of the solenoid center of energy which must be balanced by the displacement of the passing charge. This classical displacement of the passing charge is exactly what is required to account for the Aharonov–Bohm phase shift. Also, we discuss a magnetic moment model which appears frequently in the literature and note that although the model provides conservation of linear momentum, it does not satisfy the general requirements for relativistic theories. We give an example suggesting that the new equation of motion for a magnetic moment proposed by Aharonov, Pearle, and Vaidman based upon the hidden momentum of the magnetic moment is completely inappropriate. Finally, we emphasize that the Aharonov–Casher phase shift is also explained by classical electromagnetic forces exactly parallel to those explaining the Aharonov–Bohm phase shift.     

A theorem on electromagnetic properties of leptons

The following theorem is proven: Every lepton with the mass m, electric charge q and spin J belonging to any representation of a non-abelian gauge group must have the magnetic moment μ = qJm^?1, electric mean squared radius r² = qJ(J + 1)m^?2 and electric quadrupole moment Q = qJ(2J ? 1)m^?2 in the first order of the electromagnetic effects in an arbitrary renormalizable theory with the non-abelian gauge group symmetry which permits the validity of the Gerasimow-Drell-Hearn and Cabibbo-Radicati sum rules. The formula for the magnetic moment applies also for an abelian symmetry and remains valid even if the gauge symmetry is spontaneously broken.     

Collective states in 48V

The low-lying positive parity states of ⁴⁸V have been studied in the framework of deformed configuration mixing model calculations based on projected Hartree-Fock theory, within the full fp shell space. The modified Kuo-Brown effective interaction has been used. The calculated spectrum and the electromagnetic properties of these states are in good agreement with the experiment. The calculation predicts an excited low-lying collective K = 2⁺ band in the spectrum of ⁴⁸V and accounts for the observed breakdown of the “signature” selection rule arising in the shell-model calculation within the ($\text{f}\text{7}\text{2}\text{)}{}^{\mathrm{nd}}$ space. It does not favour a 5⁺ assignment to the observed 1.099 MeV level. Two sets of proton and neutron effective charges (i) e_p = 1.32e and e_n = 0.89e and (ii) Kuo and Osnes charges e_p = 1.25e and e_n = 0.47e were employed. The observed decay properties appear to favour the latter charges. Our model also explains in a semiquantitative way the observed K-value, moment of inertia parameter and the intrinsic quadrupole moment of the K = 1^?1 rotational band.     

Electric charge as a quantum of flux

Ratio of electron charge radius and Compton wavelength of electron is known to be equal to the dimensionless electromagnetic coupling constant e²/? c. It is pointed out that the coupling constant has two alternative interpretations: as a ratio of two angular momenta since Planck constant has the dimension of angular momentum, and two flux quanta e and hc/e. We argue that it has deep physical significance such that the electronic charge becomes flux itself and at a fundamental level fractional spin of quantized vortex. A unified perspective of the three interpretations of the coupling constant is presented invoking the new interpretation of the magnetic moment of the electron comprising three terms. A critical discussion on the magnetism and flux quantum is given and the implication on the spintronics is pointed out.     

Limits on the τ neutrino electromagnetic properties from single photon searches ate + e − colliders

We set limits on the magnetic moment and charge radius of the τ neutrino by examining the contributions to the processe ⁺ e ^?→v \(\bar \nu \) γ due to such interactions. We find thatK(ν_τ)<4×10^?6 (i.e.μ(ν_τ)<4×10^?6μ _B , μ _B =e/2m _e ) and 〈r ²〉<2×10^?31 cm² using the combined data of the MAC, ASP, CELLO, and Mark J collaborations for this process. We briefly discuss whether these bounds can be improved in any futuree ⁺ e ^? experiments.     

A class of exactly solvable three-body quantum mechanical problems and the universal low energy behavior

Three-body systems with two-body point interactions are studied. These systems are the universal low energy limits of three-body problems with short-range two-body forces. Hence if there are infinitely many spherically symmetric three-body bound states with energies E_n then lim_n→∞E_n/E_n+1 = e^2λσ, where σ is explicitly computed.     

Photon damping caused by electron-positron pair production in a strong magnetic field

Damping of an electromagnetic wave in a strong magnetic field is analyzed in the kinematic region near the threshold of electron-positron pair production. Damping of the electromagnetic field is shown to be noticeably nonexponential in this region. The resulting width of the photon γ→e ⁺ e ^? decay is considerably smaller than previously known results.     

New resonance-polariton Bose-quasiparticles enhances optical transmission into nanoholes in metal films

We argue the existence of fundamental particles in nature, neutral Light-Particles with spin 1, and rest mass m=1.8⋅¹⁰−4me, in addition to electrons, neutrons and protons. We call these particles Light Bosons because they create the electromagnetic field which represents Planck's gas of massless photons together with a gas of Light-Particles in the condensate. In this respect, the condensed Light-Particles, having no magnetic field, represent the constant electric field. In this context, we predict an existence of polariton-plasmon Bose-quasiparticles with effective masses ml≈¹⁰−6me and mr=0.5me, which are induced by interaction of the plasmon field and the resonance Frölich-Schafroth charged bosons with electromagnetic wave in metal. Also, we prove that the enhancement optical transmission into nanoholes in metal films and Surface Enhanced Raman Spectroscopy are provided by a new resonance-polariton Bose-quasiparticles but not model of surface plasmon-polariton. In this Letter, the quantization Fresnel's equations is presented which confirms that Light-Particles in the condensate are concentrated near on the wall of grooves in metallic grating and, in turn, represent as the constant electric field which provides the launching of the surface Frölich-Schafroth bosons on the surface metal holes.     

Intensity distribution in the bands of the D1 → X1∑+ system of PbO

Relative integrated intensities of the D1 → X¹∑⁺ system of PbO have been measured by heterochromatic photography photometry. The Morse potential has been employed to compute the Franck-Condon factors and r-centroids. The variation of electronic transition moment R_e with internuclear separation r is found to be R_e(r) = const × (0.54 r − 1) in the range 1.957 ⩽ r, Å ⩽ 2.051. Relative band strengths are derived. The effective vibrational temperature of the source was 6199 K.