Eighth-Order Vacuum-Polarization Function Formed by Two Light-by-Light-Scattering Diagrams and its Contribution to the Tenth-Order Electron g-2

We have evaluated the contribution to the anomalous magnetic moment of the electron from six tenth-order Feynman diagrams which contain eighth-order vacuum-polarization function formed by two light-by-light scattering diagrams connected by three photons. The integrals are constructed by two different methods. In the first method the subtractive counter terms are used to deal with ultraviolet (UV) singularities together with the requirement of gauge-invariance. In the second method, the Ward-Takahashi identity is applied to the light-by-light scattering amplitudes to eliminate UV singularities. Numerical evaluation confirms that the two methods are consistent with each other within their numerical uncertainties. Combining the two results statistically and adding small contribution from the muons and/or tau leptons, we obtain $0.000 399 9 (18) (\alpha/\pi)^5$. We also evaluated the contribution to the muon $g-2$ from the same set of diagrams and found $-1.263 44 (14) (\alpha/\pi)^5$.Comment: 27 page

Improved Taylor Expansion method in the Ising model

We apply an improved Taylor expansion method, which is a variational scheme to the Ising model in two dimensions. This method enables us to evaluate the free energy and magnetization in strong coupling regions from the weak coupling expansion, even in the case of a phase transition. We determine the approximate value of the transition point using this scheme. In the presence of an external magnetic field, we find both stable and metastable physical states.Comment: 13 pages, 9 figure

Tenth-order lepton g-2: Contribution of some fourth-order radiative corrections to the sixth-order g-2 containing light-by-light-scattering subdiagrams

This paper reports the tenth-order QED contribution to lepton g-2 from diagrams of three gauge-invariant sets VI(d), VI(g), and VI(h), which are obtained by including various fourth-order radiative corrections to the sixth-order g-2 containing light-by-light-scattering subdiagrams. In the case of electron g-2, they consist of 492, 480, and 630 vertex Feynman diagrams, respectively. The results of numerical integration, including mass-dependent terms containing muon loops, are 1.8418(95) (alpha/pi)^5 for the Set VI(d), -1.5918(65) (alpha/pi)^5 for the Set VI(g), and 0.1797(40) (alpha/pi)^5 for the Set VI(h), respectively. We also report the contributions to the muon g-2, which derive from diagrams containing an electron, muon or tau lepton loop: Their sums are -5.876(802) (alpha/pi)^5 for the Set VI(d), 5.710(490) (alpha/pi)^5 for the Set VI(g), and -8.361(232) (alpha/pi)^5 for the Set VI(h), respectively.Comment: 17 pages, 5 figure

Valley Instanton versus Constrained Instanton

Based on the new valley equation, we propose the most plausible method for constructing instanton-like configurations in the theory where the presence of a mass scale prevents the existence of the classical solution with a finite radius. We call the resulting instanton-like configuration as valley instanton. The detail comparison between the valley instanton and the constrained instanton in $\phi^4$ theory and the gauge-Higgs system are carried out. For instanton-like configurations with large radii, there appear remarkable differences between them. These differences are essential in calculating the baryon number violating processes with multi bosons.Comment: 37 pages, 8 eps figures, LaTeX, uses epsf.sty, citesort.sty and wrapfig2.sty. Minor modification

Dynamical Generation of Non-Abelian Gauge Group via the Improved Perturbation Theory

It was suggested that the massive Yang-Mills-Chern-Simons matrix model has three phases and that in one of them a non-Abelian gauge symmetry is dynamically generated. The analysis was at the one-loop level around a classical solution of fuzzy sphere type. We obtain evidences that three phases are indeed realized as nonperturbative vacua by using the improved perturbation theory. It also gives a good example that even if we start from a trivial vacuum, the improved perturbation theory around it enables us to observe nontrivial vacua.Comment: 31 pages, published versio

Generalized exclusion statistics and degenerate signature of strongly interacting anyons

We show that below the degenerate temperature the distribution profiles of strongly interacting anyons in one dimension coincide with the most probable distributions of ideal particles obeying generalized exclusion statistics (GES). In the strongly interacting regime the thermodynamics and the local two-particle correlation function derived from the GES are seen to agree for low temperatures with the results derived for the anyon model using the thermodynamic Bethe Ansatz. The anyonic and dynamical interactions implement a continuous range of GES, providing a signature of strongly interacting anyons, including the strongly interacting one-dimensional Bose gas.Comment: 7 pages, 3 figures, expanded versio

Recent Developments in the Theory of Tunneling

Path-integral approach in imaginary and complex time has been proven successful in treating the tunneling phenomena in quantum mechanics and quantum field theories. Latest developments in this field, the proper valley method in imaginary time, its application to various quantum systems, complex time formalism, asympton theory for the large order analysis of the perturbation theory, are reviewed in a self-contained manner.Comment: 100 pages, LaTeX, PTPTeX.sty, 36 eps figures, To be published in Progress of Theoretical Physics Supplimen

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 electron loop to the electron g-2 is 0.017 47 (11) (alpha/pi)^5. The contribution of diagrams containing muon loop is 0.000 001 67 (3) (alpha/pi)^5. The contribution of tau-lepton loop is negligible at present. The sum of all these terms is 0.017 47 (11) (alpha/pi)^5. The contribution of diagrams containing electron loop to the muon g-2 is 0.087 1 (59) (alpha/pi)^5. That of tau-lepton loop is 0.000 237 (1) (alpha/pi)^5. The total contribution to a_mu, the sum of these terms and the mass-independent term, is 0.104 8 (59) (alpha/pi)^5.Comment: 48 pages, 6 figures. References are correcte