Toichiro Kinoshita

Mass Singularities of Feynman Amplitudes

Feynman amplitudes, regarded as functions of masses, exhibit various singularities when masses of internal and external lines are allowed to go to zero. In this paper, properties of these mass singularities, which may be defined as pathological solutions of the Landau condition, are studied in detail. A general method is developed that enables us to determine the degree of divergence of unrenormalized Feynman amplitudes at such singularities. It is also applied to the determination of mass dependence of a total transition probability. It is found that, although partial transition probabilities may have divergences associated with the vanishing of masses of particles in the final state, they always cancel each other in the calculation of total probability. However, this cancellation is partially destroyed if the charge renormalization is performed in a conventional manner. This is related to the fact that interacting particles lose their identity when their masses vanish. A new description of state and a new approach to the problem of renormalization seem to be required for a consistent treatment of this limit.

Tenth-Order QED Contribution to the Electron g-2 and an Improved Value of the Fine Structure Constant

This letter presents the complete QED contribution to the electron g-2 up to the tenth order. With the help of the automatic code generator, we evaluate all 12,672 diagrams of the tenth-order diagrams and obtain 9.16 (58)(α/π)(5). We also improve the eighth-order contribution obtaining -1.9097 (20)(α/π)(4), which includes the mass-dependent contributions. These results lead to a(e)(theory)=1,159,652,181.78(77)×10(-12). The improved value of the fine-structure constant α(-1)=137.035999173 (35) [0.25 ppb] is also derived from the theory and measurement of a(e).

Complete tenth-order QED contribution to the muon g-2.

We report the result of our calculation of the complete tenth-order QED terms of the muon g-2. Our result is a(μ)((10))=753.29 (1.04) in units of (α/π)(5), which is about 4.5 s.d. larger than the leading-logarithmic estimate 663(20). We also improve the precision of the eighth-order QED term of a(μ), obtaining a(μ)((8))=130.8794 (63) in units of (α/π)(4). The new QED contribution is a(μ)(QED)=116,584,718,951 (80)×10(-14), which does not resolve the existing discrepancy between the standard-model prediction and measurement of a(μ).

The Tenth-order QED contribution to the lepton g-2: Evaluation of dominant alpha**5 terms of muon g-2

The QED contribution to the anomalous magnetic moments of electron and muon are known very precisely up to the order {alpha}{sup 4}. However, the knowledge of the {alpha}{sup 5} term will also be required when the precision of measurement improves further. This paper reports the first systematic attempt to evaluate the {alpha}{sup 5} term. Feynman diagrams contributing to this term can be classified into six gauge-invariant sets which can be subdivided further into 32 gauge-invariant subsets. Thus far we have numerically evaluated all integrals of 17 gauge-invariant subsets which contain light-by-light-scattering subdiagrams and/or vacuum-polarization subdiagrams. They cover most of leading terms of muon g-2 and lead to a preliminary result 663 (20) ({alpha}/{pi}){sup 5}, which is 8.5 times more precise than the old estimate.

Improved {alpha}{sup 4} term of the electron anomalous magnetic moment

We report a new value of electron

Revised value of the eighth-order contribution to the electron g -2

g\ensuremath{-}2

Hadronic light-by-light scattering effect on muon g-2.

, or

Improved alpha**4 term of the muon anomalous magnetic moment

{a}_{e}

Revised value of the eighth-order QED contribution to the anomalous magnetic moment of the electron

, from 891 Feynman diagrams of order

The fine structure constant

{\ensuremath{\alpha}}^{4}