A. Peterman

RECENT DEVELOPMENTS IN THE COMPARISON BETWEEN THEORY AND EXPERIMENTS IN QUANTUM ELECTRODYNAMICS.

Abstract This review is a survey of three main topics in quantum electrodynamics: fundamental bound systems anomalous magnetic moments and high energy experiments. The emphasis lies particularly in recent developments concerninf the electron and muon anomalous magnetic moments.

Renormalization Group and the Deep Structure of the Proton

Abstract The spirit of the renormalization group approach lies entirely in the observation that in a specific theory the renormalization constants such as the couplings, the masses, are arbitrary mathematical parameters which can be varied by changing arbitrarily the renormalization prescription. For example, given a scale of mass μ, prescriptions can be chosen by doing subtractions of the relevant amplitudes at the continously varying points μ et, t being an arbitrary real parameter. A representation of such a renormalization group transformatio n μ→ μ=μ e t is the transformation g→ itg (t) of the renormalized coupling into a continously varying coupling cons the so-called “running coupling constant”. If, for the theory under investigation there exists a domain of the t space where g (t) i small, then because we are ignorant of how to handle field theory beyond the perturbative approach, one should focus attention on the experimental range in which g (t) “runs” with small values. Indeed, taking momenta q0 et=q, corresponds to working with momenta q 0 and mass scale μ e−1, which by a renormalization group transformation as above is the same as working with μ and g (t)(t = log q q 0 ) . In non-Abelian gauge theories, as t increases, g (t) behaves like 1 t →0 and it is possible to find q and q0 ranges such that perturbation theory can be applied (asymptotic freedom). The study of physical quantities at different values of their energy momenta is therefore reflected by a study of these quantities at moderate energies with couplings which are not constants but vary with the energies at which one is working. The introduction of couplings varying with energy momentum is the major outcome of the renormalization group formalism. One is therefore able to follow the evolution of these couplings and masses through large appropriate domains of energy. Applicability of naive perturbation expansion to non-Abelian gauge theories of strong interactions in the domain of high energy momentum transfer is one result from the renormalization group way of looking at these problems and will probably remain its only use. Non-trivial fixed points are unlikely to occur. Emphasis is put in this paper exclusively on deep inelastic scattering of lepton off hadrons, using the light cone operator product expansion. All other processes like lepton-antilepton annihilation into hadrons, lepton pair production in hadronic collisions, large pT production in such collisions are deliberately not discussed, though we know that asymptotic freedom might apply there too; therefore a perturbation treatment in terms of the running coupling constant is sensible for parton induced reactions. Generalities on the factorization procedure are mentioned in the conclusion of this paper. Problems other than those raised in field theory must be treated on a more general basis. Noteworthy examples of critical behaviour show the existence of non-trivial fixed points and non-trivial become the applications of the renormalization group approach. Reference to these phenomena will be only shortly made in the conclusion of this paper, as excellent recent reviews exist already on the subject.

ANALYTIC 4th ORDER CROSSED LADDER CONTRIBUTION TO THE LAMB SHIFT.

Abstract A systematic investigation is made of the wotk of Soto. The algebra is redone entirely. The integrals are tested numerically. Each dubious or litigious integral is recomputed analytically. The contribution to the 4th order slope zero momentum transfer is found to be in the Feynman gauge.

A new value of the anomalous magnetic moment of the electron

Abstract The contribution to the sixth order anomaly ae(6) from light-by-light scattering subgraphs is recomputed. The result is: aeγ−γ = (α3/π3)(0.366 ± 0.010). This result agrees with a previous calculation done at SLAC. The accuracy is improved by a factor of 4. With the currently accepted values for many of the other diagrams, the sixth order anomaly is ae(6) = (1.16 ± 0.07) (σ/π)3.

Confirmation of a new theoretical value for the Lamb shift

Abstract We have performed a recalculation of the contribution to the Lamb shift from two fourth order vertex graphs. We agree with a recent calculation by Appelquist and Brodsky.

Contribution to the muon anomaly from a set of eighth order diagrams

Abstract The value of the 18 diagrams of eoghth order, containing second order vacuum polarization and scattering of light-by-light insertions is calculated, giving a value of (111.1 ± 8.1) × (α/π) 4 . It agrees with the estimate given formerly by Lautrup.

A new value for the lamb shift

Abstract The recent analytic value of the α 2 slope of the Dirac form factor of the free electron, from the crossed ladder diagram, is added to the contributions of the fourth order diagrams already evaluated by different workers. The sum is found to be F 1 ′ (0) total = ( α 2 π 2 ) {− 4819 5184 − 49π 2 432 + 1 2 π 2 log 2 − 3 4 ζ(3)} = ( α 2 π 2 ) {0.4699}. This contributes to the Lamb shift in H: ( α 2 π 2 ) α 1 2 2 mα 2 0.4699 = 0.444 MHz . The total Lamb shift in H is then: S H = (2 S 1 2 − 2 P 1 2 ) H = 1057.911 ± 0.011 MHz (s.d.), and the separation ΔE H − S H : (2 S 3 2 − 2 S 1 2 ) H = 9911.115 ± 0.031 MHz (s.d.).

On sixth-order corrections to the anomalous magnetic moment of the electron

Abstract The gauge-invariant contribution to the anomalous magnetic moment of the electron (or muon) from four diagrams has been calculated. The results is infra-red convergent and numerically equal to: ( α π ) 3 {0.477±0.023} .

On sixth-order radiative corrections toaμ—ae

SummaryThe contribution to the anomalous magnetic moment of the muon from the Feynman diagrams shown in the Figure is found to be