Proper Eighth-Order Vacuum-Polarization Function and its Contribution to the Tenth-Order Lepton g-2
This paper reports the Feynman-parametric representation of the vacuum-polarization function consisting of 105 Feynman diagrams of the eighth order, and its contribution to the gauge-invariant set called Set I(i) of the tenth-order lepton anomalous magnetic moment. Numerical evaluation of this set is carried out using FORTRAN codes generated by an automatic code generation system gencodevpN developed specifically for this purpose. The contribution of diagrams containing an electron loop to the electron g-2 is 0.017 47 . The contribution of diagrams containing a muon loop is 0.000 001 67 (3)({alpha}/{pi}){sup 5}. The contribution of a tau-lepton loop is negligible at present. The sum of all these terms is 0.017 47 . The contribution of diagrams containing an electron loop to the muon g-2 is 0.0871 (59)({alpha}/{pi}){sup 5}. This is to be compared with the unpublished asymptotic analytic result (0.252 37+O(m{sub e}/m{sub {mu}}))({alpha}/{pi}){sup 5}. The contribution of a tau-lepton loop to a{sub {mu}} is 0.000 237 (1)({alpha}/{pi}){sup 5}. The total contribution to a{sub {mu}}, the sum of these terms and the mass-independent term, is 0.1048 (59)({alpha}/{pi}){sup 5}.

title: Polarization of Electrons in Muon Decay with General Parity-Nonconserving Interactions
abstract: The polarization of electrons in muon decay is studied in the case of the four-component neutrino theory with general parity-nonconserving interactions. The spectrum for each of the two states of longitudinal polarization is described by a set of three parameters of which only two are independent By observing the electron polarization in arbitrary directions, one can determine ten parameters of which six are related to the two longitudinal polarizations and the rest to the transverse part. It is seen that the prediction of the two-component neutrino theory about the electron polarization in muon decay is quite specific and can be distinguished from that of the general case, if the latter involves the interactionB of the S, T, P types in charge-retention order. However, from the study of the polarization of electrons, it is impossible to distinguish the two-component theory from the four-component theory which involves only the vectortype interactions. It is noticed that the TCP theorem determines a detailed correspondence between the polarization provides us with an opportunity to determine experimentally whether weak interactions actually obey the TCP theorem or not.

title: Automated calculation scheme for alpha**n contributions of QED to lepton g-2: Generating renormalized amplitudes for diagrams without lepton loops
abstract: Among 12 672 Feynman diagrams contributing to the electron anomalous magnetic moment at the tenth order, 6354 are the diagrams having no lepton loops, i.e., those of quenched type. Because the renormalization structure of these diagrams is very complicated, some automation scheme is inevitable to calculate them. We developed an algorithm to write down FORTRAN programs for numerical evaluation of these diagrams, where the necessary counterterms to subtract out ultraviolet subdivergence are generated according to Zimmermann's forest formula. Thus far we have evaluated crudely integrals of 2232 tenth-order vertex diagrams which require vertex renormalization only. Remaining 4122 diagrams, which have ultraviolet-divergent self-energy subdiagrams and infrared-divergent subdiagrams, are being evaluated by giving small mass λ to photons to control the infrared problem.

title: Eighth-order magnetic moment of the electron. III. Sixth-order vertices containing a second-order vacuum polarization subdiagram
abstract: We have calculated the contribution to the eighth-order anomalous magnetic moment of the electron arising from 150 Feynman diagrams, each generated by inserting a second-order vacuum polarization loop in the photon lines of sixth-order vertices of the three-photon-exchange type. Our result is 1.419(16)(..cap alpha../..pi..)/sup 4/. The theoretical error represents the estimated accuracy (90% confidence limit) of the required numerical integrations.

title: Improved Theory of the Muon Anomalous Magnetic Moment
abstract: A new theoretical value a/sub ..mu../ = 11 659 202(20) x 10/sup -10/ is reported for the muon anomalous moment, based on the first complete calculation of the ..cap alpha../sup 4/ QED term and improvements of the ..cap alpha../sup 3/ QED term and various hadronic contributions. The remaining error is mostly due to the experimental inputs needed for evaluation of the hadronic vacuum polarization effect. Further improvement of this error seems possible. Thus the electroweak theory may be tested at the one-loop level if measurement of a/sub ..mu../ is improved by an order of magnitude.

title: VIOLATION OF THE POMERANCHUK THEOREM AND ZEROS OF THE SCATTERING AMPLITUDES.

title: First beam test on a BSO electromagnetic calorimeter
abstract: A beam test has been performed on a prototype electromagnetic calorimeter of bismuth silicate BSO crystals for the first time using electrons of 0.5–3.0 GeV. The calorimeter consists of nine BSO crystals, 22 mm × 22 mm × 180 mm (15.6 radiation lengths), arranged in a 3 × 3 array. Each crystal is coupled to a small photomultiplier tube of 20 mm in diameter. The obtained energy resolution is σ E / E = ( 0.023 ± 0.003 ) / E ( GeV ) ⊕ ( 0.017 ± 0.002 ) for incident electrons of the energy E in GeV. The position information for an electron injected onto the center crystal of the calorimeter array is given with energy deposit signals from nine BSO crystals. The RMS position resolution σ x is parameterized as σ x = [ ( 3.2 ± 0.1 ) / E ( GeV ) ⊕ ( 1.3 ± 0.1 ) ] mm at the center of the crystal. Misidentification probability of pions to electrons is found to be ∼ 10 - 3 for the pion momentum ranging from 1.0 to 3.0 GeV/ c .

title: Narrow resonance at E(gamma) = 1020-MeV in the d (gamma, eta) p n reaction
abstract: Differential and total cross sections of the D(γ, η)pn reaction have been measured for photon energies between 600 and 1150 MeV. The data provide the information of the γn → ηn reaction above Eγ ≥ 800 MeV. The total cross section shows a narrow resonance structure peaked at Eγ = 1020 MeV. The angular distribution coefficients together with the total cross section are compared with the calculation of the isobar model by using the impulse approximation. Although the spin and parity of the resonance cannot be determined unambiguously, a negative parity assignment gives better fit to the data.

title: Study of double pion photoproduction on the deuteron
abstract: The π + π − photoproductions on the proton and deuteron have been studied in a photon energy range of 0.8–1.1 GeV at the Laboratory of Nuclear Science, Tohoku University. Charged pions and protons were detected using Neutral Kaon Spectrometer. We obtained the cross sections for the p ( γ , p π + π − ) and d ( γ , p π + π − ) n . The quasi-free process with a neutron spectator was extracted by the neutron momentum cut of p n > 0.3 GeV / c . The cross section for the Δ + + Δ − production was deduced in the non-quasi-free process of the γ d → p n π + π − . It was 13.4 ± 0.4 μb at E γ = 0.82 GeV .

title: The 1.2 GeV photon tagging system at LNS-Tohoku
abstract: A tagged photon beam line has been constructed in the Stretcher–Booster ring (STB ring) at Tohoku University. The quasi-monochromatic photon beam is produced by the internal photon tagging system which consists of a solid fiber radiator and the compact tagging counter installed in a bending magnet of the STB ring. The energy range of the tagged photon is from 0.8 to 1.1 GeV with the electron energy of 1.2 GeV . The performance of the tagging system has been investigated. The system provides good quality of γ -rays for the nuclear and hadron physics experiments.

title: Beam test of a BSO calorimeter