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

This paper presents the complete QED contribution to the electron g-2 up to the tenth order. With the help of the automatic code generator, we have evaluated all 12672 diagrams of the tenth-order diagrams and obtained 9.16 (58)(\alpha/\pi)^5. We have also improved the eighth-order contribution obtaining -1.9097(20)(\alpha/\pi)^4, which includes the mass-dependent contributions. These results lead to a_e(theory)=1 159 652 181.78 (77) \times 10^{-12}. The improved value of the fine-structure constant \alpha^{-1} = 137.035 999 174 (35) [0.25 ppb] is also derived from the theory and measurement of a_e.Comment: 4 pages, 2 figures. Some numbers are slightly change

Improved α4\alpha^4 Term of the Muon Anomalous Magnetic Moment

We have completed the evaluation of all mass-dependent $\alpha^4$ QED contributions to the muon $g-2$, or $a_\mu$, in two or more different formulations. Their numerical values have been greatly improved by an extensive computer calculation. The new value of the dominant $\alpha^4$ term $A_2^{(8)} (m_\mu / m_e)$ is 132.6823 (72), which supersedes the old value 127.50 (41). The new value of the three-mass term $A_3^{(8)} (m_\mu / m_e, m_\mu / m_\tau)$ is 0.0376 (1). The term $A_2^{(8)} (m_\mu / m_\tau)$ is crudely estimated to be about 0.005 and may be ignored for now. The total QED contribution to $a_\mu$ is $116 584 719.58 (0.02)(1.15)(0.85) \times 10^{-11}$, where 0.02 and 1.15 are uncertainties in the $\alpha^4$ and $\alpha^5$ terms and 0.85 is from the uncertainty in $\alpha$ measured by atom interferometry. This raises the Standard Model prediction by $13.9 \times 10^{-11}$, or about 1/5 of the measurement uncertainty of $a_\mu$. It is within the noise of current uncertainty ($\sim 100 \times 10^{-11}$) in the estimated hadronic contributions to $a_\mu$.Comment: Appendix A has been rewritten extensively. It includes the 4th-order calculation for illustration. Version accepted by PR

The theory of canonical perturbations applied to attitude dynamics and to the Earth rotation. Osculating and nonosculating Andoyer variables

The Hamiltonian theory of Earth rotation, known as the Kinoshita-Souchay theory, operates with nonosculating Andoyer elements. This situation parallels a similar phenomenon that often happens (but seldom gets noticed) in orbital dynamics, when the standard Lagrange-type or Delaunay-type planetary equations unexpectedly render nonosculating orbital elements. In orbital mechanics, osculation loss happens when a velocity-dependent perturbation is plugged into the standard planetary equations. In attitude mechanics, osculation is lost when an angular-velocity-dependent disturbance is plugged in the standard dynamical equations for the Andoyer elements. We encounter exactly this situation in the theory of Earth rotation, because this theory contains an angular-velocity-dependent perturbation (the switch from an inertial frame to that associated with the precessing ecliptic of date). While the osculation loss does not influence the predictions for the figure axis of the planet, it considerably alters the predictions for the instantaneous spin-axis' orientation. We explore this issue in great detail

Angular momentum at null infinity in higher dimensions

We define the angular momentum at null infinity in higher dimensions. The asymptotic symmetry at null infinity becomes the Poincare group in higher dimensions. This fact implies that the angular momentum can be defined without any ambiguities such as supertranslation in four dimensions. Indeed we can show that the angular momentum in our definition is transformed covariantly with respect to the Poincare group.Comment: 13 page

In-situ epitaxial growth of superconducting La-based bilayer cuprate thin films

We investigate the epitaxial growth of bilayer cuprate La2CaCu2O6+\delta using pure ozone as an oxidant, and find that even the crystal with parent composition without cation substitution can show metallic behavior with the aid of epitaxial strain effect. The hole concentration is controlled simply by excess-oxygen doping, and the films grown under the optimum conditions exhibit superconductivity below 30 K. This is the first result on the superconductivity of bilayer La2CaCu2O6+\delta induced purely by the excess oxygen.Comment: 5 pages, 3 figures, To appear in Phys. Rev. B, Rapid Communication

Structural behavior of uranium dioxide under pressure by LSDA+U calculations

The structural behavior of UO2 under high pressure up to 300GPa has been studied by first-principles calculations with LSDA+U approximation. The results show that a pressure-induced structural transition to the cotunnite-type (orthorhombic Pnma) phase occurs at 38GPa. It agrees well with the experimentally observed ~42 GPa. An isostructural transition following that is also predicted to take place from 80 to 130GPa, which has not yet been observed in experiments. Further high compression beyond 226GPa will result in a metallic and paramagnetic transition. It corresponds to a volume of 90A^3 per cell, in good agreement with a previous theoretical analysis in the reduction of volume required to delocalize 5f states.Comment: 10 pages, 8 figure

Corrections and new developments in rigid earth nutation theory - III. Final tables "REN-2000" including crossed-nutation and spin-orbit coupling effects

We present here the new tables REN-2000 of the nutation for a rigid Earth model, starting from Hamiltonian theory, with a level of truncature at 0.1 mu as for individual coefficients instead of 5 mu as (Kinoshita & Souchay 1990). For this presentation to be achieved we first carry out the calculations of the second-order effects due to crossed-nutations and spin-orbit coupling, at the same level of truncation as above. This paper is the third and last one in the frame of the complete reconstruction of the theory of the rigid Earth nutation. It is the complementary part to previous studies concerning the luni-solar nutation involving indirect planetary effects (Souchay & Kinoshita 1996), and the influence of the second-order geopotential (J(3), J(4)) and of the direct planetary effect (Souchay & Kinoshita 1997). Quasi-diurnal and sub-diurnal nutations coming from the harmonics of degree 2, 3 and 4 of the geopotential are also included in REN-2000, their values being taken from Folgueira et al. (1998a,b). A presentation of the series REN-2000 is done at the end of the paper, with separated informations for each contribution

Dynamical Stability of Six-dimensional Warped Flux Compactification

We show the dynamical stability of a six-dimensional braneworld solution with warped flux compactification recently found by the authors. We consider linear perturbations around this background spacetime, assuming the axisymmetry in the extra dimensions. The perturbations are expanded by scalar-, vector- and tensor-type harmonics of the four-dimensional Minkoswki spacetime and we analyze each type separately. It is found that there is no unstable mode in each sector and that there are zero modes only in the tensor sector, corresponding to the four-dimensional gravitons. We also obtain the first few Kaluza-Klein modes in each sector.Comment: 46 pages, 8 figures. Version to appear in JCA

The effects of shoe temperature on the kinetics and kinematics of running

The aim of the current investigation was to examine the effects of cooled footwear on the kinetics and kinematics of running in comparison to footwear at normal temperature. Twelve participants ran at 4.0 m/s ± 5% in both cooled and normal temperature footwear conditions over a force platform. Two identical footwear were worn, one of which was cooled for 30 min. Lower extremity kinematics were obtained using a motion capture system and tibial accelerations were measured using a triaxial accelerometer. Differences between cooled and normal footwear temperatures were contrasted using paired samples t-tests. The results showed that midsole temperature (cooled = 4.21 °C and normal = 23.25 °C) and maximal midsole deformation during stance (cooled = 12.85 mm and normal = 14.52 mm) were significantly reduced in the cooled footwear. In addition, instantaneous loading rate (cooled = 186.21 B.W/s and normal = 167.08 B W/s), peak tibial acceleration (cooled = 12.75 g and normal = 10.70 g) and tibial acceleration slope (cooled = 478.69 g/s and normal = 327.48 g/s) were significantly greater in the cooled footwear. Finally, peak eversion (cooled = −10.57 ° and normal = −7.83°) and tibial internal rotation (cooled = 10.67 ° and normal = 7.77°) were also shown to be significantly larger in the cooled footwear condition. This study indicates that running in cooled footwear may place runners at increased risk from the biomechanical parameters linked to the aetiology of injuries